The boundary of iterates in Euclidean growth models

This paper defines a general Euclidean growth model via a translation invariant, monotone and local transformation on Borel subsets of . The main result gives a geometric condition for the boundary curvature of the iterates to go to 0. Consequences include estimates for the speed of convergence to the asymptotic shape, and a result about survival of Euclidean deterministic forest fires.

     

Fast immobilization of probe beads by dielectrophoresis-controlled adhesion in a versatile microfluidic platform for affinity assay

The use of probe beads for lab-on-chip affinity assays is very interesting from a practical point of view. It is easier to handle and trap beads than molecules in microfluidic systems. We present a method for the immobilization of probe beads at defined areas on a chip using dielectrophoresis (DEP)-controlled adhesion. The method is fast, i.e., it takes between 10 and 120 s--depending on the protocol--to functionalize a chip surface at defined areas. The method is versatile, i.e., it works for beads with different types of probe molecule coatings. The immobilization is irreversible, i.e., the retained beads are able to withstand high flow velocities in a flow-through device even after the DEP voltage is turned off, thus allowing the use of conventional high-conductivity analyte buffers in the following assay procedure. We demonstrate the on-chip immobilization of fluorescent beads coated with biotin, protein A, and goat-antimouse immunoglobulin G (IgG). The number of immobilized beads at an electrode array can be determined from their fluorescence signal. Further, we use this method to demonstrate the detection of streptavidin and mouse IgG. Finally, we demonstrate the feasibility of the parallel detection of different analyte molecules on the same chip.     

Probabilistic kinetic model of slow oxidation of low-density lipoprotein. 3. Hydroperoxide-free initiation

A theoretical model is presented that explains slow copper-induced oxidation of low-density lipoprotein in the systems free of seeded hydroperoxydes. The model is based on the probabilistic kinetic theory, modified to take into account different radical generation rates by oxidized and reduced forms of the metal ions. It is shown that the initiation and progression of the LDL oxidation can take place in any LDL dispersion by metal-induced oxidation of alpha-tocopherol, one of the constituents of LDL, and formation of slowly reacting alpha-tocopheroxyl radical. Selected values of several adjustable parameters define actual temporal profiles of the quantities defining the oxidation process.     

Struktur von Gläsern des Systems TeO2−VO2

Glasses from the TeO₂–VO₂ system and - and -crystalline modifications of TeO₂·VO₂ (TeVO₄) are studied by IR-spectroscopy in the 1400–400 cm^–1 range. Similarity is established in the area near 970 cm^–1 of the spectrum between TeVO₄ glass and the -form. The continuous shift of the band from 970 cm^–1 to 950 cm^–1 with increasing TeO₂ content in the glasses is connected with the indirect influence on the nonbridging V–O bond.It is shown that the local environment of the V in some glasses from TeO₂–VO₂ and TeO₂–V₂O₅ system is similar: VO₅ polyhedra.     

Flow reactor for kinetic studies with simultaneous X-ray phase analysis of a catalyst

A flow reactor for kinetic studies of heterogeneous catalytic reactions with simultaneous X-ray phase analysis of the catalyst is described. As an example, the correlation between the selectivity of acetylene hydrogenation and the -Pd hydride concentration in palladium catalysts is shown.

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, . -Pd .

     

Stability of Cellular Automata Trajectories Revisited: Branching Walks and Lyapunov Profiles

We study non-equilibrium defect accumulation dynamics on a cellular automaton trajectory: a branching walk process in which a defect creates a successor on any neighborhood site whose update it affects. On an infinite lattice, defects accumulate at different exponential rates in different directions, giving rise to the Lyapunov profile. This profile quantifies instability of a cellular automaton evolution and is connected to the theory of large deviations. We rigorously and empirically study Lyapunov profiles generated from random initial states. We also introduce explicit and computationally feasible variational methods to compute the Lyapunov profiles for periodic configurations, thus developing an analog of Floquet theory for cellular automata.     

On Bounded Local Resolvents

It is known that each normal operator on a Hilbert space with nonempty interior of the spectrum admits vectors with bounded local resolvent. We generalize this result for Banach space operators with the decomposition property (δ) (in particular for decomposable operators). Moreover, the same result holds for operators with interior points in the localizable spectrum.     

On maximal cyclic subgroups in finite p-groups

In this note we consider finite noncyclic p-groups G all of whose maximal cyclic subgroups X satisfy one of the following two properties. (a) If each subgroup H of G containing X properly is nonabelian, then p = 2 and G is generalized quaternion. (b) If X is contained in exactly one maximal subgroup of G, then G is metacyclic. This solves the problems Nr.1541 and Nr. 1594 from [1].     

SVEP for multipliers on a faithful commutative Banach algebra

We give some sufficient conditions that each multiplier on a faithful commutative Banach algebra has SVEP. On the other hand, we show that there exist a faithful commutative Banach algebra and a multiplier on it without SVEP. Such examples of multipliers can actually be found within the class of multiplication operators on unital commutative Banach algebras. This answers in negative a question that is stated as Open problem 6.2.1 by Laursen and Neumann, 2000.