Hybridization in some macrocyclic polyacetylenes

The hybridization in several cyclic polyacetylene compounds has been calculated by the maximum overlap method, assuming planar and non-planar geometries of the molecules. In the planar configuration the hybrids describing the molecular skeleton deviate from the corresponding bond directions. We have a few “bent” bonds, but in contrast to the situation in small rings, here the deviation angles are negative, i.e., the hybrids point toward the inside of the ring. Non-planar structures in which acetylene groups are kept in a plane and CCH₂ or CH₂ groups are displaced out of the plane show less deviation from the bond directions of bent bonds. Furthermore, the deviation angles decrease with an increase in the out-of-plane displacement of methylene groups. Finally, when the angle of bending of the molecules approaches 50°, the deviation vanishes, predicting a puckered conformation for the molecules. Correlation between CC stretching vibration frequencies and the corresponding CC bond overlap is discussed.     

Intertwining operator superalgebras and vertex tensor categories for superconformal algebras, II

We construct the intertwining operator superalgebras and vertex tensor categories for the superconformal unitary minimal models and other related models.

     

Spectrum planning and performance evaluation between heterogeneous satellite networks

A new network has been recently proposed for the provision of fixed broadband services via high altitude platform stations (HAPS) in the 48/47 GHz band. One of the critical issues of this technology is spectrum sharing with the fixed satellite service. This paper examines the effect of Earth-to-stratosphere co-channel interference produced by ground stations of HAPS network to geostationary orbit (GEO) satellite receivers and proposes an interference-to-noise (I/N) calculation model for the evaluation of the current HAPS ground stations power characteristics set by ITU-R. Analytical and simulation results for archetypal systems in realistic scenarios indicate that efficient use of the spectrum shared between heterogeneous HAPS and Fixed Satellite Networks is feasible. Certain consideration is needed prior to the HAPS network development in suburban areas for latitudes from 55° to 65°, and in rural areas for latitudes from 60° to 75°.     

Cocoa Shell as a Step Forward to Functional Chocolates—Bioactive Components in Chocolates with Different Composition

Chocolate is considered as both caloric and functional food. Its nutritional properties may be improved by addition of fiber; however, this may reduce polyphenols content. The aim of this research was to determine the influence of cocoa shell addition (as a source of fiber) and its combination with different ingredients (cocoa butter equivalents (CBE), emulsifiers, dairy ingredients) on polyphenols of dark and milk chocolates. Total polyphenol (TPC) and total flavonoid (TFC) contents were determined spectrophotometrically, identification and quantification of individual compounds by high pressure liquid chromatography and antioxidant capacity by ferric reducing antioxidant power (FRAP) assay. Results showed that even though addition of cocoa shell to chocolate results in reduced contents of TPC, TFC, and individual compounds, it is not significant compared to ones reported by other authors for commercial chocolates. Other ingredients influence determined values for all investigated parameters; however, additional research is needed to reveal exact mechanisms and implications.     

Vertex-algebraic structure of the principal subspaces of certain -modules, II: Higher-level case

We give an a priori proof of the known presentations of (that is, completeness of families of relations for) the principal subspaces of all the standard -modules. These presentations had been used by Capparelli, Lepowsky and Milas for the purpose of obtaining the classical Rogers–Selberg recursions for the graded dimensions of the principal subspaces. This paper generalizes our previous paper.     

The <Emphasis Type="Italic">N</Emphasis> = 1 Triplet Vertex Operator Superalgebras

We introduce a newfamily of C ₂-cofinite N = 1 vertex operator superalgebras , m ≥ 1, which are natural super analogs of the triplet vertex algebra family , p ≥ 2, important in logarithmic conformal field theory. We classify irreducible -modules and discuss logarithmic modules. We also compute bosonic and fermionic formulas of irreducible characters. Finally, we contemplate possible connections between the category of -modules and the category of modules for the quantum group , , by focusing primarily on properties of characters and the Zhu’s algebra . This paper is a continuation of our paper Adv. Math. 217, no.6, 2664–2699 (2008). The second author was partially supported by NSF grant DMS-0802962.     

Lattice construction of logarithmic modules for certain vertex algebras

A general method for constructing logarithmic modules in vertex operator algebra theory is presented. By utilizing this approach, we give explicit vertex operator construction of certain indecomposable and logarithmic modules for the triplet vertex algebra W(p){\mathcal{W}(p)} and for other subalgebras of lattice vertex algebras and their N = 1 super extensions. We analyze in detail indecomposable modules obtained in this way, giving further evidence for the conjectural equivalence between the category of W(p){\mathcal{W}(p)}-modules and the category of modules for the restricted quantum group [`(U)]_q(sl₂){\overline{\mathcal{U}}_q(sl_2)} , q = e ^{π i/p} . We also construct logarithmic representations for a certain affine vertex operator algebra at admissible level realized in Adamović (J. Pure Appl. Algebra 196:119–134, 2005). In this way we prove the existence of the logarithmic representations predicted in Gaberdiel (Int. J. Modern Phys. A 18, 4593–4638, 2003). Our approach enlightens related logarithmic intertwining operators among indecomposable modules, which we also construct in the paper.     

Influence de la temperature et du gradient de vitesse sur la viscosite des solutions diluees de xanthane

The dependence of the relative viscosity of a dilute xanthan solution (0.4 g·l^?1) has been studied as a function of temperature (20–70°) and of the ionic strength of the solvent. When the rate of shear exceeds 100 sec^?1, the viscosity can be expressed as γ&#x030A; the exponent (n ? 1) varies with the polymer conformation. In aqueous solution in the absence or in the presence of added salt at a temperature above the melting temperature T_M (depending on the ionic strength of the solvent), the exponent (n ? 1) is ?0.285 and corresponds to the unordered conformation; at temperatures below T_M, the local helical conformation is rigid and (n ? 1) is ～ ?0.44 almost independent of the temperature.     

2,4-Dioxo-4-(4-hydroxy-6-methyl-2-pyrone-3-yl)butyric acid ethyl ester: Reagent for identifying and estimating metal ions in ring oven analysis

Ligand gave variously colored or fluorescent rings when reacted with several kinds of ions on a ring oven (Schleicher and Schuell filter paper 589²). With ions of Al(III), Be(II), Co(II), Cr(III), Cu(II), Fe(III), and Ni(II) the reactions were sensitive enough to enable application of ring colorimetry or fluorometry (excitation at 366 nm) for quantitation (detection limits, 0.1–2.0 μg of metal). A procedure for estimation of Al(III), Cr(III), and Fe(III) in mixtures was based on reaction with Ligand in combination with EDTA pretreatment, but omitting ion separation. Al(III) could be estimated reliably at its detection-limit-level, in the presence of up to 100 times as much of both Cr(III) and Fe(III).