一类随机微分方程的轨道唯一性

 在漂移项系数是非Lipschitz并且是非凹的条件下，证明了如下随机微分方程的轨道唯一性：X_t=x+∑^∞_i=1∫^t₀σ_i(X_s)dWⁱ_s+∫^t₀b(X_s)ds，其中W_i, i=1,2,…, 为一串独立的标准布朗运动。     

Bpn 的迷向常数及其渐近性质

设B_pⁿ={x∈Rⁿ | ‖x‖_p≤1}是n维赋范空间 l_pⁿ 中的单位球.该文证明当1≤p≤∞时,B_pⁿ是迷向的凸体,并给出了B_pⁿ的迷向常数公式,进一步得到当n→∞和p→∞时其迷向常数的渐近性质.     

Formation, structure and properties of GeCn± and Ge2Cn± binary clusters

The binary cluster ions Ge₂C_n⁺/Ge₂C_n^- and GeC_n⁺ have been produced by laser ablation. The parity effect is present in the negative ions Ge₂C_n^-, though it is not very prominent. While the experiments tell that the parity effect is totally not shown in the positive ions Ge₂C_n⁺. An extensive theoretical investigation on GeCn/GeC_n⁺/GeC_n^-(n=1-10) and Ge₂Cn/Ge₂C_n⁺/Ge₂C_n^-(n=1-9) has been carried out by density functional theory at B3LPY level. The calculation shows that the low-lying states of GeC_n/GeC_n⁺/GeC_n^-(n=1-10) and Ge₂C_n/Ge₂C_n⁺/Ge₂C_n^-(n=1-9) are linear structure with germanium atoms locating at terminals respectively. The electronic distributions, ionization potential (IP_ad), elec-tron affinity (EA) and increasing bonding energy reveal that the parity effect of neutral species is much stronger than that of ions, which is attributed to the valence π-electrons. It is explained that the differences between experiments and cal-culations are due to the kinetic factor in the formation of Ge₂C_n^±.     

Hausdorff测度和维数与所在空间度量的依赖性

讨论在Rⁿ中具有嵌套结构的几何对象上构造新度量的问题. 主要结果是: K是Rⁿ中 具有嵌套结构的几何对象, 那么对于任何一个的连续的纲函数h(t), 可以构造一个在K上的度量,在这个新的度量空间(K, p)中, 0h (K)<+∞. 如果纲函数取h(t)=t^s,那么 对于任意0h (K)=1并且有dim_PK=dim_BK=dim_HK=s成立.     

Sm(Ⅲ)-HP配合物与DNA的作用机制

 应用紫外-可见光谱法和荧光光谱法并以中性红(NR)作光谱探针研究了Sm(Ⅲ)HP配合物与DNA的作用机制。研究表明,血卟啉(HP)与Sm(Ⅲ)的配合比n_Sm(Ⅲ)∶n_HP = 1∶ 1,Sm(Ⅲ)HP配合物与DNA的结合比n_Sm(Ⅲ)HP ∶ n_DNA = 1∶ 1,Sm(Ⅲ)HP配合物与DNA的结合常数K^θ_30℃ = 1.67×10⁴  L/mol。该过程为熵所驱动,其Δ _r H_m为4.86×10⁴ J/mol,Δ_r S_m为195.61 J/(mol·K),30 ℃时Δ_r G_m为－1.06×10⁴ J/mol。Scatchard法和探针法研究表明,Sm(Ⅲ)HP与DNA之间的结合方式主要是沟区作用。     

Kinetics of C2(a3Πu) radical reactions with NO, N2O, O2, H2 and NH3

Pulsed laser photolysis/laser-induced fluorescence (LP-LIF) is utilized to measure rate constants for C₂(a³Π_u) reactions with NO, N₂O, O₂, H₂ and NH₃. Multiphoton dissociation of C₂Cl₄ at 266 nm is employed for the generation of C₂(a³Π_u) radicals. The C₂(a³Π_u) concentration is monitored by the fluorescence of the (0, 0) band of the (d³Π_g&#8596;a³Π_u) transition at 516.5 nm. C₂(a³Π_u) removal rate constants for the reactions are determined as k_NO = (5.46 ± 0.10) × 10^-11 cm³ molecule^-1 s^-1 , k_N2O = (1.63 ± 0.20) × 10^-13 cm³ molecule^-1 s^-1 , k_N2O = (1.58 ± 0.16) × 10^-11 cm³ molecule^-1 s^-1, k_O2 = (5.92 ± 1.00) × 10^-14 cm³ molecule^-1 s^-1, k_H2< 1.0× 10^-14 cm³ molecule^-1 s^-1. Based on the data analysis and theoretical calculation, we suggest that the C₂(a³Π_u) reactions with H₂ and NH₃ proceed via the hydrogen abstraction mechanism, barriers exist at the entrance channel of the reactions of C₂(a³Π_u) with H₂ and NH₃.     

