Dual pairs and Kostant-Sekiguchi correspondence. II. Classification of nilpotent elements

We classify the homogeneous nilpotent orbits in certain Lie color algebras and specialize the results to the setting of a real reductive dual pair. For any member of a dual pair, we prove the bijectivity of the two Kostant-Sekiguchi maps by straightforward argument. For a dual pair we determine the correspondence of the real orbits, the correspondence of the complex orbits and explain how these two relations behave under the Kostant-Sekiguchi maps. In particular we prove that for a dual pair in the stable range there is a Kostant-Sekiguchi map such that the conjecture formulated in [6] holds. We also show that the conjecture cannot be true in general.     

Damping of Vibrations in a SystemWith Two Beams by Structural Friction

This paper presents the results of tests on free and forced harmonic vibrations in a system with two beams with structural friction taken into account. The beams are clamped together with uniform unitary pressure. The hysteresis loop describing the frictional-elastic properties of the system has a form of a parallelogram. The autor created a mathematical model of the vibrating system with two beams. During free vibrations of the system, its damping characteristics were tested by a digital simulation method. The vibration damping decrement as a function of amplitude displacement was determined. When vibrations were harmonically forced, the amplitude - frequency characteristics of the system were determined numerically. The system was used as a nonlinear vibration damper in a linear system with a harmonic force. The equations of motion of the nonlinear two-degree of freedom system were solved by means of a digital simulation method. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Turán numbers for odd wheels

The Turán number $\text{ex}(n,G)$ is the maximum number of edges in any $n$-vertex graph that does not contain a subgraph isomorphic to $G$. A wheel$W_n$ is a graph on $n$ vertices obtained from a $C_{n?1}$ by adding one vertex $w$ and making $w$ adjacent to all vertices of the $C_{n?1}$. We obtain two exact values for small wheels:

$\text{ex}(n,W_5)=?\frac{n^2}{4}+\frac{n}{2}?,$

$\text{ex}(n,W_7)=?\frac{n^2}{4}+\frac{n}{2}+1?.$

Given that $\text{ex}(n,W_6)$ is already known, this paper completes the spectrum for all wheels up to 7 vertices. In addition, we present the construction which gives us the lower bound $\text{ex}(n,W_{2k+1})>?\frac{n^2}{4}?+?\frac{n}{2}?$ in general case.     

On the Glivenko-Cantelli problem in stochastic programming: Mixed-integer linear recourse

Expected recourse functions in linear two-stage stochastic programs with mixed-integer second stage are approximated by estimating the underlying probability distribution via empirical measures. Under mild conditions, almost sure uniform convergence of the empirical means to the original expected recourse function is established.     

Vibrational spectra of two BEDT-TTF-based organic conductors: charge order

Infrared and Raman investigations of two phases of bis(ethylenedithio)tetrathiafulvalene (BEDT-TTF) based organic conductors with the same CF₃CF₂SO₃⁻ anion: β′-(BEDT-TTF)₂CF₃CF₂SO₃ and δ′-(BEDT-TTF)₂CF₃CF₂SO₃, are shortly reviewed and compared with the most typical infrared properties of the family of (BEDT-TTF)₂RR′SO₃ organic conductors, where R = SF₅, CF₃, and R′ are CH₂, CF₂, CHF, CHFCF₂, and CH₂CF₂. The role of the molecular structur and spatial organization of the counterions is discussed. Presented at 2-nd International Conference on Functional Materials and Devices, ICFMD 2008, June 16–19, 2008, Kuala Lumpur, Malaysia     

Risk preferences on the space of quantile functions

We propose a novel approach to quantification of risk preferences on the space of nondecreasing functions. When applied to law invariant risk preferences among random variables, it compares their quantile functions. The axioms on quantile functions impose relations among comonotonic random variables. We infer the existence of a numerical representation of the preference relation in the form of a quantile-based measure of risk. Using conjugate duality theory by pairing the Banach space of bounded functions with the space of finitely additive measures on a suitable algebra \(\varSigma \) , we develop a variational representation of the quantile-based measures of risk. Furthermore, we introduce a notion of risk aversion based on quantile functions, which enables us to derive an analogue of Kusuoka representation of coherent law-invariant measures of risk.     

