Degenerations of K3 surfaces in projective space

The purpose of this article is to study a certain kind of numerical K3 surfaces, the so-called K3 carpets. These are double structures on rational normal scrolls with trivial dualizing sheaf and irregularity . As is deduced from our study, K3 carpets can be obtained as degenerations of smooth K3 surfaces. We also study the Hilbert scheme near the locus parametrizing K3 carpets, characterizing those K3 carpets whose corresponding Hilbert point is smooth. Contrary to the case of canonical ribbons, not all K3 carpets are smooth points of the Hilbert scheme.

     

Gold(III)-pteridine compounds: synthesis, spectral, and X-ray diffraction studies on new adducts between sodium tetrabromoaurate(III) and lumazine derivatives

In aqueous hydrobromic medium, Na[AuCl₄] reacts with 1,3-dimethyllumazine (1,3-dimethyl-pteridine-2,4(1H,3H)-dione, DLM) or 1,3,6,7-tetramethyllumazine (DLMD) to give three adducts with simplified formulas Na[AuBr₄](DLMD), Na[AuBr₄](DLM), and Na[AuBr₄](DLM)₂. These compounds have been characterized by means of analytical techniques, and IR and NMR spectroscopies. Single-crystal x-ray diffraction studies have been made on the Na[AuBr₄](DLM)₂ compound. The crystals belong to the orthorhombic Pbca space group, with a = 15.249(1), b = 15.238(2), c = 21.563(2) Å, Z = 8, and R = 0.053. The structure consists of planar [AuBr₄]^– anions and Na⁺ cations weakly linked to two crystallographically independent DLM molecules. The Na⁺ cation interacts weakly with four oxygen and one nitrogen atoms from four different pteridine molecules, its environment may be described as a very distorted square pyramid.     

Intra- vs intermolecular hydrogen bonding. The crystal structure of 5-methyl-2-hydroxyacetophenone thiosemicarbazone monohydrate and salicylaldehyde-2-methylthiosemicarbazone monohydrate

The crystal structure of 5-methyl-acetophenonethiosemicarbazone monohydrate,A, and salicylaldehyde-2-methylthiosemicarbazone monohydrate,B, were determined using single crystal X-ray diffraction.A crystallizes in the monoclinic space groupC2/c, with lattice parametersa=14.161(2),b=15.753(1) ?,c=11.084(1) ?, β=112.59(1)° andZ=4, yielding a calculated density ofD _calc=1.352 mg/m³.B crystallizes in the triclinic space groupP1, witha=7.233(2) ?,b=7.371(2) ?,c=11.841(2) ?, α=82.77(2)°, β=78.33(2)°, γ=63.06(2)° andD _calc=1.371 mg/m³ forZ=2,. In bothA andB the immine nitrogen and the sulfur atom areanti with respect to N2-C8. WhileA presents the usual intramolecular six membered hydrogen bond ring,B has instead an intermolecular hydrogen bond between the hydroxy moiety of the salicyladehyde and a water molecule. AM1 calculations agree with the experimental conformations observed in both compounds. Contribution No. 1619 of the Instituto de Química, UNAM.     

Zirconocene-mediated synthesis of cyclobutabenzenes

A new, mild, one-pot method for the synthesis of cyclobutabenzenes by the zirconium-promoted cross-coupling reaction of aryllithium compounds and alkenyl bromides is reported. Formation of an arynezirconocene complex and its regioselective coupling with an alkenyl bromide are the key steps of the process. This method allows the regio- and diastereoselective synthesis of functionalized cyclobutabenzene derivatives from simple and easily available starting materials.     

Decreased optical nonlinearities upon CF3 substitution on tricyanofuran acceptors

Replacement of the tricyanofuran (TCF) acceptor by its stronger analogue CF 3-TCF results in decreased second-order optical nonlinearities in merocyanines bearing a proaromatic 1,3-dithiole donor. The TCF-containing derivatives display exceptionally high mu beta values up to 31,000 x 10(-48) esu, unprecedented for 1,3-dithiole-based NLO-phores.     

