Almost sure convergence of sample range

Let X ₁, X ₂, ... be i.i.d. random variables. The sample range is R _n = max {X _i , 1 ≤ i ≤ n} − min {X _i , 1 ≤ i ≤ n}. If for a non-degenerate distribution G and some sequences (α _k ), (β _k ) then we have

Synthesis,Crystal Structure,and NLO Property of the Chiral Sulfide Sm4InSbS9

The chiral sulfide Sm₄InSbS₉ was prepared from a stoichiometric mixture of the elements at 1223 K in an evacuated silica tube. It crystallizes in the chiral tetragonal space group P4₃2₁2 with a = 10.0042(4) Å, c = 27.6810(15) Å, V = 2770.4(2) ų, and Z = 8. The structure features infinite helical chains of [In₂Sb₂S₁₁^10–]_∞ propagating along the c direction that are separated by Sm³⁺ cations and S^2– anions. It shows the second harmonic generation with an intensity of 0.75 times that of benchmark AgGaS₂ at 2.05 µm laser in type I phase matchable behavior. UV/Vis diffuse reflectance spectroscopy study shows its optical gap of around 2.13 eV.     

抗凝血酶Ⅲ的免疫共振散射光谱分析

在pH 7.2的Tris-HCl缓冲溶液中和聚乙二醇6000（PEG-6000）存在下,羊抗人抗凝血酶Ⅲ与抗凝血酶Ⅲ（AT-Ⅲ）发生免疫反应形成疏水性的免疫复合物微粒,导致体系的共振散射强度增强,在波长为368,491和538 nm处出现3个共振散射峰,其中491 nm处的峰最强。分别考察了pH、AT-Ⅲ和PEG-6000浓度、温育时间和温度、共存物质的影响。在选定条件下,AT-Ⅲ浓度在62.5～875 ng·mL-1范围内与491 nm处体系的散射强度呈良好的线性关系,其回归方程为ΔI_RS=62.5c+1.36,相关系数为0.996,检出限为29.4 ng·mL-1。该方法简便、灵敏和选择性好,用于人血中AT-Ⅲ含量的测定,结果满意,回收率在90.2%～108.9%之间。     

RLC暂态电路的理论分析和数值模拟

利用Maple符号计算软件做RLC电路方程的拉普拉斯变换,得到电路的精确解,绘制解的图像,并且理论分析了这些解的特点,得到了一些有助于教学应用的结论.     

Charmonium States in QCD-Inspired Quark Potential Model Using Gaussian Expansion Method

We investigate the mass spectrum and electromagnetic processes of charmonium system with the nonperturbative treatment for the spin-dependent potentials, comparing the pure scalar and scalar-vector mixing linear confining potentials. It is revealed that the scalar-vector mixing confinement would be important for reproducing the mass spectrum and decay widths, and therein the vector component is predicted to be around 22?%. With the state wave functions obtained via the full-potential Hamiltonian, the long-standing discrepancy in M1 radiative transitions of J/ψ and ψ′ are alleviated. This work also provides an inspection and suggestion for the possible cc? states among the copious higher charmonium-like states. Particularly, the newly observed X(4160) and X(4350) are found in the charmonium family mass spectrum as M(2¹ D ₂)?= 4164.9 MeV and M(3³ P ₂)?= 4352.4 MeV, which strongly favor the J ^PC ?=?2^?+, 2⁺⁺ assignments respectively. The corresponding radiative transitions, leptonic and two-photon decay widths have been also predicted theoretically for the further experimental search.     

Ligand-based luminescence in lead-containing complexes: The effect of conjugated organic ligands on fluorescence

The asymmetrically substituted heterocyclic alkyne 5-(pyridin-3-ylethynyl) picolinate (P3PA) was synthesized via a one-pot Sonogashira coupling. After purification, P3PA was reacted with Pb(NO₃)₂ into the two-dimensional coordination polymer Pb(P3PA)₂(H₂O)₂ (1) under hydrothermal conditions. Coordination polymer 1 crystallizes into the monoclinic space group I2/a, with a = 15.5775(10) Å, b = 5.9949(4) Å, c = 24.8380(16) Å, and β = 90.7500(10)°. In addition, the luminescent fluorene-based ligands, fluorene-9-carboxylate (FCA) and fluorenone-2,7-dicarboxylate (FDCA), were incorporated into hybrid materials via coordination to the lead (II) cation. Coordination polymer Pb(FCA)₂ (2) crystallizes in the monoclinic space group P2₁/c (a = 8.0518(9) Å, b = 25.338(3) Å, c = 10.5842(12) Å, β = 94.913(2)°), and forms a 1-D polymeric chain. Coordination polymer Pb₃(FDCA)₃(H₂O)₃ (3) crystallizes in the triclinic space group P1 (a = 6.6990(5) Å, b = 10.1529(7) Å, c = 13.6935(9) Å, α = 81.884(2)°, β = 87.260(2)°, γ = 84.399(2)°), and forms pillared 3-D layers. These three compounds have been identified via single crystal X-ray diffraction and characterized via powder X-ray diffraction, UV–Vis spectroscopy, and fluorescence spectroscopy.     

关于Hsler-Reiss分布的一点注记

本文研究了服从二元二项分布的随机向量序列的极值分布问题.利用构造性的方法,证明了服从二元二项分布的随机向量序列之极值依分布收敛到Hsler-Reiss 分布, 将已有结论推广到离散情形.     

A Two‐Parameter Stabilized Finite Element Method for Incompressible Flows

Based on two‐grid discretizations, a two‐parameter stabilized finite element method for the steady incompressible Navier–Stokes equations at high Reynolds numbers is presented and studied. In this method, a stabilized Navier–Stokes problem is first solved on a coarse grid, and then a correction is calculated on a fine grid by solving a stabilized linear problem. The stabilization term for the nonlinear Navier–Stokes equations on the coarse grid is based on an elliptic projection, which projects higher‐order finite element interpolants of the velocity into a lower‐order finite element interpolation space. For the linear problem on the fine grid, either the same stabilization approach (with a different stabilization parameter) as that for the coarse grid problem or a completely different stabilization approach could be employed. Error bounds for the discrete solutions are estimated. Algorithmic parameter scalings of the method are also derived. The theoretical results show that, with suitable scalings of the algorithmic parameters, this method can yield an optimal convergence rate. Numerical results are provided to verify the theoretical predictions and demonstrate the effectiveness of the proposed method. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 425–444, 2017     

Two Pairs of Homochiral Coordination Polymers with Helices Based on Semi‐rigid Lactic Acid Ligands

Utilizing semirigid lactic acid derivatives (R)‐H₂CBA and (S)‐H₂CBA as chiral ligands, two pair of homochiral coordination polymers formulated as [Zn((R)‐CBA)(1,4‐DIB)] · H₂O ( 1 ‐ D ), [Zn((S)‐CBA)(1,4‐DIB)] · H₂O ( 1 ‐ L ), [Co((R)‐CBA)(1,4‐DIB)] · H₂O ( 2 ‐ D ) and [Co((S)‐CBA)(1,4‐DIB)] · H₂O ( 2 ‐ L ) were prepared under solvothermal reaction condition. Single X‐ray diffraction study reveals that all the complexes are comprised of three kinds of helical chains, which are constructed by corresponding metal ions, CBA^2– ligands, and/or 1,4‐DIB ligands. Moreover, some physical characteristics, such as PXRD, thermal stabilities, solid‐state circular dichroism (CD), luminescent and magnetic properties are also investigated.