A nonlinear programming algorithm based on non-coercive penalty functions

 We consider first the differentiable nonlinear programming problem and study the asymptotic behavior of methods based on a family of penalty functions that approximate asymptotically the usual exact penalty function. We associate two parameters to these functions: one is used to control the slope and the other controls the deviation from the exact penalty. We propose a method that does not change the slope for feasible iterates and show that for problems satisfying the Mangasarian-Fromovitz constraint qualification all iterates will remain feasible after a finite number of iterations. The same results are obtained for non-smooth convex problems under a Slater qualification condition. Received: September 2000 / Accepted: June 2002 Published online: March 21, 2003 Research partially supported by CAPES, Brazil Research partially supported by CNPq, Brazil, and CONICIT, Venezuela. Mathematics Subject Classification (1991): 20E28, 20G40, 20C20     

Pyridazine based scorpionate ligand in a copper boratrane compound

Reaction of potassium tris(mercapto-tert-butylpyridazinyl)borate K[Tn(tBu)] with copper(II) chloride in dichloromethane at room temperature led to the diamagnetic copper boratrane compound [Cu{B(Pn(tBu))(3)}Cl] (Pn = pyridazine-3-thionyl) (1) under activation of the B-H bond and formation of a Cu-B dative bond. In contrast to this, stirring of the same ligand with copper(I) chloride in tetrahydrofuran (THF) gave the dimeric compound [Cu{Tn(tBu)}](2) (2) where one copper atom is coordinated by two sulfur atoms and one hydrogen atom of one ligand and one sulfur of the other ligand. Hereby, no activation of the B-H bond occurred but a 3-center-2-electron B-H···Cu bond is formed. The reaction of copper(II) chloride with K[Tn(tBu)] in water gave the same product 2, but a formal reduction of the metal center from Cu(II) to Cu(I) occurred. When adding tricyclohexyl phosphine to the reaction mixture of K[Tn(R)] (R = tBu, Me) and copper(I) chloride in MeOH, the distorted tetrahedral Cu complexes [Cu{Tn(R)}(PCy(3))] (R = tBu 3, Me 4) were formed. Compound 4 is exhibiting an "inverted" κ(3)-H,S,S, coordination mode. The copper boratrane 1 was further investigated by density functional theory (DFT) calculations for a better understanding of the M→B interaction involving the d(8) electron configuration of Cu.     

Activation and Photoinduced Release of Alkynes on a Biomimetic Tungsten Center: The Photochemical Behavior of the W−S-Phoz System

The synthesis and structural determination of four tungsten alkyne complexes coordinated by the bio-inspired S,N-donor ligand 2-(4′,4′-dimethyloxazoline-2′-yl)thiophenolate (S-Phoz) is presented. A previously established protocol that involved the reaction of the respective alkyne with the bis-carbonyl precursor [W(CO)₂(S-Phoz)₂] was used for the complexes [W(CO)(C₂R₂)(S-Phoz)₂] (R=H, 1 a ; Me, 1 b ; Ph, 1 c ). Oxidation with pyridine-N-oxide gave the corresponding W-oxo species [WO(C₂R₂)(S-Phoz)₂] (R=H, 2 a ; Me, 2 b ; Ph, 2 c ). All W-oxo-alkyne complexes ( 2 a , b , c ) were found to be capable of alkyne release upon light irradiation to afford five-coordinate [WO(S-Phoz)₂] ( 3 ). The photoinduced release of the alkyne ligand was studied in detail by in situ ¹H NMR measurements, which revealed correlation of the photodissociation rate constant ( 2 b>2 a>2 c ) with the elongation of the alkyne C≡C bond in the molecular structures. Oxidation of [WO(S-Phoz)₂] ( 3 ) with pyridine-N-oxide yielded [WO₂(S-Phoz)₂] ( 4 ), which shows highly fluxional behavior in solution. Variable-temperature ¹H NMR spectroscopy revealed three isomeric forms with respect to the ligand arrangement versus each other. Furthermore, compound 4 rearranges to tetranuclear oxo compound [W₄O₄(μ-O)₆(S-Phoz)₄] ( 5 ) and dinuclear [{WO(μ-O)(S-Phoz)}₂] ( 6 ) over time. The latter two were identified by single-crystal X-ray diffraction analyses.     

Elektronenstossinduzierte Fragmentierung von Acetylenverbindungen—IV: Mechanistische Betrachtungen zur Bildung des Benztropyliumkations aus den Chlormethyl-Naphthalinen und 1-Chlor-Phenyl-(5)-Penten-(2)-in-(4)

Mass spectroscopic investigations of ²H- and ¹³C-labelled derivatives of e.g. 1-, 2-chloro-methyl-naphthalene and 1-chloro-phenyl(5)-pentene-(2)-in-(4) show that the [C₁₁H₉]⁺ ion, which gives [C₉H₇]⁺ by acetylene elimination, has the structure of a benztropylium cation. Model considerations show that the formation of this cation [C₁₁H₉]⁺ through a common transition state with a three-membered ring is very probable.     

