The minimal cost maximum matching of a graph

Summary This paper deals with the problem of finding the maximum matching of a weighted graph, having the minimum cost. This problem is solved via a branch and bound algorithm, derived directly fromLand andDoig's technique. The linear programming problem associated with each step of the procedure is solved through a primal-dual algorithm.

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Zusammenfassung Diese Arbeit beschäftigt sich mit demmatching problem. In einem gewichteten Graphen ist dasmaximal matching mit minimalen Kosten gesucht. Zur Lösung wird ein vonLand undDoig beschriebener Branch-and-Bound-Algorithmus verwendet. Das sich je Iterationsschritt ergebende LP-Problem wird mit einem Primal-Dual-Algorithmus gelöst.

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The authors are with the Laboratory of Automatic Control, Istituto di Elettrotecnica ed Elettronica, Politecnico di Milano, I-20133 Milano, Piazza Leonardo da Vinci, 32.     

Electric field gradients at probe nuclei in Ti and Re hosts

The electric field gradients (EFGs) at different probe nuclei in Ti and Re hosts are compared with the predictions of the conduction electron charge shift model. It is found that this model is successful in predicting the sign and, to a zero-order approximation, the magnitude of the EFG when the localized d-contributions are small and the universal correlation is obeyed.     

Cyclopentanone ring expansion leading to functionalized delta-lactams: short synthesis of simple sedum alkaloids

Monosubstituted epoxides react with (cyclopentenyloxy)trimethylsilane to afford, after subsequent oxidative fragmentation, a pair of diastereomeric 8-membered iodolactones. When these lactones are separately treated with sodium azide, followed by reduction over Lindlar's catalyst, lactone ring contraction yields 6-membered monosubstituted lactams. When (R)-1,2-epoxypentane is used in this 5 + 3 - 2 overall ring expansion sequence, one final step involving delta-lactam to piperidine reduction yields natural (-)-halosaline and (-)-epihalosaline in five steps and 12% and 23% overall yields, respectively.     

Effect of Molecular Modification on PCL Foam Formation and Morphology of PCL

Poly(ϵ-caprolactone) was chemically modified by using dicumyl peroxide from 0.25 to 2 % (w/w) and the effects of molecular architecture on the density and morphology of PCL foams were examined. The polymer was first blended with dicumyl peroxide at a low temperature (80°C), to prevent premature peroxide decomposition. The peroxide modification was then performed at different temperatures, from 110°C to 150°C. The reaction kinetic was followed by measuring the dynamical rheological properties of the melt in isothermal experiments by using a parallel plate rheometer. The evolution of the macromolecular structure during the chemical reaction was followed by analyzing the time evolution of the complex viscosity. Foams were prepared from the peroxide modified PCL with a batch foaming process using nitrogen as the foaming agent under different process conditions. As expected, the increase of the molecular modification led to a shift towards higher temperatures of the foaming window and, moreover, influenced the viscoelastic behavior of the expanding polymeric matrix so that the final foam properties are affected.     

Supramolecular hexagonal structure of a segmented liquid crystalline polyester with allyl group as lateral substituent

The molecular structure of the phase—stable at room temperature—for the polymer with formula [ p C₆H₄ COO p C₆H₃(R) p C₆H₃(R) OOC p C₆H₄ O (CH₂)₁₀O ]_x, with R =  CH₂ CHCH₂, is reported. The cell is hexagonal (a = b = 13.43 Å, c = 33.3 Å, γ = 120°), space group P6₃, six chains per unit cell (d_calcd = 1.23 g cm⁻³). The six chains are packed together to give a bundle with the center of mass set at the origin of the unit cell. The allyl groups are placed inside the bundle, thus explaining the unexpected reactivity of the double bonds to give crosslinking when fiber samples are annealed in the solid state. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 1601–1607, 1999     

Extraction of PCDD/PCDF from soil with supercritical CO2: Optimization by a three-level factorial design approach

