Packing triangles in low degree graphs and indifference graphs

We consider the problems of finding the maximum number of vertex-disjoint triangles (VTP) and edge-disjoint triangles (ETP) in a simple graph. Both problems are NP-hard. The algorithm with the best approximation ratio known so far for these problems has ratio 3/2+?, a result that follows from a more general algorithm for set packing obtained by Hurkens and Schrijver [On the size of systems of sets every t of which have an SDR, with an application to the worst-case ratio of heuristics for packing problems, SIAM J. Discrete Math. 2(1) (1989) 68-72]. We present improvements on the approximation ratio for restricted cases of VTP and ETP that are known to be APX-hard: we give an approximation algorithm for VTP on graphs with maximum degree 4 with ratio slightly less than 1.2, and for ETP on graphs with maximum degree 5 with ratio 4/3. We also present an exact linear-time algorithm for VTP on the class of indifference graphs.     

Time-resolved fluorescence of carbon nanotubes and its implication for radiative lifetimes

The temporal evolution of fluorescence from isolated single-wall carbon nanotubes (SWNTs) has been investigated using optical Kerr gating. The fluorescence emission is found to decay on a time scale of 10 ps. This fast relaxation arises from nonradiative processes, the existence of which explains the relatively low observed fluorescence efficiency in isolated SWNTs. From the measured decay rate and a determination of fluorescence quantum efficiency, we deduce a radiative lifetime of 110 ns.     

5‐Nitro‐N‐phenyl‐2‐thio­fur­amide

The title compound, C₁₁H₈N₂O₃S, crystallizes with two crystallographically independent mol­ecules, which are conformationally almost identical, per asymmetric unit. The dihedral angles between the phenyl and 2‐thio­fur­amide planes are 46.3 (1) and 47.0 (1)° for the first and second mol­ecule, respectively. Strong intramolecular N—H?O hydrogen bonds [N?O 2.664 (2) and 2.661 (2) Å] dictate an anti conformation of the C=S groups in relation to the furan‐O atoms.     

3‐[(2‐Oxo‐1‐naphthylidene)methyl­amino]­benzoic acid

The title compound, C₁₈H₁₃NO₃, exists as a keto­amino tautomer implying a fairly short N—H?O intramolecular hydrogen bond between the 2‐naphthalenone and amino moieties [N?O 2.531 (3) Å] which is enhanced by the π‐electron delocalization effect. The naphthald­imine and 3‐carboxy­phenyl fragments are inclined at an angle of 4.41 (7)°, so the mol­ecule is almost planar. The mol­ecules are connected by intermolecular O—H?O hydrogen bonds between the carboxy and keto O atoms, forming infinite chains around the twofold screw axes parallel to b .     

Synthesis and biological evaluation of two novel 2′-substituted tiazofurin analogues

Two novel tiazofurin analogues, 2-(2-benzamido-2-deoxy-β-d-ribofuranosyl)thiazole-4-carboxamide 4 and 2-(2-azido-2-deoxy-β-d-ribofuranosyl)thiazole-4-carboxamide 5, have been synthesized starting from d-glucose and evaluated for their in vitro cytotoxicity against several human leukaemia and solid tumour cell lines.     

Diamond coating deposition by synergy of thermal and laser methods—A problem revisited

Diamond coatings were deposited by synergy of the hot filament CVD method and the pulse TEA CO₂ laser, in spectroactive and spectroinactive diamond precursor atmospheres. Resulting diamond coatings are interpreted relying on evidence of scanning electron microscopy as well as microRaman spectroscopy. Thermal synergy component (hot filament) possesses an activating agent for diamond deposition, and contributes significantly to quality and extent of diamond deposition. Laser synergy component comprises a solid surface modification as well as the spectroactive gaseous atmosphere modification. Surface modification consists in changes of the diamond coating being deposited and, at the same time, in changes of the substrate surface structure. Laser modification of the spectroactive diamond precursor atmosphere means specific consumption of the precursor, which enables to skip the deposition on a defined substrate location. The resulting process of diamond coating elimination from certain, desired locations using the CO₂ laser might contribute to tailoring diamond coatings for particular applications. Additionally, the substrate laser modification could be optimized by choice of a proper spectroactive precursor concentration, or by a laser radiation multiple pass through an absorbing medium.     

Solvent and Structural Effects on the UV–Vis Absorption Spectra of Some 4,6-Disubstituted-3-Cyano-2-Pyridones

A series of 4,6-disubstituted-3-cyano-2-pyridones was synthesized and their UV?CVis absorption spectra were recorded in the region 200?C600?nm in the set of selected solvents. The effects of solvent dipolarity/polarizability and solvent?Csolute hydrogen-bonding interactions on the spectral shifts were analyzed by means of the linear solvation energy relationship concept of Kamlet and Taft. The influence of solvents as well as substituents on the 2-pyridone/2-hydroxypyridine tautomeric equilibration was evaluated. The absorption band maximum of the 2-hydroxypyridine form is found to appear at a shorter wavelength than that of the 2-pyridone form in all investigated solvents. The replacement of the methyl and phenyl groups at position 6 of the pyridone ring, by a hydroxy group, significantly changes the solvatochromic behavior of the investigated pyridones.     

