Multiplicative bijections of

Let be a compact Hausdorff space which satisfies the first axiom of countability, let and let , be the set of all continuous functions from to If , ,is a bijective multiplicative map, then there exist a homeomorphism and a continuous map such that for all and for all

     

Raman spectroscopy of laser‐induced oxidation of titanomagnetites

Titanomagnetites are important carriers of magnetic remanence in nature and can track redox conditions in magma. The titanium concentration in magnetite bears heavily on its magnetic properties, such as saturation moment and Curie temperature. On land and in the deep ocean, however, these minerals are prone to alteration which can mask the primary magnetic signals they once recorded. Thus, it is essential to characterize the cation composition and oxidation state of titanomagnetites that record the paleomagnetic field. Raman spectroscopy provides a unique tool for both purposes. Nonetheless, the heat generated by the excitation laser can itself induce oxidation. We show that the laser power threshold to produce oxidation decreases with increasing titanium content. With confocal Raman spectroscopy and magnetic force microscopy (MFM) on natural and synthetic titanomagnetites, a non‐destructive Raman imaging protocol was established. We applied this protocol to map out the composition and magnetization state within a single ex‐solved titanomagnetite grain in a deep‐sea basalt. Copyright © 2011 John Wiley & Sons, Ltd.     

ROS‐Responsive N‐Alkylaminoferrocenes for Cancer‐Cell‐Specific Targeting of Mitochondria

Mitochondrial membrane potential is more negative in cancer cells than in normal cells, allowing cancer targeting by delocalized lipophilic cations (DLCs). However, as the difference is rather small, these drugs affect also normal cells. Now a concept of pro‐DLCs is proposed based on an N‐alkylaminoferrocene structure. These prodrugs are activated by the reaction with reactive oxygen species (ROS) forming ferrocenium‐based DLCs. Since ROS are overproduced in cancer, the high‐efficiency cancer‐cell‐specific targeting of mitochondria could be achieved as demonstrated by fluorescence microscopy in combination with two fluorogenic pro‐DLCs in vitro and in vivo. We prepared a conjugate of another pro‐DLC with a clinically approved drug carboplatin and confirmed that its accumulation in mitochondria was higher than that of the free drug. This was reflected in the substantially higher anticancer effect of the conjugate.     

A validated model for a pin-slot clearance joint

The numerical modeling of joints with a certain amount of clearance and a subsequent validation of the model are important for accurate multibody simulations. For such validated modeling, not only the kinematic constraints, but also the contact models, are important. If a joint has no clearance, it is assumed to be ideal. However, in real applications, there is frequently some clearance in the joints. Adding clearance and kinematic conditions to a pin-slot joint significantly increases the number of kinematic and contact parameters. Consequently, the resulting kinematics and the contact forces can vary significantly with regard to the selection of those parameters. This research covers the development of a validated model for a pin-slot clearance joint. Different kinematic constraints and contact models are discussed. The presented model is an experimentally validated one for a pin-slot clearance joint that is commonly used in safety-critical applications like electrical circuit breakers. Special attention is given to the Hertz, Kelvin–Voigt, Johnson, and Lankarani–Nikravesh contact models. When comparing different contact models within numerical approaches and comparing the results with experimental data, significant differences in the results were observed. With a validated model of a pin-slot clearance joint, a physically consistent numerical simulation was obtained.     

Incorporation and release of drug into/from superparamagnetic iron oxide nanoparticles

The aim of this study was to attach a model drug (naproxen) onto superparamagnetic iron oxide nanoparticles (SPION). First, SPION were coated with thin layer of silica that contained micropores. We demonstrated that such surface functionalization could be optimized by the use of citric acid which prevented SPION agglomeration during the procedure. HRTEM investigation showed a uniform 1-2-nm-thick silica coating around SPION. This coating did not affect significantly the magnetic properties of the SPION. Into the coated SPION we successfully incorporated about 30 wt% of naproxen. The latter was readily released after immersion into a testing solution. The composites could be interesting for potential use in diagnostics.     

A sharper threshold for bootstrap percolation in two dimensions

Two-dimensional bootstrap percolation is a cellular automaton in which sites become ‘infected’ by contact with two or more already infected nearest neighbours. We consider these dynamics, which can be interpreted as a monotone version of the Ising model, on an n × n square, with sites initially infected independently with probability p. The critical probability p _c is the smallest p for which the probability that the entire square is eventually infected exceeds 1/2. Holroyd determined the sharp first-order approximation: p _c ~ π ²/(18?log?n) as n → ∞. Here we sharpen this result, proving that the second term in the expansion is ?(log?n)^?3/2+o(1), and moreover determining it up to a poly(log?log?n)-factor. The exponent ?3/2 corrects numerical predictions from the physics literature.     

Investigation,Modelling and Analysis of stiffened GFRP-Samples

Glasfibre structures feature high potentials for optimization and substitution of conventional materials like steel and aluminum and their alloys. The paper deals with the insertion of glasfibre trusses into thin glasfibre structures to reinforce them. The effective material properties of the glasfibre structures were estimated by experiments and simulations. Furthermore the Young's modulus of the trusses was obtained by bending tests and tension tests. A comparison between bending experiments and bending simulations is given. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Irreducible Semigroups of Matrices with Eigenvalue One

We study groups and semigroups of n x n matrices with the property that each matrix has a fixed point, i.e., 1 is an eigenvalue of each matrix. We show that for n=3 and $n\geq 5$ there are irreducible matrix groups and irreducible semigroups of nonnegative matrices with this property. In fact, for n = 3 we determine the structure of any such semigroup. We also present additional hypotheses implying reducibility.