Enumeration of Unrooted Odd-Valent Regular Planar Maps

We derive closed formulae for the numbers of rooted maps with a fixed number of vertices of the same odd degree except for the root vertex and one other exceptional vertex of degree 1. The same applies to the generating functions for these numbers. Similar results, but without the vertex of degree 1, were obtained by the first author and Rahman. We also show, by manipulating a recursion of Bouttier, Di Francesco and Guitter, that there are closed formulae when the exceptional vertex has arbitrary degree. We combine these formulae with results of the second author to count unrooted regular maps of odd degree. In this way we obtain, for each even n, a closed formula for the function f _n whose value at odd positive integers r is the number of unrooted maps (up to orientation-preserving homeomorphisms) with n vertices and degree r. The formula for f _n becomes more cumbersome as n increases, but for n > 2 each has a bounded number of terms independent of r.     

Cystic fibrosis and diabetes: isoLAB and isoDAB, enantiomeric carbon-branched pyrrolidine iminosugars

Acetonides are the only protecting groups used in the syntheses of isoDAB from d-ribose and of isoLAB from d-tagatose. isoDAB is a potent and highly specific competitive α-glucosidase inhibitor (for rice α-glucosidase, K_i = 4 μM for isoDAB compared to K_i 14 μM for DAB). isoDAB is not an—whereas DAB is a potent—inhibitor of glycogen phosphorylase. This is the first example of any potent inhibition of glycosidases by a carbon-branched iminosugar pyrrolidine. Although isoLAB shows no inhibition of any glycosidase, preliminary experiments suggest that isoLAB partially rescues the defective F508del-CFTR function and so may have a role in the study of cystic fibrosis.     

Gel growth of α and γ glycine and their characterization

The microbial free single crystals of α and γ glycine were grown from gel at room temperature in a new chemical route. These crystals showed a superior quality than the solution grown crystals. The metastable α-form and the stable γ-form of glycine were crystallized in silica gel by solubility reduction method. The form of crystallization is confirmed by single crystal and powder X-ray diffraction analyses. The crystals of α and γ glycine were found to crystallize in monoclinic and hexagonal crystal systems, respectively. For analyzing the functional group and thermal stability of α and γ glycine crystals, spectroscopic and thermal analyses have been carried out. The dielectric studies were performed to find the dielectric constant of the grown crystals and the results are discussed. Second harmonic generation efficiency of the crystal was measured by Kurtz’s powder method using Nd:YAG laser and it was found to be 2.68 times that of potassium dihydrogen phosphate crystals.     

Asymptotic enumeration of strongly connected digraphs by vertices and edges

We derive an asymptotic formula for the number of strongly connected digraphs with n vertices and m arcs (directed edges), valid for m ‐ n →∞ as n →∞ provided m = O(nlog n). This fills the gap between Wright's results which apply to m = n + O (1) , and the long‐known threshold for m, above which a random digraph with n vertices and m arcs is likely to be strongly connected. © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 2013     

Fluorine-19 solid state NMR study of vinylidenefluoride polymers using selective relaxation filters

Two fluoropolymers, poly(vinylidenefluoride) (PVDF) and a vinylidenefluoride telomer (VDFT), with molecular weights of 1 x 10(6) and 2 x 10(3) Da by GPC, respectively, have been analysed by 19F solid-state nuclear magnetic resonance (NMR) spectroscopy. Relaxation-filtered proton-decoupled magic-angle spinning (MAS) experiments, namely T1rho filter, dipolar filter (DF), direct-polarisation delayed acquisition (DPDA) and discrimination induced by variable-amplitude minipulses (DIVAM), allowed signals in the direct polarisation (DP) spectra of PVDF and the VDFT to be discussed in terms of rigid and mobile domains. Both samples showed signals, which were multi-componential, but they differ in the nature of the crystalline form present. Thus, the Vinylidenefluoride (VDF) telomer exhibited a crystalline component corresponding to beta PVDF, whereas the PVDF contained crystallites of the alpha form. Signals relating to end groups and reverse units, plus an anomalous signal displaying long-time transverse relaxation in the DPDA spectrum, were found for both polymers, though they showed diversity in chemical shift and content. Signals related to reverse units and/or end groups were seen between approximately -115 and approximately -117 ppm for both samples. High-speed MAS at higher magnetic field resulted in an increase in resolution so that signals previously attributed to single-phase characteristics are shown to indicate the possibility of several different mobilities. The results are debated with respect to molecular weight and relaxation parameters.     

The photoproduction of neutral pions from protons at forward angles in the resonance region

Differential cross sections for the photoproduction of pi-zero mesons from protons have been measured at angles between 10° and 70° c.m. in the energy range 0.85 GeV to 1.30 GeV. The values are compared with the fits to pion photoproduction data from three recent partial-wave analyses.     

Counting labelled chordal graphs

An equation is derived which is satisfied by special types of generating functions for labelled chordal graphs. This enables calculation of the numbers of labelled chordal graphs with given numbers of cliques of given sizes. From this is determined the number ofn-vertex labelled chordal graphs with given connectivity. Calculations were completed forn≤13.     

Looking glass inhibitors: L-DMDP, a more potent and specific inhibitor of alpha-glucosidases than the enantiomeric natural product DMDP

L-DMDP, prepared from D-gulonolactone, is a highly specific inhibitor of a number of plant and mammalian alpha-glucosidases [between 2 and 4 orders of magnitude more potent than the enantiomeric natural product DMDP] but is not an inhibitor of bacterial and yeast alpha-glucosidases. Additionally N-butyl-DMDP is a potent inhibitor of ceramide-specific glucosyltransferase but N-butyl-L-DMDP shows no inhibition.     

Raman and resonance-Raman spectra of CsI/I−3

Raman and resonance-Raman spectra of the I^?₃ ion isolated within CsI crystals have been studied using 647 nm and 488 nm exciting radiation. Sample temperatures between 300 and 20 K have been used. Eleven overtones of the symmetric stretching mode (nν₁) have been observed in the resonance-Raman spectrum excited by the 488 nm Ar⁺ laser line. Bands centred at 153, 170, 264 and 304 cm^?1 have been assigned as ν₃, 2ν₂, ν₁+ν₃ and 2ν₃(Σ⁺) respectively. The remaining structure between the nν₁ lines has been assigned as due to combinations of these lines with the lattice vibrations of the CsI crystal.