A factorization method for q-Racah polynomials

We develop a factorization method for q-Racah polynomials. It is inspired by the approach to q-Hahn polynomials based on the q-Johnson scheme, but we do not use association scheme theory nor Gel'fand pairs but only manipulation of q-difference operators.     

Proof of Andrews' conjecture on a 4φ3 summation

We give a new proof of a ₄φ₃ summation due to G.E. Andrews and confirm another ₄φ₃ summation conjectured by him recently. Some variations of these two ₄φ₃ summations are also given.     

Generating functions for vector partition functions and a basic recurrence relation

ABSTRACT

We define a generalized vector partition function and derive an identity for the generating series of such functions associated with solutions to basic recurrence relations of combinatorial analysis. As a consequence we obtain the generating function of the number of generalized lattice paths and a new version of the Chaundy-Bullard identity for the vector partition function.     

Ion-Selective Electrodes for the Determination of Antimony and Thallium Based on Water-Insoluble Basic Dye Salts

Abstract

Hexachloroantimonate(V) and tetrachlorothallate(III) salts of Sevron Red L (C.I. Basic Red 17), Sevron Red GL (C.I. 11,085), Flavinduline O (C.I. 50,000) and Phenazinduline O have been applied in liquid-state ion-selective electrodes for the determination of antimony and thallium. The slope of potential versus pM graphs approach full Nernstian response in the range 10 M (Sb) and 10^?6 M (T1) to 10^?2 M. An unusual feature of the electrodes is their response to antimony(III) as well as to antimony(V).     

具有隐性传染的手足口病模型分析

建立并分析了一个带有隐性传染的手足口病模型,计算了基本再生数.构造适当的Lyapunov函数证明了无病平衡点的稳定性,分析了当R_0>1时疾病的一致持续性,并进一步证明了正平衡点的存在性.     

Some fundamental issues of basic line search algorithm for linear programming problems

In this article we present the fundamental idea, concepts and theorems of a basic line search algorithm for solving linear programming problems which can be regarded as an extension of the simplex method. However, unlike the iteration of the simplex method from a basic point to an improved adjacent basic point via pivot operation, the basic line search algorithm, also by pivot operation, moves from a basic line which contains two basic feasible points to an improved basic line which also contains two basic feasible points whose objective values are no worse than that of the two basic feasible points on the previous basic line. The basic line search algorithm may skip some adjacent vertices so that it converges to an optimal solution faster than the simplex method. For example, for a 2-dimensional problem, the basic line search algorithm can find an optimal solution with only one iteration.     

改性ZrO2负载钌氨合成催化剂的制备及其构效关系研究

由ZrO(NO₃)₂水解得到的ZrO(OH)₂水凝胶经碱液回流老化、焙烧后制备了改性ZrO₂载体材料,直接浸渍K₂RuO₄溶液,经还原后用于催化氨合成反应。并运用X射线衍射(XRD)、CO₂ 程序升温脱附(CO₂-TPD)、X射线荧光光谱 (XRF)、N₂物理吸附、H₂程序升温还原技术(H₂-TPR)和CO化学吸附对其进行了表征,重点考察了催化剂性能与载体性能间的构效关系。结果表明,KOH和NH₄OH溶液回流均可提高载体的比表面积,但是KOH回流制备的载体同时还具有较强的碱性,因此,负载钌以后表现出最佳活性。在425 ℃、5 MPa、空速为10 000 h^-1条件下,出口氨浓度为5.96%,分别较催化剂K-Ru/ZrO₂-NH₄OH、K-Ru/ZrO₂-CP和Ru/ZrO₂-NH₄OH提高了11%、143%和103%。与活性组分分散度相比,载体碱性强度对活性的促进作用更为明显。     

碱性离子液体催化“一锅法”合成1,4-二氢吡喃并[2,3-c]吡唑

在碱性离子液体氢氧化1-丁基-3-甲基咪唑([bmim]OH)催化作用下,由芳香醛、丙二腈、苯甲酰乙酸乙酯和肼或苯肼"一锅法"合成了一系列1,4-二氢吡喃并[2,3-c]吡唑化合物.实验中考察了催化剂、反应温度、催化剂用量、溶剂对反应的影响,确定了最优反应条件,给出了可能的反应机理.此外催化剂可以方便地收回,且循环使用四次其催化活性并没有显著降低.目标产物经过了1H NMR,IR,MS和元素分析确证.合成方法条件温和、反应时间短、产率高且对环境友好.     

Cu_(30)Cr_5/碱性氧化铝催化2,2,6,6-四甲基哌啶酮加氢(英文)

在2,2,6,6-四甲基哌啶酮连续化加氢生成2,2,6,6-四甲基哌啶醇的反应中,Cu30Cr5/碱性氧化铝比Cu30Cr5/γ-Al2O3具有更优异的催化性能,反应的转化率和选择性分别高达99.0%和97.2%.N2物理吸附-脱附、X射线光电子能谱、X射线衍射和氨气程序升温脱附结果表明,Cu0作为催化加氢反应的活性中心,在Cu30Cr5/碱性氧化铝中具有更好的分散性,且随着碱性氧化铝的引入,催化剂酸性大幅下降,从而有效抑制副产物2,6-二甲基-4-庚酮的生成,因而产物2,2,6,6-四甲基哌啶醇的选择性显著提高.     

非线性方程组的Newton流线法

为求解非线性方程组F(x)=0, 研究了Newton流方程x_t=V(x)=-(DF(x))^-1F(x),x(0)=x⁰,及数值Newton流x^j+1=x^j+hV(x^j),h∈(0,1].导出了减幅指标g_j(h)=||F(x^j+1)||/||F(x^j)||=1-h+h²d_jh<1和m重根x^*附近的表示g_j(h)=(1-h/m)^m+h²O(||x^j-x^*||).最后基于4个可计算量g_j,d_j,K_j,q_j,提出了新的Newton流线法,如果投入大量的随机初始点, 能找到所有实根、重根和复根.