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.     

Invariance of selfinjective algebras of quasitilted type under stable equivalences

We prove that the class of finite dimensional selfinjective algebras over a field which admit Galois coverings by the repetitive algebras of the quasitilted algebras, with Galois groups generated by compositions of the Nakayama automorphisms with strictly positive automorphisms, is invariant under stable and derived equivalences. Dedicated to Claus Michael Ringel on the occasion of his sixtieth birthday     

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.     

Infinite-dimensional homology and multibump solutions

We start by introducing a Čech homology with compact supports which we then use in order to construct an infinite-dimensional homology theory. Next we show that under appropriate conditions on the nonlinearity there exists a ground state solution for a semilinear Schr?dinger equation with strongly indefinite linear part. To this solution there corresponds a nontrivial critical group, defined in terms of the infinite-dimensional homology mentioned above. Finally, we employ this fact in order to construct solutions of multibump type. Although our main purpose is to survey certain homological methods in critical point theory, we also include some new results. Dedicated to Felix Browder on the occasion of his 80th birthday     

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.     

Lipophilicity analysis of newly synthetized quinobenzothiazines by use of TLC

Lipophilicity is a very important property of chemical compound taking into consideration in drugs design. Relationships between biological activity, among others lipophilicity, and chemical structure (QSAR) of the compound are very often used by researches. Especially important is the kind of substituents connected to the basic structural fragment and how it changes the lipophilicity of the compound. The aim of this study was to determine the parameters of lipophilicity of quinobenzothiazine derivatives using reversed phase - thin-layer chromatography (RP-TLC), which would enable one to determine the structure–activity relationship. The objective of our work is a series of 15 newly synthetized quinobenzothiazines. They were analyzed by thin-layer chromatography (TLC) with the use of two different mobile phases consisting of methanol or acetone as organic modifiers. For all compounds investigated, the values of lipophilicity obtained from computational method were also determined. Cluster analysis was carried out too for all data of lipophilicity obtained. Low correlation was found between values of experimental lipophilicity and lipophilicity from computational methods for newly synthetized compounds.     

Azole. 44.

The structure analyses of racemic 3‐chloro‐1‐(4‐morpholino‐5‐nitro­imidazol‐1‐yl)­propan‐2‐ol, C₁₀H₁₅ClN₄O₄, (II), and 3‐chloro‐1‐(5‐morpholino‐4‐nitro­imidazol‐1‐yl)­propan‐2‐ol, C₁₀H₁₅ClN₄O₄, (III), have been undertaken in order to determine the position of the morpholine residue in these two isomers. The morpholine residue in (II) is connected at the 4‐position, while in (III), it is connected at the 5‐position of the imidazole ring. The morpholine mean planes and nitro groups in the two compounds deviate from the imidazole planes to different extents. The nitro groups in (II) and (III) take part in the conjugation system of the imidazole rings. In consequence, the exocyclic C—N bonds are significantly shorter than the normal single Csp²—NO₂ bond and the nitro groups in (II) and (III) show an extraordinary stability on treatment with morpholine and piperidine [Gzella, Wrzeciono & Pöppel (1999). Acta Cryst. C 55 , 1562–1565]. In the crystal lattice, the mol­ecules of both compounds are linked by O—H?N and C—H?O intermolecular hydrogen bonds.     

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.     

Synthesis, structures, and magnetic properties of face-sharing heterodinuclear Ni(II)-Ln(III) (Ln = Eu, Gd, Tb, Dy) complexes

Heterodinuclear [(Ni (II)L)Ln (III)(hfac) 2(EtOH)] (H 3L = 1,1,1-tris[(salicylideneamino)methyl]ethane; Ln = Eu, Gd, Tb, and Dy; hfac = hexafluoroacetylacetonate) complexes ( 1.Ln) were prepared by treating [Ni(H 1.5L)]Cl 0.5 ( 1) with [Ln(hfac) 3(H 2O) 2] and triethylamine in ethanol (1:1:1). All 1.Ln complexes ( 1.Eu, 1.Gd, 1.Tb, and 1.Dy) crystallized in the triclinic space group P1 (No. 2) with Z = 2 with very similar structures. Each complex is a face-sharing dinuclear molecule. The Ni (II) ion is coordinated by the L (3-) ligand in a N 3O 3 coordination sphere, and the three phenolate oxygen atoms coordinate to an Ln (III) ion as bridging atoms. The Ln (III) ion is eight-coordinate, with four oxygen atoms of two hfac (-)'s, three phenolate oxygen atoms of L (3-), and one ethanol oxygen atom coordinated. Temperature-dependent magnetic susceptibility and field-dependent magnetization measurements showed a ferromagnetic interaction between Ni (II) and Gd (III) in 1.Gd. The Ni (II)-Ln (III) magnetic interactions in 1.Eu, 1.Tb, and 1.Dy were evaluated by comparing their magnetic susceptibilities with those of the isostructural Zn (II)-Ln (III) complexes, [(ZnL)Ln(hfac) 2(EtOH)] ( 2.Ln) containing a diamagnetic Zn (II) ion. A ferromagnetic interaction was indicated in 1.Tb and 1.Dy, while the interaction between Ni (II) and Eu (III) was negligible in 1.Eu. The magnetic behaviors of 1.Dy and 2.Dy were analyzed theoretically to give insight into the sublevel structures of the Dy (III) ion and its coupling with Ni (II). Frequency dependence in the ac susceptibility signals was observed in 1.Dy.