LYAPOUNOV EXPONENTS AND LAW OF LARGE NUMBERS FOR RANDOM WALK IN RANDOM ENVIRONMENT WITH HOLDING TIMES

In this article, the authors mainly discuss the law of large number under Kalikow＇s condition for multi-dimensional random walks in random environment with holding times. The authors give an expression to the escape speed of random walks in terms of the Lyapounov exponents, which have been precisely used in the context of large deviation.     

多元随机序列泛函的强偏差定理

利用熵密度和样本偏差率的概念,建立了多元随机序列泛函关于条件期望的用不等式表示的强极限性质(称之为强偏差定理),在推论部分得到了非齐次马氏链的强偏差定理和随机条件概率的调和平均值的极限性质等相关结论.证明中给出了将条件矩母函数应用于研究多元随机序列泛函的强极限性质的一种途径.     

Synthesis and Crystal Structure of a Dialkyltin Benzamidoacetate Compound {[n-Bu2Sn（O2CCH2NHCOC6H5）]2O}2·C6H6

A dialkyltin benzamidoacetate compound {[n-Bu2Sn（O2CCH2NHCOC6H5）]2O}2· C6H6 has been synthesized by the reaction of dialkyltin oxide with benzamidoacetic acid in 1：1 molar ratio, and its structure was determined by X-ray single-crystal diffraction. The crystal belongs to orthorhombic, space group Pca21, with a = 1.9134（4）, b = 1.9605（4）, c = 2.0657（4） nm, Z = 4, V = 7.749（3） nm^3, Dc = 1.054 mg·m^-3,μ（MoKa） = 1.337 mm^-1, F（000） = 3576, the final R = 0.0405 and wR = 0.0860. According to the structural analysis, the tin atom adopts a distorted five-coordinate trigonal bipyramidal geometry, and the dimer structure is shaped by one planar four-membered Sn2O2 ring.     

Three New d~(10) Coordination Polymers with Arenedisulfonates:Syntheses,Crystal Structures and Luminescent Properties

Three new cadmium or zinc arenedisulfonate complexes [Zn（bpp）2（L）]n 1, { [Cd（bpp）2（1,5-NDS）（H2O）2]·4H2O }n 2 and { [Cd（bpp）2（H2O2）2]·（1,5-NDS） } n 3 （L = 4,4′-bis（2-sulfonatostyryl）biphenyl, bpp = 1,3-di（4-pyd-dyl）propane and 1,5-NDS = 1,5-Naphthalenedisulfonate） have been synthesized from aqueous solution and structurally characterized by infrared spectroscopy, elemental analysis and single-crystal X-ray diffraction. Crystal data for complex 1： space group P21/n, a = 10.559（3）, b = 13.138（4）, c = 17.623（5）A^°, β = 100.852（3）°, V = 2400.9（12） A^°^3 Z = 2, Dc= 1.351 g/cm^3, F（000） = 1016, μ = 0.654 mm^-1, the final R = 0.0412 and wR = 0.0994; Crystal data for complex 2： space group P^-1, a = 8.5642（19）, b = 10.076（3）, c = 12.114（3） A^°, α = 81.623（7）, β = 77.149（8）, γ = 82.787（7）°, V = 1003.6（4） A^°^3 Z = 1, Dc= 1.495 g/cm^3, F（000） = 466,μ = 0.713 mm^3, the final R = 0.0241 and wR = 0.0713; Crystal data for complex 3： space group C2/c, a = 21.6024（15）, b = 9.4608（5）, c = 18.4656（11）A^°, β = 107.359（3）°, V= 3602.0（4）A^°^3 Z = 4, Dc= 1.533 g/cm^3, F（000） = 1704,μ = 0.780 mm^-1, the final R = 0.0229 and wR = 0.0572. The X-ray single diffraction reveals that 1 exhibits a 3D metal-organic framework formed from 2D Zn（bpp）2^2＋ networks connected by L in the third dimension; 2 and 3 possess 3D and 2D architectures constructed from 1D polymeric chains through H-bond. Complexes 1-3 display photoluminescent emissions at 452 and 335 nm, respectively.     

