On the symmetric travelling salesman problem I: Inequalities

We investigate several classes of inequalities for the symmetric travelling salesman problem with respect to their facet-defining properties for the associated polytope. A new class of inequalities called comb inequalities is derived and their number shown to grow much faster with the number of cities than the exponentially growing number of subtour-elimination constraints. The dimension of the travelling salesman polytope is calculated and several inequalities are shown to define facets of the polytope. In part II (On the travelling salesman problem II: Lifting theorems and facets) we prove that all subtour-elimination and all comb inequalities define facets of the symmetric travelling salesman polytope.     

Ultrasonic depolymerization of aqueous polyvinyl alcohol.

Ultrasonication has proved to be a highly advantageous method for depolymerizing macromolecules because it reduces their molecular weight simply by splitting the most susceptible chemical bond without causing any changes in the chemical nature of the polymer. Most of the effects involved in controlling molecular weight can be attributed to the large shear gradients and shock waves generated around collapsing cavitation bubbles. In general, for any polymer degradation process to become acceptable to industry, it is necessary to be able to specify the sonication conditions which lead to a particular relative molar mass distribution. This necessitates the identification of the appropriate irradiation power, temperature, concentration and irradiation time. According to the results of this study the reactors constructed worked well in depolymerization and it was possible to degrade aqueous polyvinyl alcohol (PVA) polymer with ultrasound. The most extensive degradation took place at the lowest frequency used in this study, i.e. 23 kHz, when the input power was above the cavitation threshold and at the lowest test concentration of PVA, i.e. 1% (w/w). Thus this study confirms the general assumption that the shear forces generated by the rapid motion of the solvent following cavitational collapse are responsible for the breakage of the chemical bonds within the polymer. The effect of polymer concentration can be interpreted in terms of the increase in viscosity with concentration, causing the molecules to become less mobile in solution and the velocity gradients around the collapsing bubbles to therefore become smaller.     

Some Unusual Reactions in Organophosphorus Chemistry

Methylenephosphinophosphorane 1 reacts with azides without evolution of nitrogen to give zwitterionic phosphorazide 3 and iminophosphorazide 4 , which are in equilibrium to each other; 1 reacts with hexafluoroacetone (HFA) in a different way to give zwitterionic product 5 , which may have the ylidic structure 5' . HFA and thio-HFA react analogously with methylenediphosphines 6 to give corbodiphosphoranes 7 . Reaction of 6 with activated alkenes 9 gives monoylide 10 , which is a useful synthone for the synthesis of fluorosubstituted conjugated triene 12 and diylides 13 and 14 . Reaction of 10 with TOB gives unusually stable betaine 15 . Reaction of the other activated alkene 16 with 6 unexpectedly gave the unusual zwitterionic compound 17 .     

The Effect of Oxygen on Conversion in the Organic Peroxide-initiated High-Pressure Polymerization of Ethylene

To initiate the high-pressure polymerization of ethylene, oxygen is used together with organic peroxides in a number of tubular reactor processes. Since molecular oxygen is capable of promoting or inhibiting radical polymerization, depending on the reaction conditions chosen, controlled experiments were carried out to clarify these aspects of high pressure ethylene polymerization. In continuous polymerization tests carried out at 1700 bar and temperatures between 110 and 320°C, conversions were determined with tert-amyl perneodecanoate and di-tert-butyl peroxide initiation in the presence of various quantities of oxygen. Batch tests using a photo-initiator together with oxygen were also carried out. A comparison with polymerizations under conditions of careful elimination of oxygen shows no effect on the peroxide-initiated polymerization up to temperatures of 160 to 170°C. Although oxygen is an initiator at higher temperatures, the conversions obtained from the simultaneous addition of controlled quantities of oxygen and organic peroxides is lower than that obtained by adding together the conversions from the separate polymerizations.     

