截尾数据下非参数回归函数核估计的强收敛速度

本文考虑在右侧随机截尾模型下，非参数回归函数核估计的强收敛问题，在一组自然的条件下，得到了与完全样本情况相当的收敛速度。     

荧光法研究不同离子对溶菌酶的猝灭作用

本文利用荧光法,在生理pH(7.37±0.02)条件下,分别测定了Fe3+、Cu2+、Ni2+、Co2+、NO2-、I-、盐酸胍对溶菌酶的猝灭作用。用荧光猝灭法求得不同猝灭剂对溶菌酶的猝灭常数KSV、生成常数KA、离解常数KD、结合位点数n和热力学参数ΔrGmΘ、ΔrHmΘ、ΔrSmΘ。据此判断了体系中猝灭剂对溶菌酶的作用机理。I-对溶菌酶的猝灭是动态猝灭,而Fe3+、Cu2+、NO2-Ni2+、Co2+及盐酸胍对溶菌酶是静态猝灭;Fe3+、Cu2+、Ni2+、Co2+与溶菌酶之间的作用力主要为氢键、范德华力;NO2-与溶菌酶间的作用力主要为静电作用力;I-与溶菌酶之间的作用力主要为疏水作用力。在分子水平上理解这些外源性化合物与溶菌酶的作用机理具有及其重要意义。     

水合物法开发高寒地区湖盐的相平衡研究

高寒地区年平均气温为水合物的生成提供了天然的温度条件,也为水合物法节能开发高寒地区湖盐提供了可能.基于此,提出了水合物法开发高寒地区湖盐的新方法;以van der Waals-Platteeuw模型为基础,利用Pitzer方程与杜亚和与郭天民提出的三参数方程分别计算电解质溶液中水的活度和Langmuir常数,预测了饱和NaCl溶液中HCFC141b水合物的相平衡条件,并进行了实验验证;发现利用环境冷量实现气体水合物法开发湖盐具有实际可行性;研究结果对应用高效节能方法开发我国高寒地区湖盐有重要价值.     

非参数回归函数的基于截尾数据的估计

本文考虑截尾数据情况下非参数回归函数m(x)=E(Y|x)的估计。具体地讲,我们面对的是这样的数学模型:T是与(X,Y)独立的随机变量,我们观测到的不是Y本身,而是Z=min(Y,T)及δ=[Y≤T]。今有训练样本{(X_i,Z_i,δ_i)}_(i-1)及当前样本(X,z,δ),记ξ_i(·)=[z_i≥·], N~ (·)=sum from i=1 to n ξ_i(·), V_n(·)=multiply from i=1 to n{1 N~ (z_i)/2 N~ (z_i)}~[δ_i=_i<0], U_n(·)=sum from i=1 to n Wnt(x)ξ_i(·), 令 m_n(x)=integral from 0 to u_n U_n(y)|V_n(y)dy, 其中u_n=F_2~(-1)(n~(-a)),0<α<1/2为一实常数,F_2(·)=P(Y≥·)为Y的(右侧)分布函数。在权函数{W_(ni)(x)}_(i=1)~n及(X,Y,T)的分布函数满足一组条件下,我们证明了m_n(x)为m(x)的强相合估计,即:m_n(x)→m(x),a.s.(n→ ∞).     

多孔介质水合物中储存二氧化碳的实验研究

为了研究多孔介质中CO₂水合物的生成速率和储气量,利用1.8 L的水合反应釜研究了孔隙为13.8 nm和26.7nm的石英砂中CO₂水合物的生成过程,结果表明:孔径为26.7 nm石英砂中,1 m³的石英砂可以储存64.4 m³标准状况的二氧化碳气体,平均生成速率为0.001703 mol/min;孔径为13.8 nm石英砂中,1 m³的石英砂可以储存118.8m³标准状况的二氧化碳气体,平均生成速率为0.001803 mol/min;在多孔介质孔径范围为13.8 nm至26.7 nm之间时,粒径越小,储气量越大。     

利用三种方法计算腔内插入透明介质对激光高斯光束聚焦的影响

利用高斯光束的ABCD定律、q参数定义及高斯光束的表征和介质传输矩阵三种方法,计算得出腔内插入折射率为η的透明介质,不改变高斯光束聚焦后的腰斑大小,只改变焦斑位置,且插入的透明介质相当于长度为D/η的真空.     

