Lie groups in nonequilibrium thermodynamics: Geometric structure behind viscoplasticity

Poisson brackets provide the mathematical structure required to identify the reversible contribution to dynamic phenomena in nonequilibrium thermodynamics. This mathematical structure is deeply linked to Lie groups and their Lie algebras. From the characterization of all the Lie groups associated with a given Lie algebra as quotients of a universal covering group, we obtain a natural classification of rheological models based on the concept of discrete reference states and, in particular, we find a clear-cut and deep distinction between viscoplasticity and viscoelasticity. The abstract ideas are illustrated by a naive toy model of crystal viscoplasticity, but similar kinetic models are also used for modeling the viscoplastic behavior of glasses. We discuss some implications for coarse graining and statistical mechanics.     

Stacking in CE for Analysis of Bromate Flour Additive

In this paper we report a simple and effective on-line sample-stacking method in capillary electrophoresis for analysis of bromate ion. The detection limit is 10.9 ng mL^?1. Direct injection is performed after a simple extraction procedure. It is possible to detect 2.18 mg kg^?1 bromate ion in flour by use of this technique.     

On the Space bvp（F） of Sequences of p-bounded Variation of Fuzzy Numbers

Recently, the space bvp of real or complex numbers consisting of all sequences whose differences are in the space lp has been studied by Basar, Altay [Ukrainian Math. J. 55（1）（2003）, 136-147], where 1 ≤ p ≤ ∞. The main purpose of the present paper is to introduce the space bvp（F） of sequences of p-bounded variation of fuzzy numbers. Moreover, it is proved that the space bvp（F） includes the space lp（F） and also shown that the spaces bvp（F） and lp（F） axe isomorphic for 1 ≤ p ≤∞. Furthermore, some inclusion relations have been given.     

Multivariate design

In multivariate data analysis such as principal components analysis (PCA) and projections to latent structures (PLS), it is essential that the training set systems (objects) are selected to provide data with substantial information for model parametrization, and to represent properly any future situations where the multilvariate model is used for predictions. In the framework of multivariate projections (PCA, SIMCA and PLS), elementary concepts of statistical design (fractional factorials and composite designs) can be used with the latent variables (PC or PLS scores) as design variables. The plan of action thus becomes: (1) problem formulation (specify aim and model, make a conceptual division of the investigated system into subsystems); (2) collection of multivariate data for each type of subsystems; (3) estimation of the practical dimensionality of the data for each type of subsystems by PC or PLS analysis; (4) use of the PC or PLS scores (t) as design variables in the combination of subsystems to systems in the training set; (5) measurement of responses (Y); (6) analysis of data by PCA or PLS; (7) interpretation of results with possible feedback to steps 1, 2 or 3. The procedures are illustrated by two problems: a structure/activity relationship for a family of peptides, and optimization of an organic synthesis with respect to system variables (solvent, substrate, co-reactant_) and process variables (temperature, reactant concentrations).     

On Tauberian theorems for (<Emphasis Type="Italic">A,k</Emphasis>) summability method

Let (u _n ) be a sequence of real numbers. In this paper we introduce some Tauberian conditions in terms of regularly generated sequences for (A, k) summability method.     

Strategies on the evaluation of binomial coefficients for all integers

Binomial coefficients are used in many fields such as computational and applied mathematics, statistics and probability, theoretical physics and chemistry. For accurate numerical results, the correct calculation of these coefficients is very important. We present some new recurrence relationships and numerical methods for the evaluation of binomial coefficients for negative integers. For this purpose, we give some comparisons of the outputs for different computer programming languages in case of negative integers, and also we wrote two new algorithms for computations.     

Synthesis,crystal structure and catalytic activity for H2O2 disproportionation of the manganese(II) coordination polymer {[Mn(O2C(CF2)8CO2)(phen)2]H2O}n (phen = 1,10-phenanthroline)

The title polymeric complex {[Mn(O₂C(CF₂)₈CO₂)(phen)₂]H₂O}_n was synthesized through the reaction of 1,10-phenanthroline, perfluorosebacic acid and MnCO₃ · H₂O. The molecular structure was characterized by X-ray diffraction, elemental analysis, thermal gravimetry, IR and UV–Vis spectroscopy and its catalytic activity has been studied. X-ray structure analysis shows that each Mn(II) ion is octahedrally coordinated by two bidentate phenanthroline ligands and the carboxylate oxygen atoms from two symmetry related perfluorosebacate ligands, which are coordinated in cisoid positions. The structure consists of polymeric chains, with the perfluorosebacato ligand bridging the Mn(II) ions in a monodentate fashion. Crystallographic characterization shows a supramolecular structure involving hydrogen bonds, π–π and π-ring interactions. The catalytic results indicated that the complex has reasonably good activity towards the disproportionation of hydrogen peroxide into water and dioxygen in methanol and it does not exhibit saturation kinetics with the substrate. The initial reaction rates and their temperature and base dependencies were investigated by monitoring the dioxygen evolution. Kinetic studies revealed a first-order dependence on the catalyst concentration. Activation parameters have been calculated at 301 K.     

Ergodic dynamics of the coupled quasigeostrophic-flow-energy-balance system

The authors consider a mathematical model for the coupled atmosphere-ocean system, namely, the coupled quasigeostrophic-flow-energy-balance model. This model consists of the large-scale quasigeostrophic oceanic flow model and the transport equation for oceanic temperature, coupled with an atmospheric energy-balance model. After reformulating this coupled model as a random dynamical system (cocycle property), it is shown that the coupled quasigeostrophic-energy balance fluid system has a random attractor, and under further conditions on the physical data and the covariance of the noise, the system is ergodic, namely, for any observable of the coupled atmosphere-ocean flows, its time average approximates the statistical ensemble average, as long as the time interval is sufficiently long. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 12, No. 6, pp. 67–84, 2006.