The fixed point property in ordered sets of width two

We consider the fixed point property (FPP) in an ordered set of width two (every antichain contains at most two elements). The necessary condition of the FPP and a number of equivalent conditions to the FPP in such sets is established. The product theorem is proved, as well.     

Structure of the O-Specific Polysaccharide of Hafnia Alvei 23 Having an Oligosaccharide-Phosphate Repeating Unit

ABSTRACT

Lipopolysaccharide (LPS) of Hafnia alvei 23 has an acid-labile O-specific polysaccharide (OPS) with a pentasaccharide-phosphate repeating unit containing D-Glc1P, D-GlcNAc, L-Fuc, 6-deoxy-D-talose (D-6dTal), 4-acetamido-4,6-dideoxy-D-glucose (D-Qui4NAc), and an O-acetyl group. A partially degraded OPS was obtained by hydrolysis of LPS with 0.25 M sodium acetate in aqueous 0.5% acetic acid. Fractionation of LPS on Sephadex G-200 in DOC buffer allowed isolation of long-chain LPS species which, together with OPS, were studied by methylation analysis, chemical degradations (O-deacetylation, dephosphorylation with 48% hydrofluoric acid, Smith degradation), and ¹H and ¹³C NMR spectroscopy, including 2D COSY, TOCSY, NOESY, and H-detected ¹H,¹³C heteronuclear single-quantum coherence (HSQC) experiments. The following structure of the repeating unit of OPS was established:     

Comparison of Proton Acceptor and Proton Donor Properties of H2O and H2O2 in Organic Crystals of Drug-like Compounds: Peroxosolvates vs. Crystallohydrates

Two new peroxosolvates of drug-like compounds were synthesized and studied by a combination of X-ray crystallographic, Raman spectroscopic methods, and periodic DFT computations. The enthalpies of H-bonds formed by hydrogen peroxide (H₂O₂) as a donor and an acceptor of protons were compared with the enthalpies of analogous H-bonds formed by water (H₂O) in isomorphic (isostructural) hydrates. The enthalpies of H-bonds formed by H₂O₂ as a proton donor turned out to be higher than the values of the corresponding H-bonds formed by H₂O. In the case of H₂O₂ as a proton acceptor in H-bonds, the ratio appeared reversed. The neutral O∙∙∙H-O/O∙∙∙H-N bonds formed by the lone electron pair of the oxygen atom of water were the strongest H-bonds in the considered crystals. In the paper, it was found out that the low-frequency Raman spectra of isomorphous crystalline hydrate and peroxosolvate of N-(5-Nitro-2-furfurylidene)-1-aminohydantoin are similar. As for the isostructural hydrate and peroxosolvate of the salt of protonated 2-amino-nicotinic acid and maleic acid monoanion, the Raman spectra are different.     

Simplified spectral phase interferometry for direct electric-field reconstruction by using a thick nonlinear crystal

We propose and demonstrate a novel implementation of spectral-shearing interferometry (SSI) for reconstructing the electric field of ultrashort pulses by utilizing asymmetric group velocity matching in a long nonlinear crystal. The proposed configuration eliminates the requirement for a linearly chirped auxiliary pulse that is in common in all existing SSI methods, relying on nonlinear conversion to produce a spectral shear.     

Dilation theorems for positive definite operator kernels having majorants

Dilation theorems for Banach space valued stochastic processes and operator valued positive definite kernels are considered. It is shown, e.g., that a Banach space valued stochastic process X can be dilated to another process Y, if and only if the covariance kernel of Y is a majorant of the covariance kernel of X. Positive definite operator kernels having majorants of certain special type are characterized.     

Numerical study of light correlations in a random medium close to the Anderson localization threshold

We applied a finite-difference time domain algorithm to the study of field and intensity correlations in random media. Close to the onset of Anderson localization, we observe deviations of the correlation functions, in both shape and magnitude, from those predicted by the diffusion theory. Physical implications of the observed phenomena are discussed.     

Mechanochemical synthesis and thermal stability of phases in the Y2O3–Yb2O3 system

Substitutional, continuous solid solution of the general formula Y_2–xYb_xO₃ was obtained from the mixture of Y₂O₃ and Yb₂O₃ oxides, for the first time by the mechanochemical method in a high-energy ball milling. The monophasic samples of nanocrystalline solid solution for x?>?0.00 and x?<?2.00 were examined by the methods: XRD, DTA, SEM, IR and UV–Vis–DR. As follows from the results, the solid solution crystallizes in cubic system and is isostructural with Y₂O₃ and Yb₂O₃. The solution is stable in the air atmosphere up to at least 900°C, and its decomposition temperature decreases with the increase in x, that is, with decreasing number of Yb³⁺ ions replacing Y³⁺ ions in the crystal lattice of Y₂O₃. The energy band gap estimated for the solid solution varies from?~?5.30 eV for x?=?0.50 to?~?4.90 eV for x?=?1.50, which means that it is an insulator.

     

Simulating the dynamic behavior of planetary gearbox based on improved Hanning function

Planetary gearboxes are widely used in industrial machines. They usually work in harsh environments giving rise to damages and high maintenance costs. Condition monitoring is a key action allowing one to detect the presence of such damage ensuring healthy running conditions. The knowledge of the dynamic behavior of such a gearbox can be achieved using modeling tools as a primary step before conditioning the monitoring subject. In addition, modeling a gear set can help in the stage of design in order to optimize physical and geometric parameters of the system. Therefore, in this work, a two-dimensional lumped parameter model is adopted to build all vibration sources. The time-varying mesh stiffness is approximated as a square wave form. A novel mathematical formulation is proposed to model the amplitude modulation phenomenon due to the rotational motion of the planets around the center of the gearbox. Finally, the overall vibration signal is concluded as a summation of all vibration components influenced by the modulation function.     

Dependence of the AES backscattering correction factor on the experimental configuration

We present an analysis of the dependence of the backscattering correction factor (BCF) in Auger-electron spectroscopy (AES) on the analyzer acceptance angle. Illustrative BCF calculations are presented for Pd M₅N₄₅N₄₅ Auger electrons as a function of primary-electron energy for primary-electron angles of incidence, θ₀, of 0° and 80° and for various values of the analyzer acceptance angle. It was necessary to generalize the BCF definition for the case of an analyzer with an arbitrarily large acceptance angle; this was done with a new function, the integral emission depth distribution function. BCFs calculated from an advanced model of electron transport in the surface region of the Pd sample varied weakly with analyzer half-cone angle for θ₀ = 0° but more strongly for θ₀ = 80° where there were BCF differences varying between 19% at a primary energy of 1 keV and 6% at a primary energy of 5 keV. These BCF differences are due in part to variations of the BCF with emission angle and in part to variations of the density of inner-shell ionizations within the information depth for the detected Auger electrons. The latter variations are responsible for differences larger than 10% between BCFs from the widely used simplified BCF model and those from the more accurate advanced model for primary energies less than about 5 keV for θ₀ = 80°. For normal incidence of the primary beam, differences greater than 10% between BCFs from the simplified and advanced models were found for primary energies between 1 keV and 4 keV. These BCF differences indicate that the simplified model can provide only approximate BCF values. In addition, the simplified model does not provide any BCF dependence on Auger-electron emission angle or analyzer acceptance angle.