Application of 1-aminocyclohexane carboxylic acid to protein nanostructure computer design

Conformationally restricted amino acids are promising candidates to serve as basic pieces in redesigned protein motifs which constitute the basic modules in synthetic nanoconstructs. Here we study the ability of constrained cyclic amino acid 1-aminocyclohexane-1-carboxylic acid (Ac6c) to stabilize highly regular beta-helical motifs excised from naturally occurring proteins. Calculations indicate that the conformational flexibility observed in both the ring and the main chain is significantly higher than that detected for other 1-aminocycloalkane-1-carboxylic acids (Acnc, where n refers to the size of the ring) with smaller cycles. Incorporation of Ac6c into the flexible loops of beta-helical motifs indicates that the stability of such excised building blocks as well as the nanoassemblies derived from them is significantly enhanced. Thus, the intrinsic Ac6c tendency to adopt folded conformations combined with the low structural strain of the cyclohexane ring confers the ability to both self-adapt to the beta-helix motif and to stabilize the overall structure by absorbing part of its conformational fluctuations. Comparison with other Acnc residues indicates that the ability to adapt to the targeted position improves considerably with the ring size, i.e., when the rigidity introduced by the strain of the ring decreases.     

Hydrogen bonding in 2‐(2‐oxothiazolidin‐3‐yl)‐4,5‐dihydrothiazolium hydrogen sulfate monohydrate

The asymmetric unit of the title compound, C₆H₉N₂OS₂⁺·HSO₄⁻·H₂O, contains a heterocyclic cation, a hydrogen sulfate anion and a water molecule. There are strong hydrogen bonds between the hydrogen sulfate anions and water molecules, forming an infinite chain along the [010] direction, from which the cations are pendent. The steric, electronic and geometric features are compared with those of similar compounds. In this way, structural relationships are stated in terms of the influence of the sulfate group on the protonation of the heterocycle and on the tautomeric equilibrium in the solid state.     

A multianalyte ELISA for immunochemical screening of sulfonamide,fluoroquinolone and ß-lactam antibiotics in milk samples using class-selective bioreceptors

A multianalyte ELISA has been developed for the simultaneous determination of the most frequently used antibiotic families in the veterinary field following the typical planar microarray configuration, where the identity of the target analyte is encoded by its location in the detection platform (Master et al. in Drug Discovery Today 11:1007-1011, 2006). To accomplish this aim, two individual enzyme-linked immunosorbent assays for sulfonamide and fluoroquinolone antibiotics and an enzyme-linked receptor assay for ss-lactam antibiotics have been combined. The strategy uses microplates coated with the corresponding haptenized proteins in specific sections of the microplate. The samples are mixed with a cocktail containing the bioreagents, and distributed in the wells of the microplate. Identification of the antibiotic present in a particular sample is consequently accomplished by detecting a positive response on the corresponding microplate section. Since the bioreceptors used show a wide recognition of the congeners of each antibiotic family, the multianalyte method is able to detect more than 25 different antibiotics from the three most important antibiotic families. The detectability reached in full-fat milk samples is below the European maximum residue limits. The accuracy and reliability of this multiplexed bioanalytical method have been demonstrated by analyzing blind spiked samples.     

A colorful theorem on transversal lines to plane convex sets

We prove a colorful version of Hadwiger’s transversal line theorem: if a family of colored and numbered convex sets in the plane has the property that any three differently colored members have a transversal line that meet the sets consistently with the numbering, then there exists a color such that all the convex sets of that color have a transversal line. All authors are partially supported by CONACYT research grant 5040017.     

Zeros of the Macdonald function of complex order

The z  -zeros of the modified Bessel function of the third kind _Kν(z)$K_{\nu }(z)$, also known as modified Hankel function or Macdonald function, are considered for arbitrary complex values of the order ν$\nu$. Approximate expressions for the zeros, applicable in the cases of very small or very large |ν|$\left|\nu \right|$, are given. The behaviour of the zeros for varying |ν|$\left|\nu \right|$ or argν$\arg \nu$, obtained numerically, is illustrated by means of some graphics.