Synthesis and Structure of a Titanocene-ferrocenyl Complex

A titanocene-ferrocenyl complex, （5-ferrocenyl-2-hydroxybenzenecarboxylato- O,O′）-bis（methylcyclopentadienyl）titanium（IV） 4, and an unexpected ionic complex, [C7H8NO3]- [（C5H5）Fe（C5H4）SO3]·H2O3 were synthesized and characterized by IR, ^1H NMR and elemental analysis. Compound 3 is of triclinic, space group P1 with a = 5.954（2）, b = 13.208（5）, c = 13.252（5） A, α = 60.993（7）,β = 84.342（8）,γ = 86.933（8）°, Z = 2, V = 906.8（6）A^3, Dc = 1.601 g/cm^3, μ（MoKα） = 0.987 mm^-1, F（000） = 452, the final R = 0.0647 and wR = 0.1333 for 2311 observed reflections （I 〉 2σ（I））. Compound 4 belongs to the monoclinic system, space group P2 1/c with α = 14.3310（9）, b = 12.5065（8）, c = 12.9406（10） A, β = 95.101（4）°, Z = 4, V = 2310.2（3） A^3, Dc = 1.513 g/cm^3, μ（MoKα） = 1.004 mm^-1, F（000） = 1088, the final R = 0.0461 and wR = 0.1048 for 2112 observed reflections （1 〉 2σ（I））.     

A novel correlation for estimation of hydrate forming condition of natural gases

An inherent problem with natural gas production or transmission is the formation of gas hydrates, which can lead to safety hazards to production/ transportation systems and to substantial economic risks. Therefore, an understanding of conditions where hydrates form is necessary to overcome hydrate related issues. Over the years, several models requiring more complicated and longer computations have been proposed for the prediction of hydrate formation conditions of natural gases. For these reasons, it is essential to develop a reliable and simple-to-use method for oil and gas practitioners. The purpose of this study is to formulate a novel empirical correlation for rapid estimation of hydrate formation condition of sweet natural gases. The developed correlation holds for wide range of temperatures (265–298 K), pressures (1200 to 40000 kPa) and molecular weights (16−29). New proposed correlation shows consistently accurate results across proposed pressure, temperature and molecular weight ranges. This consistency could not be matched by any of the widely accepted existing correlations within the investigated range. For all conditions, new correlation showed average absolute deviation to be less than 0.2% and provided much better results than the widely accepted existing correlations.     

蛋白质折叠类型的分类建模与识别

蛋白质的氨基酸序列如何决定空间结构是当今生命科学研究中的核心问题之一. 折叠类型反映了蛋白质核心结构的拓扑模式, 折叠识别是蛋白质序列-结构研究的重要内容. 我们以占Astral 1.65序列数据库中α, β和α/β三类蛋白质总量41.8%的36个无法独立建模的折叠类型为研究对象, 选取其中序列一致性小于25%的样本作为训练集, 以均方根偏差(RMSD)为指标分别进行系统聚类, 生成若干折叠子类, 并对各子类建立基于多结构比对算法(MUSTANG)结构比对的概形隐马尔科夫模型(profile-HMM). 将Astral 1.65中序列一致性小于95%的9505个样本作为检验集, 36个折叠类型的平均识别敏感性为90%, 特异性为99%, 马修斯相关系数(MCC)为0.95. 结果表明: 对于成员较多, 无法建立统一模型的折叠类型, 基于RMSD的系统分类建模均可实现较高准确率的识别, 为蛋白质折叠识别拓展了新的方法和思路, 为进一步研究奠定了基础.     

基于Taylor级数的矩阵双曲余弦函数的数值算法

提出了一种基于Taylor级数的矩阵双曲余弦函数的数值逼近算法,为减少计算量使用了Paterson-Stockmeyer方法来计算矩阵Taylor多项式,对逼近误差进行了绝对后向误差分析以减少误差,并设计了算法可以较为快速且准确地求解矩阵双曲余弦函数,最后进行了数值实验,验证了算法的有效性.     

C~n中Lie球R_(Ⅳ)(n)上的偏差定理

本文引入了Lie球双曲空间上映照族Hm(RIV(n)),满足m阶Jacobi行列式为零的全纯映照子族.而且当m趋于无穷时,该映照族就是RIV(n)上的局部双全纯映照族.作者用分析的方法给出了Hm(RIV(n))上的偏差定理.当m=1和m→+∞时,结果分别都回到了Gong关于Lie球RIV(n)上的偏差定理;当n=1,其结果又回到了Liu和Minda在单位圆盘上的偏差定理.本文的方法也不同于以前.作为偏差定理的一个应用,给出了不同映照族Hm(RIV(n))上的Bloch常数估计.     

交错级数收敛性的几个结果及其应用

莱布尼兹判别法只是一个充分条件。有大量交错级数虽然不满足其条件,但却是收敛的．对于无法用莱布尼兹判别法判定的三类交错级数,利用常数项级数收敛的定义及相关结果,可以证明在一定条件下它们都是收敛的．并通过实例说明所得结果的应用价值．