Imaging of nanostructures with sub-100?nm spatial resolution using a desktop EUV microscope

Laser-produced plasma sources of short-wavelength radiation offer an interesting alternative to synchrotron and free-electron laser installations. Recently, we reported on a newly developed desktop EUV microscope based on plasma generated from a gas-puff target and diffractive optics. The half-pitch resolution of the microscope approached 50?nm. Compared to analogous microscopes based on synchrotron sources, our system is compact and cost-effective. In this paper, we present the results of imaging experiments on a thin polycrystalline object that was carried out in order to further examine the applicability of the microscope. We have demonstrated here that EUV microscopy can provide structural information that cannot be accessed by conventional optical microscopy or SEM.     

Effect of pH on deagglomeration and rheology/morphology of aqueous suspensions of goethite nanopowder

The kinetics of deagglomeration in diluted suspensions of goethite nanopowder, as well as the rheology and morphology of the resulting suspensions, strongly depends on pH. At pH 3, nanopowder can be dispersed as separate nanoparticles, and the resulting suspension is Newtonian, with the viscosity only marginally higher than the viscosity of water. At pH between 5 and 12, nanoparticles tend to reaggregate and form weak aggregates/flocs. Morphology changes from a Newtonian suspension of primary nanoparticles to a non-Newtonian, shear-thinning suspension of large, porous, interconnected flocs with the yield stress reaching a maximum at an isoelectric point. The effect of pH on morphology and rheology is reversible, and as pH is reduced to 3, the suspension becomes Newtonian, with viscosity marginally higher than the viscosity of water. The rheological models based on DLVO theory do not allow prediction of the effect of pH on viscosity and yield stress, but the flow curves of goethite suspensions can be described by a fractal model with five adjustable parameters.     

Anionic polymerization of β-lactones initiated with potassium hydride. A convenient route to polyester macromonomers

The anionic polymerization of 2-oxetanone and 4-methyl-2-oxetanone initiated with the potassium hydride/18-crown-6 complex was investigated. The α-proton abstraction of the monomer was found to proceed at the initiation step of this polymerization. The salt of the unsaturated carboxylic acid formed initiates further propagation, leading to functionalized polyesters with unsaturated, dead end-groups.     

Mechanistic aspects of the oxidative and reductive fragmentation of N-nitrosoamines: a new method for generating nitrenium cations, amide anions, and aminyl radicals

A new method for investigating the mechanisms of nitric oxide release from NO donors under oxidative and reductive conditions is presented. Based on the fragmentation of N-nitrosoamines, it allows generation and spectroscopic characterization of nitrenium cations, amide anions, and aminyl radicals. X-irradiation of N-nitroso-N,N-diphenylamine 1 in Ar matrices at 10 K is found to yield the corresponding radical ions, which apparently undergo spontaneous loss of NO* under the conditions of this experiment (1*+ seems to survive partially intact, but not 1*-). One-electron reduction or oxidation of 1 is observed upon doping of the Ar matrix with DABCO, an efficient hole scavenger, or CH2Cl2, an electron scavenger, respectively. The resulting diphenylnitrenium cation, 2+, and the diphenylamide anion, 2-, were characterized by their full UV-vis and mid-IR spectra. The best spectra of 2+ and 2- were obtained if 1 was homolytically photodissociated to diphenylaminyl radical 2* and NO* prior to ionization. 2+ and 2- are bleached on irradiation at <340 nm to form 2* or, in part, 1. DFT and CCSD quantum chemical calculations predict that the dissociation of 1*+ and 1*- is slightly endothermic, a tendency which is partially reversed if one allows for complexation of the resulting 2+ (and, presumably, 2-) with NO*. The method described in this work should prove generally applicable to the generation and study of nitrenium cations and amide anions R2N+/- under matrix and ambient conditions (i.e., in solution).