Lexicographic quasiconcave multiobjective programming

Summary Letf _i :A R ben real-valued objective functions on a convex setA -K ^m ,K:=R orC, n, mN. Letg: A R ⁿ be defined by , where for eachxA, (i ₁ (x), ..., i _n (x)) is a permutation of (1, ...,n) such that . In this paper we treat the problem of findingx ^*A such that , wherel-max denotes the lexicographic maximum. If the f_i's are strongly quasiconcave we can reduce the problem stepwise until finally it is in the form of a scalar programming problem. Further, we consider conditions for the existence and uniqueness of a solution and discuss the relationship of the problem to the vector maximum (i.e. Pareto) and maxmin (i.e. Chebychev) problems.

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Zusammenfassung f _i :AR seienn reellwertige Zielfunktionen über einer konvexen MengeA-K ^m ,K:=R oderC, n, mN. g:AR ⁿ sei definiert durch , wobei für jedesxA (i ₁ (x), ... i _n (x)) eine Permutation von (1, ...,n) derart ist, daß Wir betrachten das Problem, einx ^*A so zu finden, daß , wobeil-max das lexikographische Maximum bedeute. Falls dief _i stark quasikonkav sind, läßt sich das Problem stufenweise reduzieren, bis es schließlich die Gestalt eines skalaren Optimierungsproblems annimmt. Wir geben Existenz- und Eindeutigkeitsbedingungen an und besprechen Zusammenhänge mit dem Vektormaximumproblem (d.h. Pareto-Optimierung) und dem Maxmin-Problem (d.h. Tschebyscheff-Optimierung).

     

Face Selectivity of the Diels-Alder Additions of 2-Substituted 5,6-bis((E)-chloromethylidene)bicyclo[2.2.2]octanes

The preparation of 5,6-bis((E)-chlorommethylidene)bicyclo[2.2.2]oct-2-ene ( 13 ), 2,3-bis((E)-chloromethyl idene)-5exo,6exo- and -5endo,6endo-epoxybicyclo[2.2.2] octane ( 14 and 15 ), 5,6-bis((E)-chloromethylidene)-2exo- and -2endo-bicyclo[2.2.2] octanol ( 16 and 17 ) and 5,6-bis((E)-chloromethylidene)-2-bicyclo[2.2.2]octanone ( 18 ) are described. The face selectivity (endo-face vs. exo-face attack onto the exo-cyclic diene) of their cycloadditions to tetracyanoethylene has been determined in benzene at 20°. It is 78/22, 80/20, 60/40, 68/32, 3/97 and 30/70 for 13 , 14 , 15 , 16 , 17 and 18 , respectively.     

Spezifisches Verfahren zur quantitativen CO2-Bestimmung in natürlichen Wässern

The direct determination of CO₂ is often faulty because of certain contents of the natural water. Due to this reason a specific method was worked out. The water to be analysed and distilled water are placed side by side in a gas-tight vessel with an atmosphere free of CO₂, whereby mixing is avoided but gas-exchange is possible. After adjustment to the gas-equilibration the CO₂ content of the distilled water is determined e.g. by titration, measuring of conductivity or other methods, from where the CO₂ content in the natural water is calculated.     

Carbonyldinitrosyltris(fluorosulfato)tungstate(II) and ‐Molybdate(II) Anions: Synthesis,Spectroscopy, and Density Functional Theory Calculations

Carbonyldinitrosyltris(fluorosulfato)tungstate(II) and ‐molybdate‐(II) anions, [fac‐M(CO)(NO)₂(SO₃F)₃]^? (M=W, Mo), which are novel weakly coordinating anions that contain a metal carbonyl/nitrosyl moiety, have been generated in fluorosulfonic acid and completely characterized by multinuclear NMR, IR, and Raman spectroscopy as well as ESI mass spectrometry. ESI MS measurements performed for the first time on a superacidic solution system unambiguously reveal the formation of the monoanionic, mononuclear W and Mo complexes formulated as [M(CO)(NO)₂(SO₃F)₃]^? (M=W, Mo). Multinuclear NMR spectroscopic studies at natural abundance and ¹³C and ¹⁵N enrichment clearly indicate the presence of one CO ligand, two equivalent NO ligands, and two types of nonequivalent SO₃F^? groups in a 2:1 ratio. The IR and Raman spectra reveal that the two equivalent NO ligands have a cis conformation, thus indicating a fac structure. Density functional calculations at the B3LYP level of theory predict that these anions have a singlet ground state (¹A′) with a C_s symmetry along with C–O and N–O vibrational frequencies that are in agreement with the experimental observations. Mulliken population analysis shows that the monovalent negative charge is dispersed on the bulky sphere, the surface of which is covered by all the negatively charged O and F atoms with charge densities much lower than SO₃F^?, suggesting that [fac‐M(CO)(NO)₂(SO₃F)₃]^? (M=W, Mo) are weakly nucleophilic and poorly coordinating anions.     

The design of an irradiator for the continuous processing of liquid latex

This paper presents anew design concept for a gamma irradiation plant for the continuous processing of pumpable liquids. Typical applications of such a plant include

• * the irradiation vulcanisation of natural latex rubber

• * disinfection of municipal sewage sludge for agricultural use

• * sterilisation of liquids in the pharmaceutical and cosmetics industries

• * industrial processing of bulk liquids

The authors describe the design and operation of the latex irradiator now operating on a small production scale in Malaysia and proposed developments.