Development and Evaluation of a Kinetic‐Spectrophotometric Method for Determination of Arginine

A kinetic method for the determination of micro quantities of amino acid arginine (Arg) is described in this paper. The catalytic activity of cobalt in the reaction of oxidation of purpurin (1,2,4‐trihydroxy‐antraquinone, PP) by hydrogen peroxide in alkaline buffer solution decreases in the presence of micro quantities of arginine, because of the formation of the complex. Operating conditions for the successful determination of arginine were optimized. The optimized conditions yielded a theoretical detection limit of 1.45 μg mL^?1. Kinetic equations are proposed for the investigated process. The interference effects of certain foreign ions and amino acids upon the reaction rate were studied and removed in order to assess the selectivity of the method. The developed procedure was successfully applied to the determination of arginine in various pharmaceutical samples. The typical feature of this procedure is that determination can be carried out at room temperature and in a short analysis time. The newly developed method is simple, inexpensive and efficient for use in the analysis of a large number of samples.     

Supramolecular solid-state structure,potential energy surfaces and evaluation of antiproliferative effect of 2-benzothiazolylhydrazone derivatives in vitro

The in situ condensation reaction of 2-hydrazinobenzothiazole with salicylaldehyde, 3,4-dihydroxybenzaldehyde, 2,4-dihydroxybenzaldehyde, 2,5-dihydroxybenzaldehyde, 2,3-dihydroxybenzaldehyde, 2-hydroxy-1-naphthaldehyde, 2-methoxy-1-naphthaldehyde, 4-methoxy-1-naphthaldehyde and 6-methoxy-2-naphthaldehyde produced 9 hydrazone Schiff bases (L1–L9, respectively) which were identified and characterized by elemental analysis, IR and NMR spectroscopy. The crystal and molecular structures of four Schiff bases (L1, L7–L9) have been determined by the single-crystal X-ray diffraction method confirming the imino form of L1 and the amino tautomeric form of L7–L9 compounds. Molecular structure analysis also confirmed that reported compounds are E-isomers relative to exo C = N imino bond. The N_hydrazino–H group of amino tautomers forms N_hydrazino–H···N_thiazolyl intermolecular hydrogen bonds shaping molecules into R ₂ ² (8) rings, while imino tautomer of L1 forms C(4) infinite helical chains via N_thiazolyl–H···N_hydrazino type of intermolecular hydrogen bond. The methoxy group (L7–L9) further shaped these primary supramolecular synthons into different supramolecular arrangements via C–H···O, C–H···N and C–H···S intermolecular hydrogen bonds. The role of aryl substituents in the shaping and stabilization of supramolecular architectures of L1, L7–L9 is supported by quantum chemical calculations. Strong antiproliferative effects on tumor cells and cytotoxic effects on fibroblasts are shown for all ligands L1–L9 with exception of L6 and L7 that had no effect on fibroblast cells.     

1:1 and 1:2 Complexes of Mercury(II) Halides with 1,3-Thiazolidine-2-thione. Spectral, Thermal, and Crystal Structure Studies

The series of compounds of the general formulae HgX₂(tzdtH) and HgX₂(tzdtH)₂ (X = Cl, Br, I; tzdtH = 1,3-thiazolidine-2-thione) have been prepared, as well as Hg(tzdt)₂. IR, ¹H, and ¹³C NMR spectral data of the complexes indicate thione donation, which is confirmed by the crystal structure analyses of [HgBr₂(tzdtH)]₂, [HgI₂(tzdtH)]₂, and HgI₂(tzdtH)₂. The structures of [HgBr₂(tzdtH)]₂ and [HgI₂(tzdtH)]₂ consist of centrosymmetric doubly bridged dimers, but they are not isostructural. The asymmetry in the HgX₂Hg bridge is more pronounced in the bromo than in the iodo derivative [S–Hg–X(terminal) is 138.19(9)° for X = Br and 123.49(10)° for X = I], which is accompanied by the stronger Hg–S covalent bond in the bromo than in the iodo complex [2.435(4) vs. 2.510(3) Å]. The Hg–X(bridging) (X = Br, I) bond distances are shorter than the sum of van der Waals radii for mercury and X. Dimeric centrosymmetric complex units are held together only by van der Waals forces in [HgI₂(tzdtH)]₂, while in [HgBr₂(tzdtH)]₂ there is an intramolecular hydrogen bond of N–H Br type (3.34(1) Å). HgI₂(tzdtH)₂ exists as a mononuclear tetrahedral complex with two long Hg–S [2.672(1) Å] and two short Hg–I bond distances [2.688(1) Å] related by a twofold axis. The molecules of HgI₂(tzdtH)₂ are linked into infinite chains along the c axis by intermolecular N–H S [3.38(1) Å] hydrogen bonds.