Combining Swaps and Node Weights in an Adaptive Greedy Approach for the Maximum Clique Problem

In this work, the NP-hard maximum clique problem on graphs is considered. Starting from basic greedy heuristics, modifications and improvements are proposed and combined in a two-phase heuristic procedure. In the first phase an improved greedy procedure is applied starting from each node of the graph; on the basis of the results of this phase a reduced subset of nodes is selected and an adaptive greedy algorithm is repeatedly started to build cliques around such nodes. In each restart the selection of nodes is biased by the maximal clique generated in the previous execution. Computational results are reported on the DIMACS benchmarks suite. Remarkably, the two-phase procedure successfully solves the difficult Brockington-Culberson instances, and is generally competitive with state-of-the-art much more complex heuristics.     

Weighted approximation of functions on the real line by Bernstein polynomials

The authors give error estimates, a Voronovskaya-type relation, strong converse results and saturation for the weighted approximation of functions on the real line with Freud weights by Bernstein-type operators.     

R.F. (280 MHz) EPR imaging of extended samples: Apparatus and preliminary results

This paper presents the preliminary results obtained using an Electron Paramagnetic Resonance imaging apparatus operating at 280 MHz. The acquisition technique and the procedure used to obtain the spin density spatial localization are presented and specimen images of extended samples are given. The accuracy of the images and the spatial resolution are also discussed.     

Solvent-dependent host–guest complexation of two homologous merocyanines by a water-soluble calix[8]arene: Spectroscopic analysis and structural calculations

The sulfonated calixarene I₈C₁₂ acts as a host for homologous merocyanines Mc1 and Mc2 in organic solvents, exhibiting neither selectivity towards the guest dyes nor solvent dependence of the complexation equilibria. In water, on the contrary, only the lower homologue, Mc1, is solubilized in the presence of the calixarene. A combination of UV–visible and fluorescence spectroscopic and photophysical analysis and MD structural simulation of the calixarene-dye complexes was employed to account for the observations, and suggests that a radical change in the complexation mode occurs upon moving from an organic to an aqueous environment.     

Lithiation and electrophilic substitution of 8-chlorodibenz[b,f][1,4]-oxazepine-10-tert-butylcarbamate: The preparation of novel fused heterocyclic derivatives of 8-chlorodibenzoxazepine

Lithiation of 8-chlorodibenz[b,f][1,4]oxazepine-10-tert-butylcarbamate ( 1 ) is described. Electrophilic substitution of the resulting N-Boc dibenzoxazepine α- lithioamine 2 with ketones, aldehydes, nitriles, iso-cyanates and imines, followed by an in-situ cyclization, gave fused carbamates 5–26 , fused 2H-imidazol-2-ones 27–29 , fused hydantoins 30–32 , and fused ureas 33–35 , respectively, in 11–66% yield.     

Parallel transport in the determinant line bundle: The non-zero index case

For a product family of Weyl operators of possibly non-zero index on a compact manifoldX, we express parallel transport in the determinant line bundle in terms of the spectral asymmetry of a Dirac operator on ×X. This generalizes the results of [7], where we dealt only with invertible operators.Supported in part by NSF Grant No. PHY 8605978 and the Robert A. Welch FoundationSupported in part by NSF Grant No. PHY 8215249     

Nickel-Ruthenium Mixed-Metal Carbonyl Clusters Syntheses and Solid State Structures of the Two Tetrahedral Clusters [PPh4][NiRu3(μ3 H)(CO)9(μ-CO)3] and [NEt4]2[NiRu3(CO)8(μ-CO)4]

