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.     

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.     

Construction of metal-organic frameworks: versatile behaviour of a ligand containing mono- and bidentate coordination sites

Five new coordination polymers based on a new 2,2'-bipyridine derived ligand N,N'-bis(pyridin-4-yl)-2,2'-bipyridine-5,5'-dicarboxamide (=L) are reported herein. Isostructural three-dimensional coordination polymers with a rare (4,6)-connected network of {4(4).6(2)}(3){4(6).8(9)}(2) topology were synthesised from Cu(NO(3))(2), Zn(NO(3))(2) or a mixture of Cu(NO(3))(2)/Fe(BF(4))(2) with L in complexes {[Cu(5)L(6)]·(NO(3))(10)·(H(2)O)(18)}(∞) (1), {[Zn(5)L(6)]·(NO(3))(10)·(H(2)O)(18)}(∞) (2) and {[Fe(x)Cu(y)L(6)]·(NO(3))(10)·(H(2)O)(18)}(∞) (3; where x+y=5). Complexes with two-dimensional grid structures resulted from treatment with CoCl(2) or Cd(NO(3))(2) with L in complexes {[CoLCl(2)]·DMF}(∞) (4) and {CdL(NO(3))(2)}(∞) (5).     

DETECTION OF DNA-PSORALEN PHOTOADDUCTS in situ

Abstract— An immunological method, with the use of specific immune serum, has been developed for detection of 8-methoxypsoralen (8-MOP) photoadducts to DNA, formed in situ in cell nuclei, after combined treatment with 8MOP and UV-A irradiation (Zarçbska et al. , 1978). Lymphocytes fixed on slides or in suspension, and cryostat sections of different mammalian tissues, served as antigenic substrate, after treatment with 8-MOP and UV-A in vitro. Specific fluorescence in these substrates was detected in the nuclei after treatment with 30 ˜ 140 kJ/m² UV-A in the presence of 0.1-0.3 μg/cm² 8-MOP. PHA-stimulated-lymphocytes appeared to be the most sensitive substrate.
However, hairless mice treated with high doses of UV-A in vivo , 70 ˜ 360 kJ/m² did not reveal a specific fluorescence of epidermal nuclei, unless a high local concentration of 8-MOP was attained.
The apparent discrepancy in the level of photoadduct detection between the in vitro and in vivo treated specimens was explained by the low number of DNA-8-MOP-photoadducts formed in vivo under these experimental conditions. The relevance of these findings to the role of DNA-8-MOP-photoadducts formed during PUVA photochemotherapy is discussed.     

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.     

ON QUOTIENTS OF BRAID GROUPS

ABSTRACT.

Let G be the group ?[t, t ^?1] x ?. By studying the action of the braid group B_n on the set Gⁿ , we obtain representations of B_n into a wreath product of the symmetric group and the general linear group over ?[t, t ^?1]. This in particular recovers the Burau representation of the braid group. Furthermore, some quotients of the braid group are obtained by using the representations found.     

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.     

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.     

M3L2 metallo-cryptophanes: [2]catenane and simple cages

Crystalline M(3)L(2) complexes with either single cage or triply interlocking [2]catenane chiral structures are formed the self-assembly of host-like ligands with transition metals.