The design allows irradiation processing to be carried out under an inert or other gaseous environment.

State-of-the-art computer control system ensures the fully automatic processing operation needed by industrial computers.     

Can simple enones be useful partners for the catalytic stereoselective alkylation of indoles?

A new catalytic system for the first example of enantioselective Friedel-Crafts-type (FC) addition of indoles to simple enones is described. The use of an equimolar amount of chiral [Al(salen)Cl] and 2,6-lutidine (10 mol %) was found to be effective in promoting the conjugate addition of indoles to (E)-arylcrotyl ketones, furnishing the corresponding beta-indolyl ketones in excellent yield and high enantioselectivity (ee up to 89%). The role of the base was investigated through spectroscopic as well as computational analyses, which suggested that in situ formation of a new chiral (base.[Al(salen)]) complex was operating under our reaction conditions. In particular, a stable cationic [Al(salen)] hexacoordinate trans complex with the additive base and the enone is suggested as being responsible for the stereocontrolled reaction. Finally, detailed monitoring of the reaction course was carried out showing that a conventional FC pathway induced by [Al(salen)Cl] acting as a Lewis acid is operating.     

Phase separation of quaternary solubilized solutions or micro emulsion of hydrocarbons containing sodium oleate + phenol + benzene + water by freezing point measurements

Summary The depressions in freezing point measurements in quaternary solubilized solutions or micro-emulsion in sodium oleate + phenol + benzene + water are measured. Maxima and minima were observed, Gibbs' phase rule was applicable, eutectic points were detected, congruent melting points were obtained, loose combination of molecules or clusters, were formed, phases of the system transferred and finally unstable emulsion separated out. This is contrary to the views ofMcBain who called these solutions as thermodynamically stable. The results were compared with the conductivity, stability and heat of solubilization-concentration measurements.

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Zusammenfassung Es wird die Gefrierpunktserniedrigung von quaternären solubilisierten Lösungen im System Natriumoleat-Phenol-Benzol-Wasser gemessen. Die verschiedenen Befunde (Maxima und Minima des Gefrierpunktes in Abhängigkeit von der Zusammensetzung, Anwendbarkeit der Gibbs'schen Phasenregel, Auftreten von Eutektika, kongruente Schmelzpunkte etc.) dienen zum Beweis, daß diese Lösungen thermodynamisch instabil sind.

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With 5 figures and 1 table     

Lacidipine,a potential peroxynitrite scavenger: investigation of activity by liquid chromatography and mass spectrometry

Inflamed tissues are often characterised by the production of *NO and O(2)(-) radicals, which are known to react at an extremely fast rate to produce peroxynitrite (ONOO(-)). This highly oxidising entity reacts with protein-bound tyrosine to give 3-nitrotyrosine, which is considered a biochemical marker of peroxynitrite-induced damage. Lacidipine is a calcium antagonist indicated for the treatment of mild to moderate hypertension. In the present work, electrospray mass spectrometry with and without liquid chromatography was used to evaluate the capability of lacidipine and two other related molecules as ONOO(-) scavengers. This capability is compared with that associated with a number of commercial polyphenols described in the literature as efficient scavengers of this cytotoxic agent. The use of mass spectrometry provided rapid quantitative assessment of both the nitration and its reduction, and showed that lacidipine possesses a reasonable capability for reducing in vitro nitration of superoxide dismutase.     

Axially Dissymmetric Diphosphines in the Biphenyl Series: Synthesis of (6,6′-Dimethoxybiphenyl-2,2′-diyl)bis(diphenylphosphine)(‘MeO-BIPHEP’) and Analogues via an ortho-Lithiation/Iodination Ullmann-Reaction Approach

The new axially dissymmetric diphosphines (R)- and (S)-(6,6′-dimethoxybiphenyl-2,2′-diyl)bis(diphenyl phosphine) ((R)- and (S)- 5a ; ‘MeO-BIPHEP’) and the analogues (R)- and (S)- 5b and 5c have been synthesized in enantiomerically pure form. These ligands have become readily available by a synthetic scheme which employs, as key steps, an ortho-lithiation/iodination reaction of the (m-methoxyphenyl)diprienylphosphine oxides 8 and a subsequent Ullmann reaction of the resulting iodides 9 to provide the racemic bis(phosphine oxides) 10 . The bis(phosphine oxides) 10 subsequently are resolved with (?)-(2R,3R)- and (+)-(2S,3S)-O-2,3-dibenzoyltartaric acid and reduced to diphosphines 5 . The Ullmann reaction constitutes a new and efficient route to 2,2′-bis(phosphinoyl)-substituted biphenyl systems. Absolute configurations were established for (R)- 5a by X-ray analysis of the derived Pd complex (R,R)- 17a , and for 5b and 5c by means of ¹H-NMR comparisons of the derived Pd complexes 16 or 17 , respectively, and by means of CD comparisons. The MeO-BIPHEP diphosphine 5a proved to be as efficient as the previously described BIPHEMP diphosphine ((6,6′-dimethylbiphenyl-2,2′-diyl)bis(diphenylphosphine)) in enantioselective isomerizations and hydrogenations.