一种用4-圈和8-圈对二分图的划分

证明了如果一个平衡二分图G包含4k个点,k≥2,并且对G中每一对满足x∈V₁,y∈V₂的不相邻顶点x和y成立d(x)+d(y)≥2k+1, 则G包含k-2个4-圈和一个8-圈,并且这k-1个圈点不相交。     

关于非扩展矩阵小波的存在性

用D表示n阶可逆实矩阵的集合,Γ表示Rⁿ中的点集.小波分析的一个基本问题是对什么样的(D,Γ)存在小波.本文证明了当D={A^j,j∈Z}, A是n阶实矩阵, 满足A是对角矩阵块时, 存在(D,Zⁿ)小波. 其中, A₁是扩展矩阵,A₂是行列式不为零的幂等阵.     

PCln (n=-1,0,+1)分子离子基态的结构与势能函数

 基于Gaussian03计算软件,选用高角动量基函数6-311++g(df,pd),分别使用密度泛函理论UB3LYP和UB3P86,以及组态相互作用方法UCCSD-FC和UQCISD-FC,对PCl分子和PCl⁺,PCl^-离子基态进行了几何优化,进一步对其进行了频率计算和单点能扫描计算.用最小二乘法拟合得到了PCl^<em>n(n=-1,0,+1)分子离子基态的Murrell-Sorbie势能函数.与实验及理论结果比较表明,对PCl,PCl⁺分子离子基态光谱常数 (B_e,α_e,ω_e,ω_ex_e)的计算结果达到了很高的精度.文章还首次给出PCl^-分子离子基态光谱参数(B_e,α_e,ω_e,ω_ex_e)和PClⁿ(n=-1,0,+1)力常数(f₂,f₃,f₄)的理论数据,为PClⁿ(n=-1,0,+1)分子离子的更深层次研究和应用提供重要的理论基础.     

K2MnSnTe4的溶剂热合成和反射光谱研究

采用溶剂热法，以n(K₂Te₄)∶n(MnCl₂·4H₂O)∶n(SnTe) =1∶1∶1的摩尔比、乙二胺作溶剂，在160℃下反应6d，生成黑色块状晶体K₂MnSnTe₄。其结构由具有扩展的网状共价骨架的Zintl负离子 [(MnSnSe₄)^₂-]_n和K⁺正离子堆积而成。漫反射光谱研究表明该晶体具有 1 .75eV能隙 (E_g)，属于半导体，对太阳能具有选择吸收的特性。     

正相伴序列的矩完全收敛性

设 Xn;n≥1是一均值为0、方差有限的正相伴平稳序列.记Sn= Xk,Mn= |Sk|,n≥1.证明了在一定条件下,由E|X1|p(|X1|(1/α))∞可推出对任意的ε0,有 npα-2-αh(n)EMn-εn(1/p)+∞,其中h(n)为一在无穷处的缓变函数,x+=maxx,0.       

Special IR properties of palladium nanoparticles and their aggregations in CO molecular probe infrared spectroscopy

Dispersed Pd nanoparticles (Pdn) have been synthesized by reducing H2PdCI4 with ethanol, and stabilized using poly(vinylpyrrolidone) (PVP). The Pdn is applied to the glassy carbon substrate to form a thin film, and then the potential cyclic scanning at 50 mV.s^-1 from -0.25 to 1.25 V was carried out for about 30 min to form the aggregations of Pdn (Pdn^ag). FTIR spectroscopy of both transmission and reflection modes was employed to study CO adsorption on Pdn and Pdn^ag in both solidlliquid and solidlgas interfaces. It has been revealed that CO adsorption on Pdn film yields two IRbands near 1964 and 1906 cm-1, which are assigned to IR absorption of CO bonded on asymmetric and symmetric bridge sites, respectively. In contrast to the IR properties of CO adsorbed on Pdn, only species of CO bonded on asymmetric bridge sites was determined on Pdn^ag, and the direction of the IR band near 1963 cm^-1 is completely inverted. The full width at half-maximum (FWHM) of the COB^as band near 1964 cm^-1 is measured to be 14 cm^-1 on Pdn film, while it is 24 cm^-1 on Pdn^ag film. The results of the present study demonstrated that the inverting of the IR band direction is a general phenomenon that is closely related to the interaction between nanoparticles in aggregation of Pdn.     

