Fibrations of bigroupoids

Using Brown's construction (J. Algebra 15 (1970) 103) of an exact 6-term sequence for a fibration of groupoids we show how an exact 9-term sequence can be associated to a fibration of bigroupoids. Applications to topology and algebra are given.     

Lanthanide crown ether complexes of p-sulfonatocalix[5]arene

Two types of arrays are formed in water involving aza-crown ethers, p-sulfonatocalix[5]arene and europium(III) ions. One is a co-ordination polymer connecting calixarenes, sodium ions and lanthanide ions based on "ferris wheel" moieties incorporating aza-18-crown-6 and sodium ions. The second structure is a host-guest arrangement with di-protonated diaza-18-crown-6 in the cavity of the calixarenes as part of secondary coordination spheres of aquated europium(iii) ions.     

Hexasulfanyl analogues of cyclotriveratrylene

The synthesis of four 3,4-di(alkylsulfanyl)benzyl alcohol derivatives is described, in five steps from methyl 3,4-di(hydroxy)benzoate via a Newman–Kwart rearrangement. Incubation of these derivatives in formic acid affords 2,3,7,8,12,13-hexakis(alkylsulfanyl)-10,15-dihydro-5H-tribenzo[a,d,g]cyclononene products, which are hexa-sulfanyl analogues of the well-known supramolecular cavitand host, cyclotriveratrylene (CTV). The yield of this cyclization depends strongly on the alkylsulfanyl substituents present, in the order SMe > SEt ≈ SiPr ? SBn. A crystal structure determination of one of the cyclotrimers shows a mode of self-association that is commonly exhibited by CTV itself.     

Design and synthesis of a diverse morpholine template library

Efficient and general procedures have been developed for the solution-phase preparation of substituted morpholine derivatives, and a library has been produced around generic structure 1. This library was designed with proprietary modeling software for use as a general screening library. The 30 R1 reagents were phenols, and the 275 R2 reagents were taken from five different reagent classes, giving a variety of product classes in the final library of 8250 potential products. All of the library members were generated from a common intermediate, mesylate (5), which was synthesized efficiently, in bulk, in three steps from N-benzylethanolamine (2). High-throughput chemistry using robotics was carried out to produce the 7907 library members, which were individually characterized by reversed-phase LC/MS analysis.     

A Homotopy 2-Groupoid of a Hausdorff Space

If X is a Hausdorff space we construct a 2-groupoid G ₂ X with the following properties. The underlying category of G ₂ X is the `path groupoid" of X whose objects are the points of X and whose morphisms are equivalence classes f, g of paths f, g in X under a relation of thin relative homotopy. The groupoid of 2-morphisms of G ₂ X is a quotient groupoid X / N X, where X is the groupoid whose objects are paths and whose morphisms are relative homotopy classes of homotopies between paths. N X is a normal subgroupoid of X determined by the thin relative homotopies. There is an isomorphism G ₂ X(f,f) ₂(X, f(0)) between the 2-endomorphism group of f and the second homotopy group of X based at the initial point of the path f. The 2-groupoids of function spaces yield a 2-groupoid enrichment of a (convenient) category of pointed spaces.We show how the 2-morphisms may be regarded as 2-tracks. We make precise how cubical diagrams inhabited by 2-tracks can be pasted.     

Hausdorff means and moment sequences

We prove Schur’s theorem on the complete symmetric functions by using Hausdorff means. This approach leads to a more general result and to some new properties of moment sequences.     

A post-processing technique for extending depth of focus in conventional optical microscopy

In this paper, we propose a post-processing technique to obtain optical microscope images with extended depth of focus using a conventional microscope. With the proposed technique, we collect a sequence of images focused at different depths. We then combine the in-focus regions of each acquired frame to compose a single all-in-focus image. That is, a new image with extended depth of focus is obtained. The key to such an algorithm is in selecting the “in-focus” regions from each frame. In this paper, we describe the technique used to identify the in-focus region on every depth slice. Quantitative simulation results are presented where mean absolute error is used as a metric to assess the algorithm performance. Results using real imagery are also presented for subjective evaluation. Based on subjective evaluation and the quantitative simulation results, we believe that the proposed algorithm provides useful depth of focus extension.     

A critique on the structural analysis of lignins and application of novel tandem mass spectrometric strategies to determine lignin sequencing

This review is devoted to the application of MS using soft ionization methods with a special emphasis on electrospray ionization, atmospheric pressure photoionization and matrix‐assisted laser desorption/ionization MS and tandem MS (MS/MS) for the elucidation of the chemical structure of native and modified lignins. We describe and critically evaluate how these soft ionization methods have contributed to the present‐day knowledge of the structure of lignins. Herein, we will introduce new nomenclature concerning the chemical state of lignins, namely, virgin released lignins (VRLs) and processed modified lignins (PML). VRLs are obtained by liberation of lignins through degradation of vegetable matter by either chemical hydrolysis and/or enzymatic hydrolysis. PMLs are produced by subjecting the VRL to a series of further chemical transformations and purifications that are likely to alter their original chemical structures. We are proposing that native lignin polymers, present in the lignocellulosic biomass, are not made of macromolecules linked to cellulose fibres as has been frequently reported. Instead, we propose that the lignins are composed of vast series of linear related oligomers, having different lengths that are covalently linked in a criss‐cross pattern to cellulose and hemicellulose fibres forming the network of vegetal matter. Consequently, structural elucidation of VRLs, which presumably have not been purified and processed by any other type of additional chemical treatment and purification, may reflect the structure of the native lignin. In this review, we present an introduction to a MS/MS top–down concept of lignin sequencing and how this technique may be used to address the challenge of characterizing the structure of VRLs. Finally, we offer the case that although lignins have been reported to have very high or high molecular weights, they might not exist on the basis that such polymers have never been identified by the mild ionizing techniques used in modern MS. Copyright © 2015 John Wiley & Sons, Ltd.