Redox condensation of [Ru₃H(CO)₁₁]- with Ni(CO)₄, in tetrahydrofuran solution, under a nitrogen atmosphere, yields the tetranuclear anion [NiRu_H(CO)₁₁)-. Subsequent deprotonation with Bu'OK in acetonitrile solution leads to the formation of the related dianion. Both anions have been characterized by spectroscopic techniques, elemental analysis and single crystal X-ray diffraction. [PPh₄][NiRu₃H(CO)₁₂] crystallizes in the triclinic space group PI with unit cell dimensionsof a = 11.842(2) Å,b = 12.335(3) Å, c = 13.3080) Å,a = 91.89(2)°, = 93.35(1)°,y = 96.41(2)°, Z = 2, V= 1926.9(7) Å'. The NiRu₃, metal core of the molecule defines a distorted tetrahedron with nine terminal and three edge bridging carbonyl groups. The hydrido ligand was located by difference Fourier techniques and was found to bridge the NiRu₂ basal triangle at a distance of 0.88(6) A from this plane. Selected average distances and angles are: Ru-Ru = 2.839 Å, Ru-Ni = 2.640 Å, Ru-C, = 1.910 A,Ru-C _b = 2.084 Å, Ni-C _b = 2.022 Å, Ru-H = 1.77 Å, C-0, = 1.135 Å, C-O _b = 1.159 Å, M-C-O, = 176.3°,M-C--O _b = 139.3°;other distances are: Ni-C₁ = l.758(7) Å, Ni-H= 1.85(7) Å. [NEt₄]₂[NiRu₃(CO)₁₂] crystallizes in the orthorhombic space group Pnma (no. 62) with unit cell dimensions ofa=20.247(5) Å,b = 15.038(4)Å,c = 12.079(3) Å, Z=4, V=3678(2) A'. The molecule contains a tetrahedral NiRu₃ core with eight terminal and four edge bridging carbon monoxide groups which bridge the three Ni-Ru and one Ru-Ru bond. Average distances and angles are: Ru -Ru =2.3050A Ru-Ni 2.648 Å, Ru-C _t = 1.878 Å, Ru-C _b 2.045 Å, Ni-C _b = 2.055 Å, C-O _t = 1.145 Å, C-01,=1.157 Å, M-C-O,= 176.9°, M-C-O _b = 138.6°; other distance is: Ni-C _t = 1.754(10) Å,t = terminal,b = bridging.     

Colourants and opacifiers in seventh and eighth century glass investigated by spectroscopic techniques

Glass fragments dating from the seventh and eighth century AD were excavated in the Crypta Balbi in Rome. They were studied to detect agents involved in colour development and opacification. Reflectance spectra recorded on powdered samples revealed the contribution of Fe(II), Fe(III), Mn(III), Cu(II), and Co(II) ions in determining colour hues. The effect of the Mn/Fe atomic ratio on glass colour is discussed. It is apparent that medieval glassmakers in Italy could obtain a wide range of colours by exploiting the presence of iron and manganese as contaminants of sand and flux and controlling the amount of oxygen let into the furnace. X-ray diffraction and scanning electron microscopy coupled with energy-dispersive X-ray analysis were used to study opaque fragments. The presence of calcium antimonate was detected in white, blue, and blue-green fragments, and elemental copper was detected in a red glass.     

Analytical methodologies for identifying a polypeptide antibiotic

This article discusses the development of various analytical methods for identification and quantification of residues of antibiotics in meeting international regulatory requirements, and, as an example, overviews the screening, purification, fractionation and analytical assays of bacitracin, a commonly applied polypeptide antibiotic mixture. Attention is focused on the development of chemical methods, as they provide extraordinary performance, in terms of sensitivity and selectivity, for measuring residual levels of the various components of bacitracin in food and other matrices; the non-compound specific biological assay is discussed only briefly. Because of its advantages, state-of-the-art high-performance liquid chromatography (HPLC) coupled with various detection techniques, in particular mass spectrometry (MS), has recently gained in popularity in confirming and quantifying drug residues. In this article, the authors also outline the latest results on the application of highly sensitive and selective LC-MS in analysis of bacitracin residues in milk and animal tissues. LC-MS is suggested as the technique of choice for confirmation of polar polypeptide antibiotics and the like at trace concentrations.