有限集合上封闭集族的计数

设集合X={a1,a2,a3,…,an},f(n,m)表示X的含m个元素的不同封闭集族的数目。证明了f(n,m)={3n-2n,m=2;4n-2.3n+2n,m=3;5n-25.4n+2.3n-2n-1,m=4;6n-3.5n+3.4n-3n,m=5其中n=1,2,3,…。     

Structure and 57Fe conversion electron Mössbauer spectroscopy study of Mn-Zn ferrite nanocrystal thin films by electroless plating in aqueous solution

Mn1-xZnxFe2O4thin films with various Zn contents and of different thickness were synthesized on glass substrates directly by electroless plating in aqueous solution at 90℃ without heat treatment. The Mn-Zn ferrite films have a single spinel phase structure and well-crystallized columnar grains growing per- pendicularly to the substrates. The results of conversion electron ^57Fe Mossbauer spectroscopy （CEMS） Indicate that the cation distribution of Mn1-xZnxFe204 ferrite nanocrystal thin films fabricated by electroless plating is different from the bulk materials＇ and a great quantity of Fe^3＋ ions are still present on A sites for x〉0.5. When the Zn content of the films increases, Fe^3＋ ions in the films transfer from A sites to B sites and the hyperfine magnetic field reduces, suggesting that Zn2. has strong chemical affinity towards the A sites. On the other side, with the increase of the thickness of the films, Fe3＋ ions, at B sites in the spinel structure, increase and the array of magnetic moments no longer lies in the thin film plane completely. At x = 0.5, Hc and Ms of Mn1-xZnxFe204thin films show a minimum of 3.7 kA/m and a maximum of 419.6 kA/m, respectively.     

K2CuIn3Se6的固相合成、晶体结构和性能

采用反应性熔盐法以n(K₂Se₃ )∶n(Cu)∶n(In)∶n(Se) =2∶2∶1∶6的摩尔比,在773K下反应5d,得到四元金属硒化物K₂CuIn₃Se₆。该晶体属于单斜晶系,空间群为C2/c ,晶胞参数a =1 .1484(2)nm,b =1.1458(2)nm,c =2.1327(4)nm,β =97.81(3)^o,V=2.7802(1)nm³,Z=8.K₂CuIn₃Se₆具有层状结构,含有二维共价结构的负离子,²∞[CuIn₃Se₆]^2-.²∞ [CuIn₃Se₆]^2-由配位四面体[CuSe₄]和[InSe₄]共顶点连接而成。²∞[CuIn₃Se₆]^2-和K+ 以静电力堆积成晶体。漫反射光谱研究表明,该晶体具有1.6eV的光学能隙,属于半导体,对太阳能有选择吸收的特性。     

无机-有机杂化材料Mo8O26(H2bpp)2的合成与表征

以无水乙醇和冰乙酸为溶剂,Co(NO₃)₂·6H₂O,（1,3 二(4-吡啶基)丙烷（bpp）和(NH₄)₆［Mo₇O₂₄］·4H₂O为反应物,在150℃下进行溶剂热反应,合成了新的无机-有机杂化材料Mo₈O₂₆(H₂bpp)₂。采用单晶X-射线衍射法测定晶体结构,通过紫外-可见-近红外反射光谱表征了晶体性能。研究表明,合成产物属单斜晶系,空间群P2₁/c,晶胞参数a=10.938(2),b=9.7351(19),c=19.649(4),β=101.74(3)° ,V=2048.5(7)A° ³;晶体结构由无机的［Mo₈O₂₆］^4-_n链和有机的(H₂bpp)²⁺离子靠静电力和氢键堆积而成;此无机-有机杂化材料对紫外光具有较强的吸收,且有一定的质子导电能力。