A highly sensitive and selective voltammetric procedure is described for the simultaneous determination of eleven elements (Cd, Pb, Cu, Sb, Bi, Se, Zn, Mn, Ni, Co and Fe) in water samples. Firstly, differential pulse anodic stripping voltammetry (DPASV) with a hanging mercury drop electrode (HMDE) is used for the direct simultaneous determination of Cd, Pb, Cu, Sb and Bi in 0.1 M HCl solution (pH = 1) containing 2 M NaCl. Then, differential pulse cathodic stripping voltammetry (DPCSV) is used for the determination of Se in the same solution. Zn is subsequently determined by DPASV after raising the pH of the same solution to pH 4. Next, the pH of the medium is raised to pH 8.5 by adding NH₃/NH₄Cl buffer solution for the determination of Mn by DPASV. Ni and Co are determined in the same solution by differential pulse adsorptive stripping voltammetry (DPAdSV) after adding DMG (1 × 10^–4 M). Finally, 1 × 10^–5 M 2-(5-bromo-2-pyridylazo)-5-diethylaminophenol (5-Br-PADAP) is added to the solution for the determination of Fe by DPAdSV. The optimal conditions are described. Relative standard deviations and relative errors are calculated for the eleven elements at three different concentration levels. The lower detection limits for the investigated elements range from 1.11 × 10^–10 to 1.05 × 10^–9 M, depending on the element determined. The proposed analysis scheme was applied for the determination of these eleven elements in some ground water samples.     

Wijsman topology on function spaces

LetC(X,Y) be the space of continuous functions from a metric space (X,d) to a metric space (Y, e).C(X, Y) can be thought as subset of the hyperspaceCL(X×Y) of closed and nonempty subsets ofX×Y by identifying each element ofC(X,Y) with its graph. We considerC(X,Y) with the topology inherited from the Wijsman topology induced onCL(X×Y) by the box metric ofd ande. We study the relationships between the Wijsman topology and the compact-open topology onC(X,Y) and also conditions under which the Wijsman topology coincide with the Fell topology. Sufficient conditions under which the compactopen topology onC(X,Y) is weaker than the Wijsman topology are given (IfY is totally bounded, then for every metric spaceX the compactopen topology onC(X,Y) is weaker than the Wijsman topology and the same is true forX locally connected andY rim-totally bounded). We prove that a metric spaceX is boundedly compact iff the Wijsman topology onC(X, ℝ) is weaker than the compact-open topology. We show that ifX is a σ-compact complete metric space andY a compact metric space, then the Wijsman topology onC(X,Y) is Polish.     

Playing with PtII and ZnII Coordination to Obtain Luminescent Metallomesogens

Blue–green luminescent terpyridine-containing Pt^II and Zn^II complexes are reported. Equipped with lipophilic gallate units, which act as monodentate ancillary coordinating ligands and/or as anions, they display low-temperature mesomorphic properties (lamello-columnar and hexagonal mesophases for Pt^II and Zn^II complexes, respectively). The mesomorphic properties were investigated by polarised optical microscopy, differential scanning calorimetry, thermogravimetric analysis and X-ray scattering of bulk materials and oriented thin films. The model of self-assembly into the lamello-columnar phase of the Pt^II complex has been described in detail. The optical properties of the complexes were investigated in the liquid and condensed liquid crystalline states, highlighting the delicate balance between the role of the metal in determining the type of excited state responsible for the emission, and the role of the ancillary ligand in driving intermolecular interactions for proper mesophase formation.     

Transport properties of poly(ethylene terephthalate)/Rodrun 3000 blends

The transport properties of incompatible blends of poly(ethylene terephthalate) (PET) and a thermotropic liquid crystalline polymer (TLCP) composed of 40 mol% of PET and 60 mol% of p-hydroxybenzoic acid (Rodrun 3000) have been investigated using dichloromethane as permeant. Films, obtained by a blown film extrusion process, were analyzed and compared with the same samples stored 2 and 15 days at 60°C. With respect to the as-blown films, blends submitted to physical aging show a decrease in permeability by a percentage that increases with the amount of the LC phase present and a larger contribution derived from the polymeric matrix. The decrease of permeability is essentially attributed to a lowering of sorption because diffusional behavior for the different samples is the same.     

Q-switched Ti:Er:LiNbO3 waveguide laser

Q-switched operation of a Ti:Er:LiNbO3 waveguide laser has been achieved with up to 2.4 W pulse peak power (0.18J) at 2kHz repetition frequency with an intracavity Mach–Zehnder-type amplitude modulator. A theoretical model has been developed to describe the laser operation. Good agreement between numerical and experimental results has been achieved. Significant potential for improvement is predicted.