The Henicosaphosphide Iodides of Potassium and Rubidium,K4P21I and Rb4P21I

The novel ternary polyphosphides M₄P₂₁I (M = K, Rb) have been synthesized from the elements in single crystalline form, representing further examples for the formation of mixed crystals between simple salts and binary phosphides. They form as ruby‐red platelets and dark‐red prisms, respectively, and are only slightly sensitive to moisture and oxygen. The compounds are isotypic (Ccmm (no 63); Z = 4; oP104; K₄P₂₁I: a = 12.853Å; b = 21.795Å; c = 9.748Å; 1168 hkl, R = 0.033; Rb₄P₂₁I: a = 13.281Å; b = 21.868Å; c = 9.771Å; 777 hkl, R = 0.053) and feature corrugated 2D networks formed from two different types of polymerized P₇ units. The networks form large cavities filled by M⁺ and I^‐ ions. Zigzag chains of condensed trigonal M₆ prisms, centered by the I^‐ anions, separate the polyphosphide nets. The mean homoatomic P‐P bond length (d = 2.216Å) corresponds to a P‐P single bond. However, the individual P‐P distances vary with position and function (2.126 ‐ 2.247Å) and these are compared with those of the isolated P₂₁^‐3 anion.     

On the singular graph and the Weyr characteristic of anM-matrix

LetA be anM-matrix in standard lower block triangular form, with diagonal blocksA _ii irreducible. LetS be the set of indices such that the diagonal blockA is singular. We define the singular graph ofA to be the setS with partial order defined by > if there exists a chain of non-zero blocksA _i, A_ij, , A_l.Let ₁ be the set of maximal elements ofS, and define thep-th level _p ,p = 2, 3, , inductively as the set of maximal elements ofS \( _{1 p-1}). Denote by _p the number of elements in _p . The Weyr characteristic (associated with 0) ofA is defined to be (A) = ( ₁, ₂,, _h ), where ₁ + + _p = dim KerA ^p ,p = 1, 2, , and _h > 0, _h+1 = 0.Using a special type of basis, called anS-basis, for the generalized eigenspaceE(A) of 0 ofA, we associate a matrixD withA. We show that(A) = ( ₁, , _h) if and only if certain submatricesD _p,p+1 ,p = 1, , h – 1, ofD have full column rank. This condition is also necessary and sufficient forE(A) to have a basis consisting of non-negative vectors, which is a Jordan basis for –A. We also consider a given finite partially ordered setS, and we find a necessary and sufficient condition that allM-matricesA with singular graphS have(A) = ( ₁, , _h). This condition is satisfied ifS is a rooted forest.The work of the second-named author was partly supported by the National Science Foundation, under grant MPS-08618 A02.     

A comparative molecular field analysis (CoMFA) study using semiempirical, density functional, ab initio methods and pharmacophore derivation using DISCOtech on sigma 1 ligands

The Comparative Molecular Field Analysis (CoMFA) was developed to investigate a three-dimensional quantitative structure activity relationship (3D-QSAR) model of ligands for the sigma 1 receptor. The starting geometry of sigma-1 receptor ligands was obtained from the Tripos force field minimizations and conformations were decided from DISCOtech using the SYBYL 6.8. program. The structures of 48 molecules were fully optimized at the ab initio HF/3-21G* and semiempirical AM1 calculations using GAUSSIAN 98. The electrostatic charges were calculated using several methods such as semiempirical AM1, density functional B3LYP/3-21G*, and ab initio HF/3-21G*, MP2/3-21G* calculations within GAUSSIAN 98. Using the optimized geometries, the CoMFA results derived from the HF/3-21G method were better than those from AM1. The best CoMFA was obtained from HF/3-21G* optimized geometry and charges (R2 = 0.977). Using the optimized geometries, the CoMFA results derived from the HF/3-21G methods were better than those from AM1 calculations. The training set of 43 molecules gave higher R2 (0.989-0.977) from HF/3-21G* optimized geometries than R2 (0.966-0.911) values from AM1 optimized geometries. The test set of five molecules also suggested that HF/3-21G* optimized geometries produced good CoMFA models to predict bioactivity of sigma 1 receptor ligands but AM1 optimized geometries failed to predict reasonable bioactivity of sigma 1 receptor ligands using different calculations for atomic charges.     

