Moments of an exponential functional of random walks and permutations with given descent sets

The exponential functional of simple, symmetric random walks with negative drift is an infinite polynomial Y = 1 + ξ₁ + ξ₁ξ₂ + ξ₁ξ₂ξ₃ + ⋯ of independent and identically distributed non-negative random variables. It has moments that are rational functions of the variables μ _k = E(ξ ^k ) < 1 with universal coefficients. It turns out that such a coefficient is equal to the number of permutations with descent set defined by the multiindex of the coefficient. A recursion enumerates all numbers of permutations with given descent sets in the form of a Pascal-type triangle. This revised version was published online in August 2006 with corrections to the Cover Date.     

Fundamental reactions in TiO2 nanocrystallite aqueous solutions studied by pulse radiolysis

Reactions of the hydrated electron, H atoms, 2-propanol, and methanol radicals with the TiO₂ nano-particles have been studied either directly or by competition kinetics. The radicals were produced by radiolysis of 2-propanol, t-butanol, or methanol aqueous solutions in acid pH's. The reactions involve electron injection to the conduction band. As expected, the t-butanol radical is inert towards TiO₂ under our conditions, while the other reducing radicals react with TiO₂. The reactivity decreases in the order: e_aq⁻>H>CH₃COHCH₃>CH₂OH. Two TiO₂ nanocrystallite sizes, with average diameters of 1.0 and 4.7 nm were compared. For equal concentrations (in terms of TiO₂ molecules), the rate of electron injection shows relatively little dependency on particle size. The rates of interfacial electron transfer and transfer coefficient are also reported.     

Weighted approximation of functions on the real line by Bernstein polynomials

The authors give error estimates, a Voronovskaya-type relation, strong converse results and saturation for the weighted approximation of functions on the real line with Freud weights by Bernstein-type operators.     

Comparing decision problem for various paradigms of algebraic logic

We show that in many cases the decision problems for varieties of cylindric algebras are much harder than those for the corresponding relation algebra reducts. We also give examples of varieties of cylindric and relation algebras which are algorithmically more complicated than the subvarieties of their representable algebras.     

Haplotyping by capillary electrophoresis

The investigation of the genetic background and phenotype structures of complex diseases, such as cardiovascular or psychiatric disorders and tumors, is one of the most scrutinized fields of the post genomic era. Besides the multiplex analysis of genetic markers and polymorphisms throughout the whole genome, more and more attention is focused on the interaction between the etiological factors of these traits. Haplotype determination, rather than multiplex genotyping seems to be one of the first building blocks of this endeavor. This review focuses on the importance and theoretical background of haplotyping, and summarizes the recent examples of novel and emerging haplotyping techniques by capillary gel electrophoresis based DNA fragment analysis, a powerful tool for the examination of the inheritance of complex traits.     

13C NMR study of polarizations and polarization ranges of vinylene groups in seven series of related compounds

Polarizations, polarization ranges and ratios of polarization ranges for vinylene groups in seven series, namely chalcone derivatives, ferrocene analogues of chalcone, stilbene derivatives, ferrocene analogues of stilbene, and styrene derivatives, were studied. The polarization ranges spanning the intervals between ¹³C NMR chemical shifts of the derivatives substituted by p-NO₂ and p-NMe₂ groups are compared in these related compounds. The influence of the side-chain groups in the vinylene moiety and of the sign of the polarization on the substituent-effect are discussed.     

Environmental and economic comparison of waste solvent treatment options

The sustainable development and consumption need more efficient use of natural resources. As a consequence, the use of industrial solvents demands their recovery instead of end-of-pipe treatment. It is not always clear, however, which treatment alternative should be applied. Based on an industrial case study, the environmental and economic evaluation and comparison of the treatment alternatives of a non-ideal solvent mixture containing azeotropes is investigated for determining the preferable option. For the recovery of the industrial solvent mixture, two different separation alternatives are evaluated: a less effective alternative and a novel design based on hybrid separation tools. An end-of-pipe treatment alternative, incineration, is also considered and the split of the solvent mixtures between recovery and incineration is investigated. The environmental evaluation of the alternatives is carried out using ‘Eco-indicator 99 life-cycle impact assessment methodology’. Economic investigation is also accomplished. The economic features clearly favour the total recovery, however, the environmental evaluation detects that if a recovery process of low efficiency is applied, its environmental burden can be similar or even higher than that of the incineration. This motivates engineers to design more effective recovery processes and reconsider the evaluation of process alternatives at environmental decision making.     

Correction to: Preface

Foundations of Computational Mathematics -