Optical properties of anatase and rutile TiO_2 studied by GGA + U

The optical properties of thermally annealed TiO_2 samples depend on their preparation process, and the TiO_2 thin films usually exist in the form of anatase or rutile or a mixture of the two phases. The electronic structures and optical properties of anatase and rutile TiO_2 are calculated by means of a first-principles generalized gradient approximation(GGA) +U approach. By introducing the Coulomb interactions on 3d orbitals of Ti atom(U~d) and 2p orbitals of O atom(U~p), we can reproduce the experimental values of the band gap. The optical properties of anatase and rutile TiO_2 are obtained by means of the GGA+U method, and the results are in good agreement with experiments and other theoretical data. Further, we present the comparison of the electronic structure, birefringence, and anisotropy between the two phases of TiO_2. Finally,the adaptability of the GGA+U approach has been discussed.     

最近邻判别法中错误概率估计的强收敛速度(英文)

本文考虑最近邻判别法中错误概率估计的强收敛速度.设(X,θ),(X_1,θ_1),…,(X_n,θ_n)为取值于 R~m×{1,2,…,M}的 i.i.d.样本,m≥1,M≥2为正整数.记θ′_n 为θ的最近邻判别,错判概率 R_n=p(θ′_n≠θ),恒有(?)R_n=R.(?)_n 为基于 X,并借助于训练样本(X_1,θ_1),…,(X_nθ_n)的 R_n 的估计量.我们证明了在一组条件下,及对适当选取的α>0,有(?)_n-R=0(1/(n~α)).     

Electronic structures and optical properties of HfO_2–TiO_2 alloys studied by first-principles GGA + U approach

The phase diagram of HfO_2–TiO_2 system shows that when Ti content is less than 33.0 mol%, HfO_2–TiO_2 system is monoclinic; when Ti content increases from 33.0 mol% to 52.0 mol%, it is orthorhombic; when Ti content reaches more than 52.0 mol%, it presents rutile phase. So, we choose the three phases of HfO_2–TiO_2 alloys with different Ti content values. The electronic structures and optical properties of monoclinic, orthorhombic and rutile phases of HfO_2–TiO_2 alloys are obtained by the first-principles generalized gradient approximation(GGA) +U approach, and the effects of Ti content and crystal structure on the electronic structures and optical properties of HfO_2–TiO_2 alloys are investigated. By introducing the Coulomb interactions of 5 d orbitals on Hf atom(U_1~d), those of 3 d orbitals on Ti atom(U_2~d), and those of 2 p orbitals on O atom(Up) simultaneously, we can improve the calculation values of the band gaps, where U_1~d, U_2~d, and Up values are 8.0 eV, 7.0 eV, and 6.0 eV for both the monoclinic phase and orthorhombic phase, and 8.0 eV, 7.0 eV, and 3.5 eV for the rutile phase. The electronic structures and optical properties of the HfO_2–TiO_2 alloys calculated by GGA +U_1~d(U_1~d= 8.0 eV) +U_2~d(U_2~d= 7.0 eV) +U~p(U~p= 6.0 eV or 3.5 eV) are compared with available experimental results.     

绝对值损失下单边截断型分布族参数的经验Bayes估计

本文在绝对值损失下,构造了单边截断型分布族参数的EB估计,并证明了在一组条件下,其Bayes风险的收敛速度为0((ln n/n)~(λγ/(2r+))·M_n),其中0<λ,γ≤1,M_n≤ln ln n(n充分大),M_n为一无穷大量。