A new approach in analyzing extinction probability of Markov branching process with immigration and migration

We use a new approach to consider the extinction properties of the Markov branching process with immigration and migration recently discussed by Li and Liu [Sci. China Math., 2011, 54: 1043–1062]. Some much better explicit expressions are obtained for the extinction probabilities of the subtle super-interacting case.     

Synthesis and Crystal Structure of [2-Hydroxy- 5-（4-hydroxy-3-phenyliminomethylbenzyl）-benzylidene]-phenyl-amine

The title compound [2-hydroxy-5-（4-hydroxy-3-phenyliminomethyl-benzyl）-benzylidene]-phenyl-amine （C27H22N2O2, Mr = 406.47） was synthesized by 5,5′-methylene-bissalicylal- dehyde with aminobenezene, and its crystal structure was determined by single-crystal X-ray diffraction. The crystal belongs to the monoclinic system, space group C2/c with a = 4.4026（6）, b = 1.501（13）, c = 0.95818（12） nm, β = 90.868（2）°, V= 4.2813（9） nm^3, Z= 8, Dc= 1.292 g/cm^3,μ = 0.010, F（000） = 1744, R = 0.0576 and wR = 0.1450 for 3766 observed reflections with I 〉 2σ（I）. X-ray analysis reveals that the molecule has a pair of intramolecular OH…N hydrogen bonds.     

非线性两点边值问题的存在唯一性

对于非线性两点边值问题x″=f(t,x,x′),　x(0)=A,　x(1)=B,我们在f,fx,fx′,β(t),α′(t)都连续,且fx≥-β(t), -α(t)≤fx′≤M(1+|x′|),max β(t)-α2(t)+2α′(t)4t∈[0,1] ≤λ2<π24,α(1)≤2λcotλ,这些条件之下证明解之存在且唯一.     

电荷转移配合物[Himi]4[Mo8O26]·16H2O的合成与表征

本文以钼酸钠和咪唑(C_3H_4N_2,imi)为原料,合成了组成为[Himi]_4[Mo_8O_(26)]·16H_2O的电荷转移配合物。通过元素分析、红外光谱、紫外光谱、热重-差热分析对其进行了初步表征。红外光谱表明,固态配合物的阴、阳离子间存在电荷转移作用;紫外光谱显示,稀水溶液中配合物完全解离,彼此无相互作用。     

电荷转移盐(C_3H_5N_2H)_3[PMo_(12)O_(40)]的合成与热分解及光致变色反应动力学

用磷钼酸与咪唑合成了一种新的杂多酸-有机电荷转移盐(C3H5N2H)3[PMo12O40]。通过元素分析、红外光谱、固体漫反射光谱、电子自旋共振及热分析等测试技术对其进行了表征,用单扫描法(Achar法和Coats-Redfern法)对合成化合物的TG分析结果进行了非等温热分解动力学研究。推断结果表明,合成化合物的第1步热分解为球对称的三维扩散机理(n=2),其动力学方程为dα/dt=1.58×108[1-(1-α)1/3]-1(1-α)2/3exp(-40931.0/T),求得分解反应的表观活化能E=340.30kJ/mol,指前因子A=1.05×108s-1。标题化合物对紫外光具有光致变色性质,用固体漫反射光谱研究了其光致变色反应动力学。结果显示,其光致变色反应表现为一级或准一级动力学,速率常数k=9.80×10-5s-1。     

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.     

格子Boltzmann方法中三维运动边界的统一模型

格子Boltzmann方法(LBM)中边界条件的处理很复杂,在现有的边界条件处理方法中,动力学格式能够精确满足宏观边界条件,但由于要解一个不定方程,必须引入附加假设确保方程非奇异.作为动力学格式和反弹格式的一种扩展,提出一种处理三维任意速度运动边界的统一模型,其中人口速度和固体壁面速度是该模型的特殊情形.给出用于三维15速度的表达式.为了检验该模型,模拟对角顶盖驱动三维空腔流,并将结果与有限差分法计算的结果进行比较,说明所提出的统一模型是合理可行的.     

