The Number of Edge Colorings with no Monochromatic Cliques

Let F(n,r,k) denote the maximum possible number of distinctedge-colorings of a simple graph on n vertices with r colorswhich contain no monochromatic copy of K_k. It is shown thatfor every fixed k and all n>n₀(k), and , where t_k–1(n)is the maximum possible number of edges of a graph on n verticeswith no K_k (determined by Turán's theorem). The caser=2 settles an old conjecture of Erds and Rothschild, whichwas also independently raised later by Yuster. On the otherhand, for every fixed r>3 and k>2, the function F(n,r,k)is exponentially bigger than . The proofs are based on Szemerédi's regularity lemmatogether with some additional tools in extremal graph theory,and provide one of the rare examples of a precise result provedby applying this lemma.     

Incidence Theorems for Pseudoflats

We prove Pach-Sharir type incidence theorems for a class of curves in Rⁿ and surfaces in R³, which we call pseudoflats}. In particular, our results apply to a wide class of generic irreducible real algebraic sets of bounded degree.     

13C Nuclear magnetic resonance spectra of cyclodextrin monomers,derivatives and their complexes with methyl orange

Low molecular mass fractions of water soluble -, -, and -cyclodextrin epichlorohydrin polymer products (cdx-Ep) were characterized by¹³C nuclear magnetic resonance. The derivatives proved not to be polymers, but substituted cdx having one or two glyceryl groups per one glucose at the C-2, C-3 and C-6 positions. Spectra of analogous hydroxy-propyl -cdx indicate that the degree of substitution is rather higher at the C-6 position. Methyl orange (MO) was included into nine kinds of cdx having different inner diameters and hydrophobic torus heights; -, -, and -cdx monomers, 2, 6-dimethyl and 2, 3, 6-trimethyl -cdx, water soluble -, -, and -cdx-Ep and ethyleneglycol-bis(epoxy-propyl) ether products. The inclusion shifts were compared with each other and with the dioxane-induced solvent shift of MO. TheN, N-dimethyl-aniline side of MO shifted to a higher field site with the increase of the inner diameter in cdx. By substituting cdx with ether groups of different length, the mechanism of inclusion formation remains substantially the same, but by lengthening the hydrophobic cavity, the hydrophobic interaction becomes stronger, as a better resemblance of inclusion shifts and solvent shifts can be observed.Presented at the Fourth International Symposium on Inclusion Phenomena and the Third International Symposium on Cyclodextrins, Lancaster, U.K., 20–25 July 1986.     

Glow Discharge as a Tool for Surface and Interface Analysis

Abstract

This review article focuses on the analytical capabilities of glow discharge optical emission spectrometry (GD‐OES) and mass spectrometry (GD‐MS) to perform compositional depth profiling (GD‐CDP). The properties of the Grimm‐type glow discharge as well as basic processes of sputtering are described and their influence on the GD as a surface and interface analytical tool are discussed. A series of examples from recent literature ranging from computer hard disks to molecular monolayers on copper substrates are presented to illustrate the excellent depth resolution that can be achieved with GD surface analytical techniques. The conditions for obtaining nanometer or even atomic‐layer depth resolution are discussed. Following this introduction is the possibilities of the technique a selection of applications principally chosen from our laboratories, demonstrating that GD‐OES and GD‐MS can be successfully employed as an analytical tool assisting the development of new materials and coatings. The applications cover common industrial tasks such as heat treatments, studies of diffusion processes at interfaces, and electrochemical depositions for biocompatible material. However, limitations and known artifacts are also discussed.     

Maximally Clustered Elements and Schubert Varieties

We introduce and study a class of “maximally clustered” elements for simply laced Coxeter groups. Such elements include as a special case the freely braided elements of Green and the author, which in turn constitute a superset of the iji-avoiding elements of Fan. We show that any reduced expression for a maximally clustered element is short-braid equivalent to a “contracted” expression, which can be characterized in terms of certain subwords called “braid clusters”. We establish some properties of contracted reduced expressions and apply these to the study of Schubert varieties in the simply laced setting. Specifically, we give a smoothness criterion for Schubert varieties indexed by maximally clustered elements. Received December 30, 2005     

Time resolved spectroscopy with femtosecond soft-x-ray pulses

The most challenging application of time resolved spectroscopy is to directly observe the structural and electronic dynamics. Here we present the combination of x-ray absorption spectroscopy with laser driven x-ray sources, offering atomic spatial and temporal resolution. Our new approaches for optimization of laser driven x-ray sources resulted in the demonstration of spatially coherent sub-20 fs x-ray pulses in a range up to several keV. We excited polycrystalline silicon with an ultrashort laser pulse and characterized the collective motion of atoms with time resolved x-ray absorption spectroscopy at a temporal resolution of less than 20 fs. Finally, we have shown the feasibility of probing the dynamics of the electronic structure of silicon and carbon with near edge x-ray absorption spectroscopy.     

BaTiO3 and PbTiO3 perovskite as catalysts for methane combustion

Unsupported and γ-Al₂O₃-supported Ba and Pb titanate catalysts were prepared, characterized and studied in the combustion of methane, as a test reaction for VOCs’ catalytic combustion. They present good catalytic activities, and after dispersion (5%) on γ-Al₂O₃ the specific activity of the supported perovskite phase increased 25 and 30 times, respectively, compared with the unsupported samples. PbTiO₃/γ-Al₂O₃ shows the best catalytic properties among the tested samples.