Bounds for ratios of eigenvalues using traces

Let A be an n × n matrix with real eigenvalues λ₁ ? … ? λ_n, and let 1 ? k < l ? n. Bounds involving trA and trA² are introduced for λ_k/λ_l, (λ_k ? λ_l)/(λ_k + λ_l), and {kλ_k + (n ? l + 1)λ_l}²/{kλ²_k + (n ? l + 1)λ²_l}. Also included are conditions for λ_l >; 0 and for λ_k + λ_l > 0.     

On functional representation of normed algebras

Let A be a commutative algebra over complex numbers with a space norm ‖⋅‖ making the multiplication on A separately continuous. We will study the Gelfand representation of this type of normed algebra. In particular, we look at the cases where the standard Gelfand representation (i.e., the use of supremum-norm on the Gelfand transform algebra ) gives different properties from the original algebra (A,‖⋅‖). We show that there are even Banach algebras for which this type of difficulty may happen. We will provide with some weighted supremum-norm and by using these weights we can avoid the difficulties mentioned above. For the definition of these weights we adopt the ideas of Cochran represented in [A.C. Cochran, Representation of A-convex algebras, Proc. Amer. Math. Soc. 30 (1973) 473-479].     

Formation of tethered bilayer lipid membranes on gold surfaces: QCM-Z and AFM study

Recently, tethered bilayer lipid membranes (tBLMs) have shown high potential as biomimetic systems due to their high stability and electrical properties, and have been used in applications ranging from membrane protein incorporation to biosensors. However, the kinetics of their formation remains largely uninvestigated. By using quartz crystal microbalance with impedance analysis (QCM-Z), we were able to monitor both the kinetics and viscoelastic properties of tether adsorption and vesicle fusion. Formation of the tether monolayer was shown to follow pseudo-first-order Langmuir kinetics with association and dissociation rate constants of 21.7 M-1 s(-1) and 7.43 x 10-6 s(-1), respectively. Moreover, the QCM-Z results indicate a rigid layer at the height of deposition, which then undergoes swelling as indicated by AFM. The deposition of vesicles to the tether layer also followed pseudo-first-order Langmuir kinetics with observed rate constants of 5.58 x 10(-2) and 2.41 x 10-2 s(-1) in water and buffer, respectively. Differential analysis of the QCM-Z data indicated deposition to be the fast kinetic step, with the rate-limiting steps being water release and fusion. Atomic force microscopy pictures taken complement the QCM-Z data, showing the major stages of tether adsorption and vesicle fusion, while providing a road map to successful tBLM formation.     

Preparation of copper–silicon dioxide nanoparticles with chemical vapor synthesis

Atmospheric pressure chemical vapor synthesis was used to produce copper nanoparticle composites in an amorphous silicon dioxide, i.e., either copper nanoparticles coated with amorphous silicon dioxide or copper nanoparticles embedded in amorphous silicon dioxide matrix. Synthesized metal–organic copper(I) complex was used as a precursor that provided well-defined ratio (1:2) of copper and silicon. The thermal decomposition of the Cu(I) complex molecule leads to homogenous nucleation and formation of copper nanoparticles which are subsequently coated with Si/SiO₂ in the gas phase. The decomposition was greatly enhanced when reductive atmosphere, i.e., H₂/N₂ 10 v% were used instead of pure nitrogen. A narrow size distribution with the geometric mean diameter of the particle agglomerates around 30 nm was observed while the primary size of the copper core particles was around 5 nm.     

A novel particle sampling system for physico-chemical and toxicological characterization of emissions

Several studies have shown that combustion-derived fine particles cause adverse health effects. Previous toxicological studies on combustion-derived fine particles have rarely involved multiple endpoints and a detailed characterization of chemical composition. In this study, we developed a novel particle sampling system for toxicological and chemical characterization (PSTC), consisting of the Dekati Gravimetric Impactor (DGI) and a porous tube diluter. Physico-chemical and toxicological properties of the particles emitted from various combustion sources were evaluated in two measurement campaigns. First, the DGI was compared with the High-Volume Cascade Impactor (HVCI) and to the Dekati Low-Pressure Impactor (DLPI), using the same dilution system and the same sampling conditions. Only small differences were observed in the mass size distributions, total particulate matter (PM), and particulate matter with diameter smaller than 1 um (PM(1)) concentrations and geometric mass mean diameters (GMMD) between these three impactors. Second, the PSTC was compared with the HVCI sampling system, which has been optimal for collection of particulate samples for toxicological and chemical analyses. Differences were observed in the mass size distributions, total PM and PM(1) emissions, and GMMDs, probably due to the different sampling and dilution methods as well as different sampling substrates which affected the behavior of semi-volatile and volatile organic compounds. However, no significant differences were detected in the in vitro measurements of cytotoxicity between the samples collected with the PSTC and the HVCI systems. In measurements of genotoxicity, significant differences between the two sampling systems were seen only with the particles emitted from the sauna stove. In conclusion, due to compact size, PSTC is an applicable method for use in particle sampling as part of the toxicological and chemical characterization of particulate emissions from different combustion sources. It offers some advantages compared to the previously used high-volume sampling methods including compactness for field measurements, simple preparation of sample substrates and high extraction efficiency.     

Topological Geon Black Holes in Einstein-Yang-Mills Theory

We construct topological geon quotients of two families of Einstein-Yang-Mills black holes. For Künzle??s static, spherically symmetric SU(n) black holes with n?>?2, a geon quotient exists but generically requires promoting charge conjugation into a gauge symmetry. For Kleihaus and Kunz??s static, axially symmetric SU(2) black holes a geon quotient exists without gauging charge conjugation, and the parity of the gauge field winding number determines whether the geon gauge bundle is trivial. The geon??s gauge bundle structure is expected to have an imprint in the Hawking-Unruh effect for quantum fields that couple to the background gauge field.     

The total synthesis of (+)-tedanolide--A macrocyclic polyketide from marine sponge Tedania ignis

Tedanolide, which was isolated by Schmitz in 1984 from the marine sponge Tedania ignis, is a highly cytotoxic macrolide leading to strong growth inhibition of P338 tumor cells in bioassays. A unique structural feature of the known tedanolides is the primary hydroxyl group incorporated in the macrolactone. This unusual motif for macrolactones originated from PKS biosynthesis might arise through lactonizations others than those derived by the thioesterase reaction. First experimental data that support this hypothesis and reflect the inherent preference of PKS-induced macrolactonization were obtained during this synthesis. The inherent preference for the formation of a 14-membered macrocyclization is discussed together with the pivotal steps in the synthesis.