螺丝钉连结的组合樑

In this paper, it is proved that the problem of composite beams jointed by bolts can be solved in terms of certain equivalent continuous beams. The equivalent beam is specified as follows: 1) It consists of supports of the original beam and equivalent supports situated at the points where bolts are used. 2) It is loaded by the given load on the original beam.Then the reactions at the bolts in the original composite beam are equal to a constant C times the reactions at various supports of the equivalent continuous beam. The constant is equal to C=(E′J′-k(EJ+E′J′))/(EJ+E′J′), where EJ and E′J′ are flexaral rigidities of the first and second parts of the composite beam respectively, and k is the distributing ratio of load on the second part.The solution of the problem is then greatly simplified.This method can be generalized for composite beams consisting of more than two parts, on which the given load is not proportionately distributed.     

湖北十堰蓝色“水波纹”绿松石的谱学特征

“水波纹”绿松石是一种在外观上呈现水波纹状花纹图案的天然绿松石,产量稀少却深受消费者喜爱,前人对绿松石的研究较丰富,但对“水波纹”绿松石的研究较少。对一块基底呈浅蓝白色,条纹呈蓝绿色的“水波纹”绿松石样品用显微激光拉曼光谱仪、显微红外光谱仪、微区X射线衍射、激光剥蚀电感耦合等离子体质谱仪、扫描电镜、显微紫外-可见-近红外光谱仪等测试其各种性能。结果表明,条纹区与非条纹区的主要矿物均为绿松石;红外光谱和拉曼光谱均显示绿松石的光谱;条纹区与非条纹区的化学成分不同,条纹区Al₂O₃,SiO₂,MgO,V,Co,Ni,U及Y,Mo,Cd的含量较非条纹区含量高,而非条纹区P₂O₅,CuO,K₂O及Na₂O的含量较条纹区含量高;扫描电镜微形貌显示,条带区的晶体多为厚板状、晶体颗粒大、排列紧密,几乎不可见孔隙,非条带区的晶体多为大小不一的柱状、碎片状,杂乱排列,可见孔隙;微区X射线衍射表明条带区的结晶度较非条带区的结晶度高;显微紫外-可见-近红外光谱表明条带区与非条带区的致色离子相同,均在426和660 nm处有可见吸收峰,致色离子均为Fe3+和Cu2+。“水波纹”绿松石样品的谱学特征表明,条纹处与非条纹处的颜色差异与致色离子没有明显关系,而颜色及透明度差异与绿松石的结晶程度、致密程度有主要关系,“水波纹”绿松石中绿松石结晶度的变化表明了绿松石形成环境的不稳定性,结晶度的周期性变化表明了形成绿松石的外界环境具有周期性变化的规律,为研究绿松石的颜色成因及绿松石的成矿环境提供数据支撑。     

Improvement of the electrochemical properties of a LiNi<Subscript>0.5</Subscript>Mn<Subscript>1.5</Subscript>O<Subscript>4</Subscript> cathode material formed by a new solid-state synthesis method

In order to avoid the shortcomings of large particle size and poor uniformity of material synthesized by the traditional solid-state method, this paper utilizes a simple improvement of calcination process (i.e., calcination–milling–recalcination) based on the traditional solid-state synthesis to successfully prepare a large number of well-distributed, micrometer-sized, spherical secondary LiNi_0.5Mn_1.5O₄ particles. Each particle is composed of nano- and/or sub-micrometer-sized grains. Results of the electrochemical performance tests show that the material exhibits a remarkable cycle performance and rate capability compared with that obtained from traditional synthesis method; the spherical LiNi_0.5Mn_1.5O₄ particles can deliver a large capacity of 135.8 mAh g^?1 at a 1 C discharge rate with a high retention of 77 % after 741 cycles and a good capacity of 105.9 mAh g^?1 at 10 C. Cyclic voltammetry measurements confirm that the significantly improved electrochemical properties are due to enhanced electronic conductivity and lithium-ion diffusion coefficient resulting from the optimized morphology and particle size. This improved method is more suitable for mass production.