Partition Lattice q-Analogs Related to q-Stirling Numbers

We construct a family of partially ordered sets (posets) that are q-analogs of the set partition lattice. They are different from the q-analogs proposed by Dowling [5]. One of the important features of these posets is that their Whitney numbers of the first and second kind are just the q-Stirling numbers of the first and second kind, respectively. One member of this family [4] can be constructed using an interpretation of Milne [9] for S[n, k] as sequences of lines in a vector space over the Galois field F _q. Another member is constructed so as to mirror the partial order in the subspace lattice.     

The pentacene films on the glass/ITO surface: structure and optical properties

Abstract

The structure, morphology and optical transmittance spectra of pentacene films on the (glass/ITO) surface were studied. The films were grown by two methods - the thermal vacuum deposition (TVD) and pulsed laser deposition (PLD). The electron diffraction pattern from thermally deposited pentacene films confirms their polycrystalline structure while the diffraction pattern of PLD-coated layers has a diffusion character. The results obtained showed that layers deposited by the TVD method has an optical spectrum that is characteristic for the pentacene film in contrary to the layers deposited by the PLD method. It is found a sensitivity of the optical transmittance of pentacene films to the ammonia action, which may be used for development the optical gas sensor.     

Properties and separation method of enantiomers of the mono- and bis-substituted derivatives of 3,3′,4,4′-tetramethyl-1,1′-diphosphaferrocene: structural analysis using X-ray diffraction and circular dichroism

This work expands on the recent separation of the enantiomers of the C₂-symmetrical bis-substituted derivatives of 1,1′-diphosphaferrocene. The effective separation of mono-substituted 1,1′-diphosphaferrocenes by the proposed method is demonstrated. The absolute configuration of the three separated components was established using X-ray diffraction. Circular dichroism spectra were collected for all of the separated compounds. The spectrum of each compound shows a characteristic curve, and the curves for the enantiomers are symmetrical. We also show that the correct absolute configuration for similar species can be assigned on the basis of the obtained data. We propose an explanation for the abnormal ¹H NMR spectra of phospholyl protons in some derivatives of 1,1′-diphosphaferrocene. A density functional theory (DFT) study of the conformation, as well as circular dichroism and NMR spectra of the chosen species, is also presented.     

Heat transfer in the plastic phases I and II of cyclopentane

Thermal conductivity of solid cyclopentane C₅H₁₀ has been measured at isochoric conditions in the plastic phases I and II for samples of different densities. Isochoric thermal conductivity is nearly constant in phase II and increases with temperature in phase I. Such behaviour is attributed to weakening of the translational orientational coupling which, in turn, leads to a decrease of phonon scattering on rotational excitations. The experimental data are described in terms of a modified Debye model of thermal conductivity with allowance for heat transfer by both low-frequency phonons and diffusive modes.     

Thermo-mechanical behavior of electrospun thermoplastic polyurethane nanofibers

Analysis of the thermo-mechanical behavior of electrospun thermoplastic polyurethane (TPU) block co-polymer nanofibers (glass transition temperature ∼−50 °C) is presented. Upon heating, nanofibers began to massively contract, at ∼70 °C, whereas TPU cast films started to expand. Radial wide-angle X-ray scattering (WAXS) profiles of the nanofibers and the films showed no diffraction peaks related to crystals, whereas their amorphous halo had an asymmetric shape, which can be approximated by two components, associated with hard and soft segments. During heating, noticeable changes in the contribution of these components were only observed in nanofibers. These changes, which were accompanied with an endothermic DSC peak, coinciding with the start of the nanofibers contraction, can be attributed to relaxation of an oriented stretched amorphous phase created during electrospinning. Such structure relaxation becomes possible when a portion of the hard segment clusters, forming an effective physical network, is destroyed upon heating.     

Parametrix for the localization of the Bergman metric on strictly pseudoconvex domains

We give the parameter version of a localization theorem for the Bergman metric near the boundary points of strictly pseudoconvex domains. The approximation theorem for square integrable holomorphic functions on such domains in the spirit of Graham-Kerzman is proved in the hereby paper, as well.