Ecotoxicological characterisation of exhaust particulates from diesel-powered light-duty vehicles

Diesel exhaust is one of the major sources of fine and ultrafine particulate matter in urban air. Toxicity of diesel-powered engine emissions has been quite widely assessed, however, much less information is available on their ecotoxicity. In our study the kinetic version of the Vibrio fischeri bioluminescence inhibition bioassay, based on the ISO 21338:2010 standard, was used to characterise the ecotoxicity of diesel-powered cars. The method is sensitive enough to test the ecotoxic effect of the emission of individual vehicles. In general, significant positive correlation was found between ecotoxicity (expressed as Toxic Unit /TU/values) and total carbon (TC) as well as between TU and polycyclic aromatic hydrocarbon (PAH) concentrations.      

On Resin Modification of Monosaccharides

Ellman's dihydropyran resin was used for selective protection of monosaccharide thioglycosides and glycosides. Following on‐resin acylation and subsequent cleavage of the polymer‐bound intermediates, product components having selectively unblocked hydroxyl functions could be obtained.      

Synthesis of Sialyl Lewis X Analogues

Abstract

Sialyl Lewis X (SLe^x) analogs 2a and 2b were synthesised, where the N-acetyl-D-glucose and the D-galactose units of SLe^x 1 were replaced with an alkyl and a heteroalkyl spacer. Sulphate ester 6i was also synthesised from alcohol 6b and chlorosulphonic acid. A novel promoter, silver mercaptoethanesulphonate, was used to synthesise α-sialosides 2c. 7b and 7c.     

Synthesis of PAF,an Antifungal Protein from P. chrysogenum,by Native Chemical Ligation: Native Disulfide Pattern and Fold Obtained upon Oxidative Refolding

The folding of disulfide proteins is of considerable interest because knowledge of this may influence our present understanding of protein folding. However, sometimes even the disulfide pattern cannot be unequivocally determined by the available experimental techniques. For example, the structures of a few small antifungal proteins (PAF, AFP) have been disclosed recently using NMR spectroscopy but with some ambiguity in the actual disulfide pattern. For this reason, we carried out the chemical synthesis of PAF. Probing different approaches, the oxidative folding of the synthetic linear PAF yielded a folded protein that has identical structure and antifungal activity as the native PAF. In contrast, unfolded linear PAF was inactive, a result that may have implications concerning its redox state in the mode of action.     

Heterobimetallic Cuprates Consisting of a Redox‐Switchable,Silicon‐Based Metalloligand: Synthesis,Structures, and Electronic Properties

A series of bimetallic silyl halido cuprates consisting of the new tripodal silicon‐based metalloligand [κ³N‐Si(3,5‐Me₂pz)₃Mo(CO)₃]^? is presented (pz=pyrazolyl). This metalloligand is straightforwardly accessible by reacting the ambidentate ligand tris(3,5‐dimethylpyrazolyl)silanide ({Si(3,5‐Me₂pz)₃}^?) with [Mo(CO)₃(η⁶‐toluene)]. The compound features a fac‐coordinated tripodal chelating ligand and an outward pointing, “free” pyramidal silyl donor, which is easily accessible for a secondary coordination to other metal centers. Several bimetallic silyl halido cuprates of the general formula [CuX{μ‐κ¹Si:κ³N‐Si(3,5‐Me₂pz)₃Mo(CO)₃}]^? (X=Cl, Br, I) have been synthesized. The electronic and structural properties of these complexes were probed in detail by X‐ray diffraction analysis, electrospray mass spectrometry, infrared‐induced multiphoton dissociation studies, cyclic voltammetry, spectroelectrochemistry, gas‐phase photoelectron spectroscopy, as well as UV/Vis and fluorescence spectroscopy. The heterobimetallic complexes contain linear two‐coordinate copper(I) entities with the shortest silicon–copper distances reported so far. Oxidation of the anionic complexes in methylene chloride and acetonitrile solutions at ${E{{0\hfill \atop 1/2\hfill}}}$ =?0.60 and ?0.44 V (vs. ferrocene/ferrocenium (Fc/Fc⁺)), respectively, shows substantial reversibility. Based on various results obtained from different characterization methods, as well as density functional theory calculations, these oxidation events were attributed to the Mo⁰/Mo^I redox couple.