Asymptotic analysis of heat conducting elastic materials

In this paper, an asymptotic one dimensional model for a clamped curved rod is rigorously derived as a limit of respective three dimensional models. The rod is made of isotropic elastic, heat conductive linearly responding material. Asymptotic analysis is used with respect to the thickness of domains.     

On diagonal actions of branch groups and the corresponding characters

We introduce notions of absolutely non-free and perfectly non-free group actions and use them to study the associated unitary representations. We show that every weakly branch group acting on a regular rooted tree acts absolutely non-freely on the boundary of the tree. Using this result and the symmetrized diagonal actions we construct for every countable branch group infinitely many different ergodic perfectly non-free actions, infinitely many II₁-factor representations, and infinitely many continuous ergodic invariant random subgroups.     

Justification of Asymptotic Two-dimensional Model for Steady Navier-Stokes Equations for Incompressible Flow

We study the asymptotic behavior of solutions to steady Navier-Stokes equations for incompressible flow in thin three-dimensional deformed cylinders. We prove that a sequence of the solutions converges strongly to a solution of a corresponding two-dimensional asymptotic model if the thickness of the cylinders converges to zero.     

Updating the Chemiluminescence Oxygen‐Aftereffect Method for Determining the Rate Constant of the Peroxy‐Radical Self‐Reaction: Oxidation of Cyclohexene

Updating the facile chemiluminescence oxygen‐aftereffect method, most suitable for determining the rate constant (k_t) of the peroxy‐radical self‐reaction (main chemiluminescence channel), pertained to considering the sensitivity of such a method toward a disturbing influence of the peroxy radicals of the initiator of the chain oxidation process. Such a disturbance may derive from the side chemiluminescent reaction, which involves peroxy radicals of both hydrocarbon and initiator. To examine the applicability and limitations of the chemiluminescence method under present scrutiny, cyclohexene was used as the model oxidizable hydrocarbon substrate. Computer simulations of the reaction and chemiluminescence kinetics have demonstrated the validity of the considered methodology at the value of the rate constant of the propagation of the overall chain process by peroxy radicals of the initiator higher than 1 m ^?1 s^?1. Despite that the chemiluminescence time profile and the stationary level of the total chemiluminescence intensity depend on the kinetics of the side chemiluminescence channel and on the ratio of the excited‐state generation yields in the mentioned reaction channel and in the main chemiluminescence process, the value of k_t assessed by the oxygen‐aftereffect method has been found independent of variation of these characteristics.     

Transformations of 5-(2-arylethynyl)-2-methyl-2H-tetrazoles under superelectrophilic activation

Reaction of 5-arylethynyl-2-methyl-2H-tetrazoles (acetylene tetrazoles) with arenes under the action of Brønsted superacid CF₃SO₃H or acidic zeolite HUSY CBV-720 gives rise to E-/Z-5-(2,2-diarylethenyl)-2-methyl-2H-tetrazoles, as products of hydroarylation of acetylene bond, in yields up to 98% with predominant formation of E-isomers. Cationic intermediates of these reactions have been studied theoretically by DFT calculations. Addition of CF₃SO₃H to the triple bond of acetylene tetrazoles leads to the corresponding E-/Z-vinyl triflates in high yields. Hydration of triple bond in these tetrazoles in H₂SO₄ results in the formation of 5-(2-aryl-2-oxoethyl)-2-methyl-2H-tetrazoles. Tandem hydroarylation-ionic hydrogenation of acetylene tetrazoles in the systems acid(CF₃SO₃H or AlCl₃)-arene-cyclohexane affords 5-(2,2-diarylethyl)-2-methyl-2H-tetrazoles.     

On the Boolean Model of Wiener Sausages

The Boolean model of Wiener sausages is a random closed set that can be thought of as a random collection of parallel neighborhoods of independent Wiener paths in space. It describes e.g. the target detection area of a network of sensors moving according to the Brownian dynamics whose initial locations are chosen in the medium at random. In the paper, the capacity functional of this Boolean model is given. Moreover, the one- and two-point coverage probabilities as well as the contact distribution function and the specific surface area are studied. In and , the one- and two-point coverage probabilities are calculated numerically by Monte Carlo simulations and as a solution of the heat conduction problem. The corresponding approximation formulae are given and the error of approximation is analyzed. Research supported by the grant GACR 201/06/0302.     

Ergodic decomposition of group actions on rooted trees

We prove a general result about the decomposition into ergodic components of group actions on boundaries of spherically homogeneous rooted trees. Namely, we identify the space of ergodic components with the boundary of the orbit tree associated with the action, and show that the canonical system of ergodic invariant probability measures coincides with the system of uniform measures on the boundaries of minimal invariant subtrees of the tree. Special attention is paid to the case of groups generated by finite automata. Few examples, including the lamplighter group, Sushchansky group, and so-called universal group, are considered in order to demonstrate applications of the theorem.     

Urinary calculi — atypical source of information on mercury in human biomonitoring

Chemical analysis of various biological matrices is routinely used for assessment of human exposure to various toxic metals. In this work, 489 samples of urinary calculi originating from almost the whole of The Czech Republic, were collected and subjected to mineralogical and elemental analysis. This study was aimed at mercury, the content of which was determined using thermo-oxidation — cold vapor — atomic absorption spectrometry. The effects of mineralogical composition, sex, age and region were recorded in order to verify the applicability of urinary calculi for biomonitoring. Relationships with other minor and trace elements were also investigated. Association of mercury with whewellite mineral was observed as well as a remarkable relationship with selenium, confirming the role of selenium in mercury excretion. No statistically significant effect was observed on the mercury content in stones with regard to the sex or region. Median values in age groups follow a trend with the maximum median value 0.365 mg kg^?1 in the group of 41–50 year old donors, decreasing to 0.060 mg kg^?1 for the oldest group (81–92 years). Our results confirm that urinary calculi can be helpful in providing complementary information on human exposure to mercury and its excretion.

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