Hopf structure in nambu-lien-algebras

We define and study the Hopf structures in the ternary (and n-ary) Nambu-Lie algebra. The fundamental concepts of 3-coalgebra, 3-bialgebra, and Hopf 3-algebra are introduced. Some examples of the Hopf structures and analyzed. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 114, No. 1, pp. 87–93, January, 1998.     

The Kμ-Transformation on McBride's Spaces of Generalized Functions

In this paper we define the K_μ- transformation on certain spaces of generalized functions introduced by A.C. McBride by employing the kernel method. we also establish relations between the generalized K_μ- transformation and certain fractional integral operators.     

Adsorption of nucleic acid bases on clays: an investigation using Langmuir and Freundlich isotherms and FT-IR spectroscopy

In the present paper, the adsorption of nucleic acid bases (A, adenine; C, cytosine; U, uracil; and T, thymine) on clays (bentonite, kaolinite, and montmorillonite) was studied at different pH (2.00 and 7.20). It should be pointed out there is no reported study of adsorption of nucleic acid bases on clays using seawater (with the major elements), and a wide range of pH. The main finding of this study was that the ratio of A and T adsorbed on clays ranged from 4.68 to 25.1, much higher than the ratio of their occurrence in organisms ranging from 0.95 to 1.05. The weaker adsorption of U and T on clays raises the question of the possibility of a genetic code based on purines only. The FT-IR spectra at pH 2.00 showed that the interaction of A, C, T, and U with the clays occurs through positively charged, protonated groups. Correspondence: Dr. Dimas A. M. Zaia, Departamento de Química-CCE, Universidade Estadual de Londrina, 86051-990 Londrina-PR, Brazil.     

Estimation of population spectrum for linear processes with random coefficients

A set of time series generated by stationary linear processes with an absolutely continuous spectral distribution is analysed. The time series can then be considered realizations of a linear process of random coefficients. Likewise, each spectral density function is a realization of a stochastic process whose function of means is called a population spectrum. We propose a kernel estimator for the population spectrum and give conditions for its consistency. We then illustrate the properties of this estimator in a simulation study and compare its performance with an alternative parametric estimator that can be found in the literature.      

Synthesis of poly(ester amide)s with lateral groups from a bulk polycondensation reaction with formation of sodium chloride salts

Poly(ester amide)s with a regular sequence and derived from diamine, dicarboxylic acid, and glycolic acid units can be easily synthesized by using a thermal polycondensation method based on the formation of metal halide salts as a driving force. These new poly(ester amide)s have tuneable properties depending on the number of methylene groups and constitute a group of materials with potential interest as biodegradable materials in applications such as surgical sutures. The present work reveals that the proposed synthesis can also be applied when esters of L ‐lysine are used as a diamine unit since no secondary reactions such as transesterification occur under the required polymerization conditions. The possibility of linking compounds with pharmacological activity to the carboxylic acid groups of lysine extends the interest of the referred materials, for example, as drug delivery systems. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 661–667, 2008     

Branched α-1,4-glucan from the gastropod mollusk Strombus gigas

From the mantle of the Caribbean Sea gastropod molluskStrombus gigas a bioglycan containing carbohydrates (73%), protein (22%), and lipid (about 5%) components has been isolated. It has been shown by hydrolysis, periodate oxidation, and methylation that the bioglycan is a D-glucan constructed of -1,4-bound D-glucose residues and has side chains of D-glucose residues linked by -1,6-bonds.Pacific Ocean Institute of Bioorganic Chemistry, Far Eastern Scientific Center, Academy of Sciences of the USSR, Vladivostok. Translated from Khimiya Prirodnykh Soedinenii, No. 1, pp. 36–40, January–February, 1988.     

Note On the equality of star products

We study the problem of finding conditions for two star products of n vectors to be equal when the vectors in each star product are not linearly independent, and the problem of finding conditions for one star product to be zero. We reprove results of M. Marcus and J. Chollet in a very simple way. We present also some open problems.