List coloring triangle‐free hypergraphs

A triangle in a hypergraph is a collection of distinct vertices u, v, w and distinct edges e, f, g with , and . Johansson [Tech. report (1996)] proved that every triangle‐free graph with maximum degree Δ has list chromatic number . Frieze and Mubayi (Electron J Comb 15 (2008), 27) proved that every linear (meaning that every two edges share at most one vertex) triangle‐free triple system with maximum degree Δ has chromatic number . The restriction to linear triple systems was crucial to their proof. We provide a common generalization of both these results for rank 3 hypergraphs (edges have size 2 or 3). Our result removes the linear restriction from 8 , while reducing to the (best possible) result [Johansson, Tech. report (1996)] for graphs. In addition, our result provides a positive answer to a restricted version of a question of Ajtai Erd?s, Komlós, and Szemerédi (combinatorica 1 (1981), 313–317) concerning sparse 3‐uniform hypergraphs. As an application, we prove that if is the collection of 3‐uniform triangles, then the Ramsey number satisfies for some positive constants a and b. The upper bound makes progress towards the recent conjecture of Kostochka, Mubayi, and Verstraëte (J Comb Theory Ser A 120 (2013), 1491–1507) that where C₃ is the linear triangle. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 47, 487–519, 2015     

Hypergraphs with independent neighborhoods

For each k ≥ 2, let ρ _k ∈ (0, 1) be the largest number such that there exist k-uniform hypergraphs on n vertices with independent neighborhoods and (ρ _k + o(1))( _k ⁿ ) edges as n → ∞. We prove that ρ _k = 1 − 2logk/k + Θ(log log k/k) as k → ∞. This disproves a conjecture of Füredi and the last two authors.     

Spectrophotometric determination of Rauwolfia alkaloids: estimation of reserpine in pharmaceuticals.

A simple, sensitive and economically viable spectrophotometric method for the determination of some Rauwolfia alkaloids (ajmaline, ajmalicine, reserpine and yohimbine-HCl) has been developed. The method involves the oxidation of Rauwolfia alkaloids by iron(III) and subsequent complexation of iron(II) with 1,10-phenanthroline, forming a red-colored complex having the maximum absorbance at 510 nm. The method is applied to the determination of reserpine in tablets of pharmaceutical formulations. The common excipients do not interfere with the proposed method. A statistical comparison of these results with those of a reported method shows good agreement and indicates no significant difference in the precision.     

Chromatographic studies of some cephalosporins on thin layers of silica gel G–zinc ferrocyanide

A simple, selective and precise thin‐layer chromatographic method has been developed for the analysis of eight cephalosporin antibiotics, namely cephadroxil, cephalexin, cefixime, cefaclor, cefpodoxime proxetil, cefuroxime axetil, cefotaxime sodium and ceftriaxone sodium. The hR_F values of these cephalosporins were investigated on silica gel G–zinc ferrocyanide layers. Mixing of zinc ferrocyanide with silica gel G resulted in a decrease in hR_F values, removal of tailing and better resolutions. The influence of silica gel G–zinc ferrocyanide ratio and mobile phases on the chromatographic behavior of cephalosporins on thin layers was investigated. Cephalosporins were selectively separated in their binary and ternary synthetic mixtures and pharmaceutical formulations. Quantitative separations of cephalosporins from their synthetic mixtures were also achieved with good recoveries (97.8–100.3%). Copyright © 2010 John Wiley & Sons, Ltd.     

Preparation, characterization, and reactivities of thienyl nickel complexes bearing indenyl ligands

The complexes (1-R, 2-R′-indenyl)NiPPh₃(thienyl) (R′=H, R=Me (1); Et (2); i-Pr (3); CH₂Ph (4); R′=Ph, R=Me (5)) have been prepared and characterized by spectroscopic techniques and, in the case of 1, 2 and 5, by X-ray crystallographic studies. When combined with MAO, these compounds catalyze the polymerization of phenylacetylene to cis-transoidal poly(phenylacetylene) with M_w in the range of 5-7.5×10⁴ Da. NMR studies have revealed that MAO methylates these complexes without ionizing the Nithienyl bond; this implies that the polymerization reactions likely follow a non-cationic mechanism similar to that catalyzed by the corresponding NiCCPh complexes studied previously. Complexes 1-5 reacted with CF₃SO₃H to produce the corresponding NiOSO₂CF₃ compounds by protonation at the α-C of the thienyl moiety. The compound (1-Bzindenyl)Ni(PPh₃)(OSO₂CF₃) (9) has been isolated and fully characterized.     

Constructions of non-principal families in extremal hypergraph theory

A family F of k-graphs is called non-principal if its Turán density is strictly smaller than that of each individual member. For each k?3 we find two (explicit) k-graphs F and G such that {F,G} is non-principal. Our proofs use stability results for hypergraphs. This completely settles the question posed by Mubayi and Rödl [On the Turán number of triple systems, J. Combin. Theory A, 100 (2002) 135-152].Also, we observe that the demonstrated non-principality phenomenon holds also with respect to the Ramsey-Turán density as well.     

Synthesis of a New Cu(II)-Ion Imprinted Polymer for Solid Phase Extraction and Preconcentration of Cu(II)

A new Cu(II)-ion imprinted polymer (IIP) has been synthesized by copolymerizing salicylic acid and formaldehyde as a monomer and crosslinker, respectively in the presence of Cu(II)-4-(2-pyridylazo) resorcinol complex. The imprinted Cu(II) ions were completely removed by leaching the IIP with 0.05 M EDTA. The maximum adsorption capacity for Cu(II) ions was 310 μg g⁻¹ at pH 6. The IIP was repeatedly used in adsorption–desorption experiments for seven times with recoveries ~95%. The relative selectivity factor (α _r) values of Cu(II)/Zn(II), Cu(II)/Cd(II), Cu(II)/Ni(II) and Cu(II)/Co(II) are 3.17, 2.90, 2.47 and 3.37, respectively. The detection limit corresponding to three times the standard deviation of the blank was found to be 3.0 μg L⁻¹. The developed IIP has also been tested for preconcentration and recovery of Cu(II) ions from water samples.

     

NOTE New Upper Bounds for a Canonical Ramsey Problem

f (l,k) be the minimum n with the property that every coloring yields either with , or with all distinct. We prove that if , then as . This supports the conjecture of Lefmann, R?dl, and Thomas that . Received July 2, 1998