Non-aqueous,reversed-phase,high-performance,thin-layer chromatography and column liquid chromatography of metal complexes of porphine

Summary The chromatographic mobility of 21H, 23H-porphine and its Ni(II), Cu(II), Zn(II) and Pd(II) complexes were investigated by high-performance thin-layer chromatography on an octadecyl-bonded, silica gel plate with various polar organic solvents including alcohols, acetonitrile, dimethylsulfoxide and propylenecarbonate. The mobility generally decreases according to the central metal ion of the complex as follows: Zn(II)>(free porphine)>Ni(II)>Pd(II)>Cu(II). Methanol is a good choice of solvent for the separation of these metal porphine complexes. Successful separation of porphine and the four metal complexes is accomplished within 13 min on a LiChrosorb RP-18 column with methanol eluent.     

两种气相色谱固定相的研究

使用硫杂冠醚、穴醚[2.2.2]作气相色谱固定相制备毛细管柱,考察两种固定相的使用比例、极性、热稳定性,并对甲苯-苯、乙苯-甲苯、甲基苯酚（o/p）、二氯苯（o/p,m）、硝基氯化苯（m,o）、苯-环己烷、庚醇-辛醇、苯胺-N,N二甲基苯胺等混合样品进行色谱分离.实验结果表明：两种固定相在OV-1701中的比例均为15%时有较好的分离效果,都属于中等极性的固定相.硫杂冠醚、穴醚[2.2.2]的平均极性分别为815、832,其中硫杂冠醚固定相的热稳定性较好,有较高的使用温度（185℃）,而穴醚[2.2.2]的最高使用温度为120℃,因此穴醚[2.2.2]的使用温度受到一定的限制.从它们较好的分离性能看,固定相硫杂冠醚、穴醚[2.2.2]均具有较好的应用前景.     

Convergence of Padé approximants for aq-hypergeometric series (Wynn's Power Series I)

We investigate the convergence of sequences of Padé approximants for power series

The extraction,antioxidant and against β-amyloid induced toxicity of polyphenols from Alsophila spinulosa leaves

Alsophila spinulosa is a tree-like fern, and many evidences suggested that plant polyphenols had the potential therapeutic for Alzheimer s disease (AD). Herein, polyphenols (ASP) was isolated from A. spinulosa leaves and its major constituent were isoorientin and vitexin. ASP displayed excellent antioxidant activity and obvious anti-lipid peroxidation capacity in vitro. ASP improved the survival rate of C. elegans under high temperature by enhancing the antioxidant enzymes activities and decreasing the lipid peroxidation level. Moreover, ASP alleviated β-amyloid (Aβ) induced paralysis and reduced Aβ deposition, decreased reactive oxygen species (ROS) accumulation and improved the level of skn-1 mRNA. In addition, ASP decreased the levels of pdk-1 and akt-1 mRNA in P13K/AKT signaling pathway. In conclusion, ASP may be a potential ingredient for the alleviation of AD.     

Splitting‐characterizations of the Papangelou process

For point processes we establish a link between integration‐by‐parts‐ and splitting‐formulas which can also be considered as integration‐by‐parts‐formulas of a new type. First we characterize finite Papangelou processes in terms of their splitting kernels. The main part then consists in extending these results to the case of infinitely extended Papangelou and, in particular, Pólya and Gibbs processes.     

A two-component geodesic equation on a space of constant positive curvature

We propose a new two-component geodesic equation with the unusual property that the underlying space has constant positive curvature. In the special case of one space dimension, the equation reduces to the two-component Hunter–Saxton equation.     

Determinant of a matrix that commutes with a Jordan matrix

Given a Jordan matrix J, we obtain an explicit formula for the determinant of any matrix T that commutes with it.