Nano-sized Cu(II) and Zn(II) complexes and their use as a precursor for synthesis of CuO and ZnO nanoparticles: A study on their sonochemical synthesis,characterization, and DNA-binding/cleavage,anticancer, and antimicrobial activities

Two new divalent copper (C1) and zinc (C2) chelates having the formulae [M(PIMC)₂] (where M = Cu(II), Zn(II) and PIMC = Ligand [(E)-3-(((3-hydroxypyridin-2-yl)imino)methyl)-4H-chromen-4-one] were obtained and characterized by several techniques. Structures and geometries of the synthesized complexes were judged based on the results of alternative analytical and spectral tools supporting the proposed formulae. IR spectral data confirmed the coordination of the ligands to the copper and zinc centers as monobasic tridentate in the enol form. Thermal analysis, UV-Vis spectra and magnetic moment confirmed the geometry around the copper center to be tetrahedral, square pyramidal and octahedral. Study of the binding ability of the synthesized compounds with Circulating tumor DNA (CT-DNA) bas been evaluated applying UV-Vis spectral titration and viscosity measurements. The copper and zinc oxides were achieved from the copper and zinc nano-particles structures Schiff base complexes as the raw material after calcination for 5 hr at 600°C. On the other hand, synthesized of C1 and C2 NPs were used as suitable precursors to the preparation of CuO and ZnO NPs. Finally, the synthesized of the two complexes exhibited enhanced activity against the tested bacterial (Staphylococcus aureus and Escherichia Coli) and fungal strains (Candida albicans and Aspergillus fumigatus) as compared to HPIMC. Among all these synthesized compounds, C1 exhibits good cleaving ability compared to other newly synthesized C2.     

D3h‐Symmetric Porphyrin‐Based Rigid Macrocyclic Ligands for Multicofacial Multinuclear Complexes in a One‐Nanometer‐Sized Cavity

The one‐step synthesis of D_3h‐symmetric cyclic porphyrin trimers 1 composed of three 2,2′‐[4,4′‐bis(methoxycarbonyl)]bipyridyl moieties and three porphyrinatozinc moieties was achieved from a nickel‐mediated reductive coupling of meso‐5,15‐bis(6‐chloro‐4‐methoxycarbonylpyrid‐2‐yl)porphyrinatozinc. Although cyclic trimers 1 were obtained as a mixture that included other cyclic and acyclic porphyrin oligomers, an extremely specific separation was observed only for cyclic trimers 1 when using columns of silica gel modified with pyrenylethyl, cyanopropyl, and other groups. Structural analysis of cyclic trimers 1 was carried out by means of NMR spectroscopy and X‐ray crystallography. Treatment of an η³‐allylpalladium complex with a cyclic trimer gave a tris(palladium) complex containing three η³‐allylpalladium groups inside the space, which indicated that the bipyridyl moieties inside the ring could work as bidentate metalloligands.     

Synthesis,Crystal Structure,and Magnetic Properties of a New Dinuclear Iron Complex with Schiff Base Ligand

A new dinuclear iron(Ⅲ) complex has been synthesized and structurally characterized by X-ray crystallography: [FeⅢ2(L)(C6H5COO)(SO4)(CH3OH)2]·CH3CN·CH3OH(1, H3 L = N,N'-bis(salicylidene)-1,3-diamino-2-propanol). Complex 1 belongs to orthorhombic space group Pna21 with a = 11.4400(8), b = 22.9705(2), c = 12.5712(9) , V = 3303.5(4) 3, Z = 4, F(000) = 1576, Dc = 1.531 g·cm–3, Mr = 761.36, μ = 1.007 mm–1, S = 1.014, the final R = 0.0505 and wR = 0.1018. The crystal packing is stabilized by intermolecular O–H···O hydrogen bonds, forming an extended one-dimensional chain structure. The temperature dependence of magnetic susceptibility measurement shows that antiferromagnetic interaction is propagated between the metal centers. Fit as dinuclear arrangement gave parameters of J = 19.7 cm-1, g = 1.89 and R2 = 0.9999.     

一阶最优性条件研究

本对由Botsko的关于多变量函数取极值的一阶导数检验条件定理^[1]进行了分析研究，给出了更实用而简捷的差别条件。最后，举出若干例子予以说明。     

Diastereoselective Alkylation of (Diene-Aldehyde)Fe(CO)3 Complexes with Functionalized Zinc-Copper Reagents NuCu(CN)Znl

Addition of functionalized zinc-copper reagents to the title complexes proceeds in a highly diastereoselective fashion to afford dienol complexes. The relative configurations of adducts 3d were determined by single X-ray diffraction analysis.     

SINGULAR PERTURBATION OF BOUNDARY VALUE PROBLEM FOR NONLINEAR HIGHER ORDER ORDINARY DIFFERENTIAL EQUATIONS INVOLVING TWO SMALL PARAMETERS

The singularly perturbed boundary value problem for nonlinear higher order ordinary differential equation involving two small parameters has been considered. Under appropriate assumptions, for the three cases:ε/μ2→0(μ→0),μ2/ε→0 (ε→0) andε=μ2, the uniformly valid asymptotic solution is obtained by using the expansion method of two small parameters and the theory of differential inequality.     

Estimating a reduced rank regression model for non-normal variables

A method using third order moments for estimating the regression coefficients as well as the latent state scores of the reduced-rank regression model when the latent variable(s) are non-normally distributed is presented in this paper. It is shown that the factor analysis type indeterminacy of the regression coefficient matrices is eliminated. A real life example of the proposed method is presented. Differences of this solution with the reduced-rank regression eigen solution are discussed.     

An efficient numerical scheme for precise time integration of a diffusion-dissolution/precipitation chemical system

A numerical scheme based on an operator splitting method and a dense output event location algorithm is proposed to integrate a diffusion-dissolution/precipitation chemical initial-boundary value problem with jumping nonlinearities. The numerical analysis of the scheme is carried out and it is proved to be of order 2 in time. This global order estimate is illustrated numerically on a test case.

     

仓库容量有限条件下的随机存贮管理问题的评注

给出2005年全国部分高校研究生数学建模竞赛D题的研究背景,对参赛论文作了简要评注,并提供了一种参考解答.     

Some formulae for the q-Bernoulli and Euler polynomials of higher order

The purpose of this paper is to give a proof of Kummer type congruence for the q-Bernoulli numbers of higher order, which is an answer to a part of the problem in a previous publication (see Indian J. Pure Appl. Math. 32 (2001) 1565-1570).