一类球面带形平移网络算子的逼近

借助于球调和多项式的de la Vallée Poussin和构造出了单位球面S^q上一类带形平移网络算子，并给出了其对L^p(S^q)中函数一致逼近的收敛速度.      

The spherical oil agglomeration of barite suspensions in the presence of surfactant and cosurfactant

The spherical agglomeration of barite particles using oil in the presence of both surfactant and cosurfactant was studied. It was found that the mineral suspension needed a critical surfactant concentration to initiate oil agglomeration. The addition of long-chain aliphatic alcohols to the organic phase decreased the critical surfactant concentration. This phenomenon was ascribed to a screening effect of alcohol molecules in the adsorption layer of surfactant. When sodium chloride was added to the solution the spherical agglomeration disappeared even though the surfactant adsorption at the barite/solution interface increased. It was concluded that the disappearance of oil agglomeration was caused by a bilayer of the surfactant which was formed on the barite surface. In the barite—surfactant—alcohol—oil—brine system the agglomeration process is only realized with the long-chain alcohols. This behaviour can be explained by microemulsion formation at the mineral/solution interface.     

Optimal lower bounds for cubature error on the sphere

We show that the worst-case cubature error E(Q_m;H^s) of an m-point cubature rule Q_m for functions in the unit ball of the Sobolev space H^s=H^s(S²),s>1, has the lower bound , where the constant c_s is independent of Q_m and m. This lower bound result is optimal, since we have established in previous work that there exist sequences of cubature rules for which with a constant independent of n. The method of proof is constructive: given the cubature rule Q_m, we construct explicitly a ‘bad’ function f_mH^s, which is a function for which Q_mf_m=0 and . The construction uses results about packings of spherical caps on the sphere.     

The skew elliptical distributions and their quadratic forms

In this paper, a family of the skew elliptical distributions is defined and investigated. Some basic properties, such as stochastic representation, marginal and conditional distributions, distribution under linear transformations, moments and moment generating function are derived. The joint distribution of several quadratic forms is obtained. An example is given to show that the distributions of some statistics as the functions of the quadratic forms can be derived for various applications.     

Synthesis of spherical LiNi1/3Co1/3Mn1/3O2 cathode materials for Li-ion batteries

Spherical LiNi_1/3Co_1/3Mn_1/3O₂ was successfully prepared by controlled crystallization. The preparation started with the spherical coprecipitate of Ni_1/3Co_1/3Mn_1/3CO₃ from NiSO₄, CoSO₄, MnSO₄, NH₄HCO₃, and NH₃·H₂O, followed by pyrolysis of Ni_1/3Co_1/3Mn_1/3CO₃ at 600°C for 3 h. The X-ray diffraction analysis showed that the homogeneous cubic (Ni_1/3Co_1/3Mn_1/3)₃O₄ was obtained after the pyrolysis. Spherical LiNi_1/3Co_1/3Mn_1/3O₂ was obtained by sintering of the mixture of as-obtained (Ni_1/3Co_1/3Mn_1/3)₃O₄ and LiOH·H₂O at 900°C for 6 h in air. As-prepared spherical LiNi_1/3Co_1/3Mn_1/3O₂ presented initial discharge capacity of 162.9 mA h g⁻¹ and capacity retention of 98% at 50th cycle.     

Microwave-assisted synthesis of spherical monodispersed magnesium fluoride

Spherical monodispersed magnesium fluoride has been obtained using the microwave-assisted precipitation technique from magnesium nitrate and ammonium fluoride solutions. Studies aimed at optimizing synthesis conditions from the point of view of preparing spherical MgF₂ particles of possibly high monodispersity were performed. Spherical MgF₂ particles of 0.25-0.36 μm in diameter have been obtained with relative standard deviation from the average value ranging from 7 to 15%. It has been established that a certain optimal range of Mg(NO₃)₂ and NH₄F concentrations exists that enables a highly monodispersed MgF₂ to be prepared. The range is narrow (0.01-0.03 mol dm⁻³) for both precursors. Spherical MgF₂ particles have been characterized by SEM, XRD, DTG/DTA and FTIR techniques.     

线弹簧模型法在含表面裂纹球壳中的应用

本文应用线弹簧模型法,基于Sih.G.C.含二维裂纹球壳理论建立了含表面裂纹球壳的控制方程,采用数值方法选取位移试函数及合理地处理了对偶奇异积分方程使计算大为简化,通过电算实现了计算求解过程,从而获得了球壳表面裂纹前沿各点的应力强度因子之值。 最后将计算结果与考虑“膨胀效应”后的Ncwoun-Raju 解进行了比较,同时研究了曲率因素对表面裂纹线弹性断裂性态的影响。     

球面介质作用下的测度值分枝过程

我们考虑空间上一粒子系统，当其受到分布于求面上的介质作进行粒子分枝和衍生，产生新了体，而新粒子仍按原粒子的运动规则继续空间运动。通过合理的假设和极限过程，粒子在空间的散布一测度值分枝过程来刻划。     

Extendibility of spherical matrix distributions

We investigate the structure of distributions for matrices which can be embedded in arbitrarily large matrices whose distributions have properties of invariance under orthogonal rotations.     

Multi-vector Spherical Monogenics, Spherical Means and Distributions in Clifford Analysis

New higher-dimensional distributions have been introduced in the framework of Clifford analysis in previous papers by Brackx, Delanghe and Sommen. Those distributions were defined using spherical co-ordinates, the ＂finite part＂ distribution Fp x＋^μ on the real line and the generalized spherical means involving vector-valued spherical monogenics. In this paper, we make a second generalization, leading to new families of distributions, based on the generalized spherical means involving a multivector-valued spherical monogenic. At the same time, as a result of our attempt at keeping the paper self-contained, it offers an overview of the results found so far.