On-line fractionation and characterization of aquatic humic substances by means of sequential-stage ultrafiltration

A five-stage tangential-flow ultrafiltration (UF) device equipped with advanced membrane filters (molecular weight cut-off: 1, 5, 10, 50 and 100 kDalton) of the polyethersulfone type is described and applied for the analytical on-line fractionation of a series of aquatic humic substances (HS) originating from surface or groundwaters. Fractionation patterns of HS (6 fractions each) evaluated by this UF device exhibit their particular dependence on the HS concentration, the pH-value and the salt content of the sample (10 ml) to be analyzed. Fundamental parameters (e.g., washing volume) governing the molecular-size fractionation of HS by means of multistage UF are discussed, too. The fractionation of an aquatic reference HS (BOC 3/9.5) by means of the above UF procedure reveals considerable differences preferably characterized by the UV-VIS absorption ratio E₃₅₀/E₄₅₀ and metal complexing capacity (Cu(II)) of the produced fractions. Moreover, molecular spectroscopy investigations (FTIR, ¹H-NMR) of the fraction series of this HS indicate that carbohydrate substructures (preferably found in fractions >50 k Dalton) and aromatic ones (preferably in fractions <5 k Dalton) are unevenly distributed.Dedicated to Professor Dr. Dieter Klockow on the occasion of his 60th birthday     

Algebraic index theorem

We prove the Atiyah-Singer index theorem where the algebra of pseudodifferential operators is replaced by an arbitrary deformation quantization of the algebra of functions on a symplectic manifold.Partially supported by NSF Grant DMS-9101817.     

Supervised fuzzy pattern recognition

This paper is devoted to the problem of supervised fuzzy pattern recognition. The cases with non-fuzzy and fuzzy labels are considered. Based on the properties of linearly separable fuzzy classes, some algorithms are proposed for building matching functions of these classes. All algorithms are computer oriented and can be implemented for the automatic recognition of fuzzy patterns.     

Polynomial pseudosupersymmetry underlying a two-level atom in an external electromagnetic field

We study chains of transformations introduced in B.F. Samsonov and V.V. Shamshutdinova: J. Phys. A: Math. Gen. 38 (2005) 4715, in order to obtain electric fields with a time-dependent frequency for which the equation of motion of a two-level atom in the presence of these fields can be solved exactly. We show that a polynomial pseudosupersymmetry may be associated to such chains. Presented at the 3rd International Workshop “Pseudo-Hermitian Hamiltonians in Quantum Physics”, Istanbul, Turkey, June 20–22, 2005.     

Large orbital magnetism

At low temperatures the orbital magnetic susceptibility χ of a finite size metallic sample can be much larger than the macroscopic Landau value χ₀. The value of χ depends on sample size and shape, it can have either sign and it is sensitive to the position of the Fermi level. Some old and recent work on the phenomenon of large orbital magnetism is reviewed.     

Bayesian analysis of constant elasticity of variance models

This paper focuses on the estimation of some models in finance and in particular, in interest rates. We analyse discretized versions of the constant elasticity of variance (CEV) models where the normal law showing up in the usual discretization of the diffusion part is replaced by a range of heavy‐tailed distributions. A further extension of the model is to allow the elasticity of variance to be a parameter itself. This generalized model allows great flexibility in modelling and simplifies the model implementation considerably using the scale mixtures representation. The mixing parameters provide a means to identify possible outliers and protect inference by down‐weighting the distorting effects of these outliers. For parameter estimation, Bayesian approach is adopted and implemented using the software WinBUGS (Bayesian inference using Gibbs sampler). Results from a real data analysis show that an exponential power distribution with a random shape parameter, which is highly leptokurtic compared with the normal distribution, forms the best CEV model for the data. Copyright © 2006 John Wiley & Sons, Ltd.     

Decompositions of semigroups

Communicated by Gerard J. Lallement     

Optimum Discarding in a Bufferless System

This paper considers queueing systems without buffer. The problem is finding an optimum discipline that gives the minimal number of request discards in a given interval or the minimum discard probability. In the case of a single server fed by an arbitrary request input flow, it is proved that the discipline that discards the request having the maximum residual life is optimal. This result is extended to the system with more than one server. For G/G/1/0, it is given a condition under which the discipline that discards the request in service minimizes the discard probability. Also for a G/G/1/0, we state the problem of finding optimum discipline in terms of the discrete age Markov chain. The problem of minimization of one-step discard probability is stated. It is solved for a system with C servers and general point process of new arrivals.