A theorem on integer flows on cartesian products of graphs

It is shown that the Cartesian product of two nontrivial connected graphs admits a nowhere‐zero 4‐flow. If both factors are bipartite, then the product admits a nowhere‐zero 3‐flow. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 93–98, 2003     

A remark on Mansfield's imprimitivity theorem

We show that the Morita equivalence part of Mansfield's Imprimitivity Theory can be obtained by Green's Imprimitivity Theorem (and duality theory).

     

Stereoselective synthesis of cis-p-menth-8-ene-1,7-diol, cis-p-menthane-1,7-diol, and cis-p-menthane-1,7,8-triol

The natural products cis-p-menthane-1,7-diol (cis-IV), cis-p-menth-8-ene-1,7-diol (cis-I) and cis-p-menthane-1,7,8-triol (cis-II) are obtained starting from the corresponding cis-cyanohydrins, cis-2 and cis-7, respectively, by chemical transformation of the cyano into the hydroxymethyl group. The key step of the synthesis is the very high cis-selectivity (> or = 96 %) of the MeHNL-catalyzed HCN addition to 4-alkylcyclohexanones. From 4-isopropylcyclohexanone (1) the cyanohydrin cis-2 and from 4-(1-methylvinyl)cyclohexanone (6) the cyanohydrin cis-7 result almost quantitatively. Regioselective hydroxylation of cis-I affords the triol cis-II. X-ray crystal structure determinations of the final products confirm their cis-configuration.     

Physico-chemical aspects of polyethylene processing in an open mixer. Part 21: Improved product yields on true bimolecular hydroperoxide decomposition

The product yields from the reaction between two hydroperoxide groups have been re-calculated. This is a consequence of the fact that β-scission of secondary alkoxy radicals cannot be neglected in the high temperature range of the polyethylene processing experiments (170-200 °C). It must be taken into account in addition to disproportionation/combination and hydrogen abstraction by alkoxy radicals. The increased complexity caused by the additional reaction results mainly from the larger number of caged radical pairs involved in the reactions and also in the calculations. Among other products it becomes possible to calculate the yields of aldehyde and vinyl groups that would not result from hydroperoxide decomposition in the absence of β-scission. The yields of the main oxidation products such as alcohols, ketones and trans-vinylene groups are reduced to some extent in comparison with the values calculated if β-scission is neglected. The vinyl group yield corresponds to slightly more than 10% of the yield of trans-vinylene groups in the temperature range of the experiments. The aldehyde yield is significantly larger than the vinyl group yield and is important in the whole temperature range examined. Main-chain scissions are important at the temperatures of the experiments. They become more important than the sum of the different combination reactions from a temperature of 200 °C on.     

First lipase catalysed resolution of epoxy enol esters

We report the first enzyme-catalysed kinetic resolution of epoxy enol esters. The lipase-promoted hydrolysis of these compounds provided α-hydroxyketones or α-hydroxyaldehydes (arising from the spontaneous rearrangement of the epoxy enols) and the residual esters with moderate to good enantioselectivity (E up to 100).     

Glass and polymeric membrane electrodes for the measurement of pH in milk and cheese

While there is a considerable interest in the food industry in determining various analytes using ion-selective electrodes (ISEs), only few reports describe their use for direct measurements in food. In this study, the suitability of glass electrodes and ionophore-based solvent polymeric ISEs for the determination of pH in Process cheese, Cheddar cheese and milk was investigated. The liquid junction potential between a 3 M KCl bridge electrolyte and diluted as well as undiluted Process cheese was found to be negligible. Reference electrodes with ceramic plug and sleeve-type junctions performed well, although precautions needed to be taken to prevent plugging at the junctions. While the protein rennet casein posed no problems in pH measurements, the extraction of neutral lipophilic compounds or hydrophobic peptides into solvent polymeric membranes was evident, resulting in some loss of selectivity for monovalent cations upon exposure to cheese. However, it was found that ISEs based on tridodecylamine (R₃N) as ionophore and o-nitrophenyl octyl ether (oNPOE) as plasticizer can be used to accurately measure the pH of milk and, after desensitization of the electrodes in a cheese emulsion, of diluted Process cheese. Since pH measurements with a glass electrode showed that emulsions of cheese moderately diluted to a cheese content of 70% have the same pH as undiluted cheeses, it is possible to determine the pH in cheese with ionophore-based ISEs. R₃N membranes also performed well in undiluted milk.     

Intramolecular,Stoichiometric (Li,Mg, Zn) and Catalytic (Ni,Pd, Pt) Metallo-Ene Reactions in Organic Synthesis [New Synthetic Methods (75)]

Metallo-ene reactions, hardly recognized until very recently, have experienced a breathtaking development when applied in an intramolecular sense. Efficient regio- and stereoselective magnesium-ene cyclizations have served as a cornerstone for numerous syntheses of structurally diverse natural products (e.g., sesquiterpenes of marine or plant origin, alkaloids, fragrances, insect defense compounds, and a fungitoxin). A brilliant example is the synthesis of the elusive odorant (+)-khusimone which outshines 20 years of work in the field of tricyclovetivane synthesis. Palladium-, platinum-, and nickel-catalyzed versions of the metallo-ene reaction are in a comparatively early stage of exploration, but, nevertheless, reveal intriguing potential. Hence an almost 100% stereospecific C? O→C? ;Pd-→ C? C chirality transfer permits simple and selective, cis- or trans-annelation processes. The mild cyclization conditions are compatible with various functional groups, such as nitrogen moieties, which offer interesting perspectives for the preparation of heterocycles (e.g., alkaloids) difficult to obtain by other methods. Carbon monoxide insertion reactions of the cyclized σ-metal intermediates were shown to afford annelated cyclopentanones and cyclopentenones with concomitant stereocontrolled formation of four carbon–carbon bonds. These and other observations, highlighted in this article, provide a platform for further extensions and applications of this powerful method in organic synthesis.     

A simple and regioselective α-bromination of alkyl aromatic compounds by two-phase electrolysis

Electrochemical bromination of toluene and substituted toluenes by two-phase electrolysis yields the corresponding α-brominated products. The reaction has been carried out in a single compartment cell with platinum electrodes at 0 °C in chloroform using an aqueous sodium bromide solution (60%) containing a catalytic amount of HBr. Two-phase electrolysis results in high yields (60-95%) of monobromo compounds with very high regioselectivity (>95%).     

Bia-amperometric quantification of salbutamol in pharmaceutical products

This paper presents a simple, rapid and reproducible method of analysis of salbutamol in pharmaceutical products, utilizing batch injection analysis (BIA) associated with amperometric detection. A study of salbutamol oxidation demonstrated a strong dependence between electrode fouling and pH. All determinations were done utilizing a glassy carbon electrode in presence of 3.0 mol l⁻¹ NaOH. A large linear dynamic range from 8×10⁻⁷ to 2×10⁻⁴ mol l⁻¹ was obtained by using an injected volume of 100 μl with a detection limit of 2.5×10⁻⁷ mol l⁻¹. R.S.D. of 0.92% for 50 successive injections of 4×10⁻⁶ mol l⁻¹ of salbutamol and a sample throughput of 60 samples per hour were achieved. The method was applied for salbutamol quantification in syrups.