Sylow Theory for Quasigroups II: Sectional Action

The first paper in this series initiated a study of Sylow theory for quasigroups and Latin squares based on orbits of the left multiplication group. The current paper is based on so‐called pseudo‐orbits, which are formed by the images of a subset under the set of left translations. The two approaches agree for groups, but differ in the general case. Subsets are described as sectional if the pseudo‐orbit that they generate actually partitions the quasigroup. Sectional subsets are especially well behaved in the newly identified class of conflatable quasigroups, which provides a unified treatment of Moufang, Bol, and conjugacy closure properties. Relationships between sectional and Lagrangean properties of subquasigroups are established. Structural implications of sectional properties in loops are investigated, and divisors of the order of a finite quasigroup are classified according to the behavior of sectional subsets and pseudo‐orbits. An upper bound is given on the size of a pseudo‐orbit. Various interactions of the Sylow theory with design theory are discussed. In particular, it is shown how Sylow theory yields readily computable isomorphism invariants with the resolving power to distinguish each of the 80 Steiner triple systems of order 15.     

Colored graphs without colorful cycles

A colored graph is a complete graph in which a color has been assigned to each edge, and a colorful cycle is a cycle in which each edge has a different color. We first show that a colored graph lacks colorful cycles iff it is Gallai, i.e., lacks colorful triangles. We then show that, under the operation mon ≡ m + n − 2, the omitted lengths of colorful cycles in a colored graph form a monoid isomorphic to a submonoid of the natural numbers which contains all integers past some point. We prove that several but not all such monoids are realized. We then characterize exact Gallai graphs, i.e., graphs in which every triangle has edges of exactly two colors. We show that these are precisely the graphs which can be iteratively built up from three simple colored graphs, having 2, 4, and 5 vertices, respectively. We then characterize in two different ways the monochromes, i.e., the connected components of maximal monochromatic subgraphs, of exact Gallai graphs. The first characterization is in terms of their reduced form, a notion which hinges on the important idea of a full homomorphism. The second characterization is by means of a homomorphism duality. The first author would like to express his thanks for support by project LN 00A056 of the Ministry of Education of the Czech Republic. The second author would like to express his thanks for support by project LN 00A056 of the Ministry of Education of the Czech Republic, by the NSERC of Canada and by the Gudder Trust of the University of Denver.     

A note on Thomassen?s conjecture

In 1983 C. Thomassen [8] conjectured that for every k,g∈N there exists d such that any graph with average degree at least d contains a subgraph with average degree at least k and girth at least g. A result of Pyber, Szemerédi, and the second author implies that the conjecture is true for every graph G with average .We strengthen this and show that the conjecture holds for every graph G with average for some constants α, β depending on k and g.     

UV-VIS detection of amino acids in liquid chromatography: online post-column solid-state derivatization with Cu(II) ions

In this work, we describe the introduction of a post-column solid-state reactor in the HPLC system used for the analyses of amino acids. The reactor used was filled with copper(II) oxide. Passage of the analytes through the reactor leads to the formation of Cu(II) complexes. Unlike free amino acids, the Cu-complexes show significant absorbance in the UV region and accordingly sensitivity of UV-VIS detection is increased by two to three orders of magnitude. As a result of this improvement in sensitivity, we have obtained LOD values in micromolar range and good linearity over the studied concentration range (5.0×10(-5) to 2.0×10(-3) mol/L). The method exhibits advantages typical of solid-state reactors, such as negligible loss of efficiency due to the derivatization, simplicity of realization and a long-term durability. The presented system brings an easy and versatile solution for UV-VIS detection of coordinating compounds, which do not normally absorb well in the UV-VIS region.     

On a conjecture of Thomassen concerning subgraphs of large girth

In 1983 C. Thomassen conjectured that for every k, g∈? there exists d such that any graph with average degree at least d contains a subgraph with average degree at least k and girth at least g. Kühn and Osthus [2004] proved the case g = 6. We give another proof for the case g = 6 which is based on a result of Füredi [1983] about hypergraphs. We also show that the analogous conjecture for directed graphs is true. © 2010 Wiley Periodicals, Inc. J Graph Theory 67:316‐331,2011     

Lanthanide complexes as imaging agents anchored on nano-sized particles of boehmite

The synthesis of boehmite nanoparticles modified with lanthanides (Eu, Tb and Gd) is described. Their synthesis, characterization and in vitro assays with HeLa cells were performed. The nuclear magnetic relaxation dispersion (NMRD) profiles of the two chelating moieties were studied. Imaging data from laser scanning confocal fluorescence microscopy and flow cytometry revealed that the nanoscaffolds were taken up by the cells, distributed throughout the cytoplasm and showed no toxicity. This platform could represent an alternative to silica-based inert matrices as imaging vehicles.     

Note on the point character of l 1-spaces

We prove that for any ordinal α, any integer t ≥ 0, the point character of the space l ₁(ω _{α + t} ) is no more than ω _α . Combined with an earlier result from [5], this yields that for any infinite cardinal κ the point character of l ₁(κ) is the largest cardinal ω _α ≤ κ where α = 0 or a limit ordinal.     

A continuum model for yttria-stabilized zirconia incorporating triple phase boundary,lattice structure and immobile oxide ions

A continuum model for yttria-stabilized zirconia (YSZ) in the framework of non-equilibrium thermodynamics is developed. Particular attention is given to (i) modeling of the YSZ-metal-gas triple phase boundary, (ii) incorporation of the lattice structure and immobile oxide ions within the free energy model and (iii) surface reactions. A finite volume discretization method based on modified Scharfetter-Gummel fluxes is derived in order to perform numerical simulations. The model is used to study the impact of yttria and immobile oxide ions on the structure of the charged boundary layer and the double layer capacitance. Cyclic voltammograms of an air-half cell are simulated to study the effect of parameter variations on surface reactions, adsorption and anion diffusion.

     

A comparison of natural and experimental long-term corrosion of uranium-colored glass

The alteration features of historical U-colored glasses exposed to natural weathering for over 150 years were compared with the experimental alteration of similar glass with ～0.3 wt% of uranium using a long-term (up to 426 days) kinetic laboratory batch leaching test in deionized water. Two types of natural corrosion crusts were identified by a combination of SEM/EDS, HRTEM/SAED, EPMA and XRD: (i) formation of a leached layer (up to ～600 μm thick) depleted in alkalis and enriched in Si with stable concentration of U and Al and (ii) formation of lamellae depleted in alkalis, Si and U and enriched in Al. The presence of newly formed gibbsite (Al(OH)₃) and kaolinite (Al₂Si₂O₅(OH)₄) were confirmed in the second type of corrosion crust by HRTEM. Dissolution of the glass components including uranium was determined during the laboratory leaching test. Several μm thick alkali-depleted alteration zones with stable U content relatively enriched in Si and Al were formed on the glass surface. The PHREEQC-2 modeling also predicted the precipitation of secondary gibbsite and kaolinite in the late stages of the leaching. These phases may form especially when sufficient amounts of Al are available from the environment (e.g., soil). Furthermore, they provide surfaces for sorption and may, in some cases, affect the mobility of U ions released from the glass in dependence on pH and U speciation.