Bivariate Bernoulli Weighted Sums and Distribution of Single-Period Tontine Benefits

This paper studies the distribution of particular weighted sums of Bernoulli random variables. The computing methods are applied to derive the probability distribution of the random amount of survivor credits to be shared among surviving participants in single-period tontine schemes. The effectiveness of this new arrangement can then be evaluated beyond the classical analysis based on crude approximations for the two first moments, only.     

On the interplay between fast reaction and slow diffusion in the concrete carbonation process: a matched-asymptotics approach

A matched-asymptotics approach is proposed to show the occurrence of two distinct characteristic length scales in the carbonation process. The separation of these scales arises due to the strong competition between reaction and diffusion effects. We show that for sufficiently large times τ the width of the carbonated region is proportional to \(\sqrt{\tau}\), while the width of the reaction front is proportional to \(\tau^{\frac{p-1}{2(p+1)}}\) for carbonation-reaction rates with a power law structure like k[CO₂] ^p [Ca(OH)₂] ^q , where k>0 and p,q>1 and identify the proportionality coefficient asymptotically. We emphasize the occurrence of a water barrier in the reaction zone which may hinder the penetration of CO₂ by locally filling with water air parts of the pores. This non-linear effect may be one of the causes why a purely linear extrapolation of accelerated carbonation test results to natural carbonation settings is (even theoretically) not reasonable. Finally, we compare our asymptotic penetration law against measured penetration depths from Bune (Zum Karbonatisierungsbedingten Verlust der Dauerhaftigkeit von Außenbauteilen aus Stahlbeton, 1994). The novelty consists in the fact that the factor multiplying \(\sqrt{\tau}\) is now identified asymptotically by solving a non-linear system of ordinary differential equations, and hence, fitting arguments are not necessary to estimate its size. We offer an alternative to the (asymptotic) \(\sqrt{\tau}\) expression of the carbonation-front position obtained in Papadakis et al. (AIChE J. 35:1639, 1989).     

Qualitative Analyse von Kationen

Analytical and Bioanalytical Chemistry -     

Functional Convergence of Linear Processes with Heavy-Tailed Innovations

We study convergence in law of partial sums of linear processes with heavy-tailed innovations. In the case of summable coefficients, necessary and sufficient conditions for the finite dimensional convergence to an \(\alpha \)-stable Lévy Motion are given. The conditions lead to new, tractable sufficient conditions in the case \(\alpha \le 1\). In the functional setting, we complement the existing results on \(M_1\)-convergence, obtained for linear processes with nonnegative coefficients by Avram and Taqqu (Ann Probab 20:483–503, 1992) and improved by Louhichi and Rio (Electr J Probab 16(89), 2011), by proving that in the general setting partial sums of linear processes are convergent on the Skorokhod space equipped with the \(S\) topology, introduced by Jakubowski (Electr J Probab 2(4), 1997).     

On the Distribution of a Sum of Sarmanov Distributed Random Variables

Built from given marginals with a flexible dependency structure, Sarmanov’s family of multivariate distributions became of interest in various fields. In this paper, we present some formulas for the density of the sum of several random variables joined by Sarmanov’s distribution, with accent on the particular case of exponentially distributed marginals. Such results are useful in solving, e.g., financial and actuarial problems.     

Metallophthalocyanine Based Carbon Paste Electrodes for the Determination of 2′,3′‐Dideoxyinosine

Novel electrochemical sensors based on carbon paste impregnated with metallopthalocyanine (MPc, M=Co, Fe) complexes, have been constructed for the assay of anti‐HIV drug 2′,3′‐dideoxyinosine (didanosine, DDI). Both modified electrodes showed electrocatalytic activity towards the oxidation of dideoxyinosine in phosphate buffer pH 7.4 with a working concentration range of 10^?6–10^?4 mol/L and a detection limit of 10^?7 mol/L magnitude order. The sensor proved to be highly reliable for the assay of the purity of DDI ‐ raw material as well as for the uniformity content test of Videx tablets.     

Self-organization of polybases neutralized with mesogenic wedge-shaped sulfonic acid molecules: an approach toward supramolecular cylinders

Complexes consisting of poly(4-vinylpyridine) and mesogenic wedge-shaped ligands 4'-[3",4",5"-tris(dodecyloxy)benzoyloxy]azobenzene-4-sulfonic acid and 4'-[3",4",5"-tris(octyloxy)benzoyloxy]azobenzene-4-sulfonic acid have been prepared with different monomer/ligand ratios. Upon protonation of the poly(4-vinylpyridine) chains by the wedge-shaped sulfonic acid molecules a hypsochromic and hyperchromic effect was observed with the pi-pi* transition of the azo-chromophor, allowing us to monitor the neutralization process by means of UV-vis spectroscopy in solution. The changes of the absorption characteristics implied a conformational change of the polymer backbone. In the bulk the interaction between pyridine and sulfonic acid moieties was proved by FT-IR spectroscopy. Polarizing optical microscopy, differential scanning calorimetry, and X-ray diffraction measurements were used to study the bulk structure of the complexes. The complexes formed a liquid crystalline lamellar phase at low degrees of substitution, while a hexagonal columnar mesophase was observed at degrees of neutralization of 80% and higher.     

Heterogeneous reactivity of chlorine atoms with ammonium sulfate and ammonium nitrate particles

In this laboratory study, model particles of ammonium sulfate (AS) and ammonium nitrate (AN) were exposed to chlorine atoms and uptake experiments were performed in a coated wall flow tube reactor coupled to a molecular beam mass spectrometer. The reactive surfaces were prepared by coating the inner surface of the reactor using two different methods: either by depositing size-selected particles on the halocarbon wax or by spray depositing thin films using a constant output atomizer. The observed uptake coefficients vary for (NH(4))(2)SO(4), ranging from γ(Cl)(AS)≈ 1 × 10(-3) for size-selected particles to γ(Cl)(AS)≈ 6 × 10(-2) for thin films prepared by spray. An uptake coefficient of γ(Cl)(AN)≈ 2.5 × 10(-3) of Cl˙ on size-selected NH(4)NO(3) particles was measured. A heterogeneous recombination of Cl atoms to from Cl(2) molecules was observed for the two surfaces. Furthermore, an ageing process was observed for AS particles, this phenomenon leading to the formation of new chlorine species on the solid substrate.