Comparisons of the Expectations of System and Component Lifetimes in the Failure Dependent Proportional Hazard Model

Methodology and Computing in Applied Probability - In the failure dependent proportional hazard model, it is assumed that identical components work jointly in a system. At the moments of...     

On-line arbitrarily vertex decomposable trees

A tree T is arbitrarily vertex decomposable if for any sequence τ of positive integers adding up to the order of T there is a sequence of vertex-disjoint subtrees of T whose orders are given by τ. An on-line version of the problem of characterizing arbitrarily vertex decomposable trees is completely solved here.     

Ergodicity of Rokhlin cocycles

We develop a general study of ergodic properties of extensions of measure preserving dynamical systems. These extensions are given by cocycles (called here Rokhlin cocycles) taking values in the group of automorphisms of a measure space which represents the fibers. We use two different approaches in order to study ergodic properties of such extensions. The first approach is based on properties of mildly mixing group actions and the notion of complementary algebra. The second approach is based on spectral theory of unitary representations of locally compact Abelian groups and the theory of cocycles taking values in such groups. Finally, we examine the structure of self-joinings of extensions. We partially answer a question of Rudolph on lifting mixing (and multiple mixing) property to extensions and answer negatively a question of Robinson on lifting Bernoulli property. We also shed new light on some earlier results of Glasner and Weiss on the class of automorphisms disjoint from all weakly mixing transformations. Answering a question asked by Thouvenot we establish a relative version of the Foiaş—Stratila theorem on Gaussian—Kronecker dynamical systems. Research partially supported by KBN grant 2 P03A 002 14 (1998).     

Hausdorff Measures versus Equilibrium States of Conformal Infinite Iterated Function Systems

Dealing with infinite iterated function systems we introduce and develop the ergodic theory of Hölder systems of functions similarly as in [HU] and [HMU]. In the context of conformal infinite iterated function systems we prove the volume lemma for the Hausdorff dimension of the projection onto the limit set of a shift invariant measure. This can be considered as a Billingsley type result. Our cenral goal is to demonstrate the appearance of the "singularity-absolute continuity" dichotomy for equilibrium states of Hölder systems of functions which has been observed in [PUZ,I] and [PUZ,II] (see also [DU1] and [DU2]) in the setting of rational functions of the Riemann sphere.     

Topological equivalences between organic and coordination polymer crystal structures: an organic ladder formed with three-connected molecular and supramolecular synthons

[structure: see text] Crystal engineering of an organic ladder can be achieved with a T-shaped molecule, 4,4-bis(4'-hydroxyphenyl)-1-cyclohexanol, having three hydroxyl functionalities that can form O-H...O hydrogen-bonded helices. The topology of this network structure finds a parallel in three-connected coordination polymers.     

Topological density of ccc Boolean algebras--Every cardinality occurs

For every uncountable cardinal there is a ccc Boolean algebra whose topological density is .

     

Power residue problem on elliptic curves

Let E be an elliptic curve defined over a number field K, without complex multiplication, S a finite subset of E(K) and l a rational prime being good modulus for E/K. The main result of the paper asserts that if |S|l²+l and for almost all prime ideals P of _K S contains an element R satisfying R mod P = lQ with QE(_K/P) then S contains an element R which satisfies R=lQ with some QE(K). It improves the result of S.Wong [6], where the above statement is proved under the stronger assumption |S|l². Moreover we show that the bound |S|l²+l is optimal.     

The Role of Singlet Oxygen in Photoreactivity and Phototoxicity of Curcumin

Curcumin is a plant-derived yellow-orange compound widely used as a spice, dye and food additive. It is also believed to have therapeutic effects against different disorders. On the other hand, there are data showing its phototoxicity against bacteria, fungi and various mammalian cells. Since the mechanism of its phototoxic action is not fully understood, we investigated here the phototoxic potential of curcumin in liposomal model membranes and in HaCaT cells. First, detection of singlet oxygen (¹O₂) luminescence proved that curcumin generates ¹O₂ upon blue light irradiation in organic solvent and in liposomes. Then, HPLC-EC(Hg) measurements revealed that liposomal and cellular cholesterol is oxidized by ¹O₂ photogenerated by curcumin. Enrichment of liposome membranes with curcumin significantly increased the oxygen photo-consumption rate compared to the control liposomes as determined by EPR oximetry. Cytotoxicity measurements, mitochondrial membrane potential analyses and protein hydroperoxides detection confirmed strong phototoxic effects of curcumin in irradiated HaCaT cells. These data show that since curcumin is advertised as a valuable dietary supplement, or a component of cosmetics for topical use, caution should be recommended especially when skin is exposed to light.