Synthesis, spectral characterization and in vitro microbiological evaluation of novel glyoxal, biacetyl and benzil bis-hydrazone macrocyclic Schiff bases and their Co(II), Ni(II) and Cu(II) complexes

A series of binuclear Co(II), Ni(II) and Cu(II) complexes were synthesized by the template condensation of glyoxal, biacetyl or benzil bis-hydrazide, 2,6-diformyl-4-methylphenol and Co(II), Ni(II) or Cu(II) chloride in a 2:2:2 M ratio in ethanol. These 22-membered macrocyclic complexes were characterized by elemental analyses, magnetic, molar conductance, spectral, thermal and fluorescence studies. Elemental analyses suggest the complexes have a 2:1 stoichiometry of the type [M₂LX₂]·nH₂O and [Ni₂LX₂2H₂O]·nH₂O (where M = Co(II) and Cu(II); L = H₂L¹, H₂L² and H₂L³; X = Cl; n = 2). From the spectroscopic and magnetic studies, it has been concluded that the Co(II) and Cu(II) complexes display a five coordinated square pyramidal geometry and the Ni(II) complexes have a six coordinated octahedral geometry. The Schiff bases and their metal complexes have also been screened for their antibacterial and antifungal activities by the MIC method.     

Nano‐emulsion use for the synthesis of polyaniline nano‐grains or nano‐fibers

We report that nano‐emulsions can be creatively used as a morphology selective synthesis method to prepare not only nano‐grains but also nano‐fibers with high selectivity. Synthesis of the two different morphological materials was demonstrated using polyaniline synthesis as a model case. Polyaniline nano‐grains were synthesized from aniline molecules in nano‐size aqueous droplets as polymerization sites whose droplets were generated by inverse water‐in‐oil nano‐emulsion use, and polyaniline nano‐fibers were synthesized from aniline in aqueous nano‐dimensional channels as polymerization sites whose channels were generated by direct oil‐in‐water nano‐emulsion use containing high population of oil droplets. Using the approaches, we successfully synthesized nano‐fibers of 60 nm diameter with 0.5 µm length and also nano‐grains having diameter of 60–80 nm. The two different polymerization sites of nano‐scale dimension were made by changing the ratio among surfactant, aqueous aniline/HCl solution, and oil, i.e. organic solvent. We found the nano‐fibers synthesized from the channels formed by the direct oil‐in‐water nano‐emulsion have higher bulk electrical conductivity than the nano‐grains which were synthesized from the droplets formed by the inverse water‐in‐oil emulsion. We also found that the emulsion use allows us to use a room temperature synthesis unlike conventional synthesis methods which require to use ice bath temperature. Physical properties of both nano‐fibers and nano‐grains synthesized were characterized by Fourier transform infrared (FTIR), UV–Vis spectra, scanning electron microscopy (SEM), and four probes conductivity measurement. Copyright © 2009 John Wiley & Sons, Ltd.     

A-optimal designs for an additive cubic model

Chan et al. (1998a) obtained A-optimal designs for an additive quadratic mixture model for q≥3 mixture components. In this paper, we obtain the A-optimal designs for an additive cubic model for q≥3 mixture components using the class of symmetric weighted centroid designs based on barycentres of various depths. We observe that barycentres of depths 0 and 2 are possible support points for an A-optimal design. We have also given the optimal weights of A-optimal designs for 3≤q≤17.     

Fourth-order finite difference methods for three-dimensional general linear elliptic problems with variable coefficients

In this article, we give a simple method for deriving finite difference schemes on a uniform cubic grid. We consider a general, three-dimensional, second-order, linear, elliptic partial differential equation with variable coefficients. We derive two simple fourth-order schemes. When the coefficients of the second-order mixed derivatives are equal to zero, the fourth-order scheme requires only 19 grid points. When the coefficients of the mixed derivatives are not equal to zero and the coefficients of U_xx, U_yy, and U_zz are equal, we require the 27 points of the cubic grid. Numerical examples are given to demonstrate the performance of the two schemes derived. There does not exist a fourth-order scheme involving 27 grid points for the general case.     

On a theorem of M. Deuring and I. R. Šafarevič

Let F/K be a field of algebraic functions of one variable, K algebraically closed of characteristic p≠0. Let E/K be a cyclic extension of F/K of degree ?, a prime not necessarily different from p. Let ξ, ρ denote the ?-ranks of the null class groups of E and F respectively. If E/F is ramified, Deuring proved that ξ=?ρ+(t?δ)(??1) where t is the number of ramified primes and δ is 1 or 2 according as ? equals p or not. ?afarevi? proved the same relation in the unramified case for ?=p where ξ, ρ denote the ranks of the Hasse-Witt matrices. Subrao gave a unified proof for ?=p. Rosen and Sullivan have proved the theorem in special cases. In this paper, using galois cohomology, Deuring's method of proof is modified so as to give a proof of the theorem in all cases.     

Galois module structure of Tate modules

Dedicated to Professor Peter Roquette Received 1 February 1996; in final form 26 April 1996     

Dynamic stiffness matrix of a general cable element

Summary A computational scheme for determining the dynamic stiffness coefficients of a linear, inclined, translating and viscously/hysteretically damped cable element is outlined. Also taken into account is the coupling between inplane transverse and longitudinal forms of cable vibration. The scheme is based on conversion of the governing set of quasistatic boundary value problems into a larger equivalent set of initial value problems, which are subsequently numerically integrated in a spatial domain using marching algorithms. Numerical results which bring out the nature of the dynamic stiffness coefficients are presented. A specific example of random vibration analysis of a long span cable subjected to earthquake support motions modeled as vector gaussian random processes is also discussed. The approach presented is versatile and capable of handling many complicating effects in cable dynamics in a unified manner.The work reported in this paper has been carried out as a part of a research project on dynamics of extensible cables funded by the Department of Science and Technology, Government of India. The financial support received is gratefully acknowledged.