Elektronenstossinduzierte Fragmentierung von Acetylenverbindungen. IX—Struktur der Stabilen [C9H11]+-Ionen aus Isomeren C9H11-Chloriden

The structure of stable [C₉H₁₁]⁺ ions from different model compounds with the molecular formula C₉H₁₁Cl has been estimated by energy measurements. It has further been shown that acetylenic compounds cyclise to form aromatic ions in the range of the appearance potentials.     

Mikrobestimmung des Fluors in organischen Substanzen

Zusammenfassung Es wurde ein Mikroverfahren zur Bestimmung von organisch gebundenem Fluor ausgearbeitet. Die Substanz wird mit Kalium im Glasröhrchen aufgeschlossen. Die Röhrchen werden vorher durch Auskochen mit Salzsäure blindwertfrei gemacht. Die Titration des Fluoridions kann durch geeignete Maßnahmen direkt in der Aufschlußlösung erfolgen, so daß die zeitraubende Abdestillation des Fluorids erspart wird. Die Titration selbst wird in bekannter Weise mittels Thoriumnitrat durchgeführt. Als Indikatoren dienen Alizarinrot S, dem Wasserblau oder Chinablau zugesetzt ist. ZurpH-Einstellung dient ein Glycin-Perchlorsäure-Puffer.

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Summary A method was developed for the determination of organically bound fluorine. The sample is decomposed by heating with potassium in a small glass tube. The tubes are treated ahead of time with hot hydrochloric acid to render them blank-free. The titration of the fluoride ion can be conducted directly in the decomposition solution if proper precautions are taken. The time-consuming distilling off of the fluoride is thus avoided. The titration itself is made in the usual manner by thorium nitrate. The indicator is alizarin red S, to which is-added water blue or China blue. A glycerol-perchloric acid buffer is used to-adjust the p_h.

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Résumé Mise au point d'un procédé de microdosage du fluor dans les composés-organiques. La substance est attaquée par le potassium dans de petits tubes de verre. Ceux-ci sont préalablement traités dans l'acide chlorhydrique bouillant pour éviter toute correction d'essai à blanc. Le titrage de l'ion fluorure peut être exécuté directement dans la solution provenant de l'attaque sous réserve de respecter des conditions appropriées; on évite ainsi la longue séparation du fluorure par distillation. Le titrage proprement dit est effectué de la façon habituelle à l'aide de nitrate de thorium en présence d'un indicateur constitué par du rouge d'alizarine S auquel on a ajouté du bleu soluble (Wasserblau ou Chinablau). On opère àpH constant à l'aide du tampon glycocolle — acide perchlorique.

     

Synthesis,structure and catalytic properties of bis[2‐(trifluoromethyl)phenyl]silanediol

A novel trifluoromethylaryl‐substituted disilanol, bis[(2‐trifluoromethyl)phenyl] silanediol, was prepared by hydrolysis of the precursor dichloride and fully characterized. Single‐crystal X‐ray diffraction indicates doubly linked hydrogen bonded dimers and also hydrogen bonding to tetrahydrofuran solvent. The acidity of the silanol functions is enhanced by the presence of the trifluoromethyl groups and the compound is found to be active in promoting a standard Diels–Alder reaction, increasing yields by a factor of three.     

Solubilisation of camptothecin by nonionic surfactants and alkyldimethylamine oxides

The solubilisation of poorly soluble antineoplastic drug camptothecin by nonionic surfactants (polysorbates and octylphenol ethoxylates) and alkyldimethylamine oxide surfactants with the alkyl chain length 8 to 16 carbon atoms was investigated. The hydrophobicity of the solubilising agent turned out to be the primary structural parameter controlling the solubility efficiency of camptothecin in an aqueous solution. The quantitative parameter of solubilisation (drug loading coefficient) provided values in the range of 0.1–1.2% and 0.1–1.0% for alkyldimethylamine oxides and nonionic surfactants, respectively. The decreasing number of oxyethylene units and the extension of the hydrophobic part of nonionic surfactant molecule resulted in the increase of camptothecin solubility. From the dynamic light scattering measurements, the hydrodynamic diameter values of camptothecin-loaded alkyldimethylamine oxide and nonionic micelles were found in the range of 4–42 nm and 5–120 nm, respectively. The experimental values confirmed the increase in micellar size with the increasing alkyl chain length. The values of the packing parameter of camptothecin-loaded dodecyldimethylamine oxide micelles indicate their spherical shape at all the investigated surfactant concentrations. A simple computer model of camptothecin-loaded dodecyldimethylamine oxide micelle provided the diameter of the structure cross section which is consistent with the experimental values.      

Effects of gemini surfactants on egg phosphatidylcholine bilayers in the fluid lamellar phase

The influence of 1,4-butanediamonium-N,N'-dialkyl-N,N,N',N'-tetramethyl dibromides (CmA, m = 7-16 is the number of alkyl carbons) on the egg yolk phosphatidylcholine (EYPC) bilayer thickness and lipid surface area at the bilayer-aqueous phase interface is studied using X-ray diffraction on fluid lamellar CmA + EYPC + H2O phases as a function of CmA:EYPC and H2O:EYPC molar ratios and the alkyl chain length m. At the constant CmA:EYPC = 0.4 and H2O:EYPC = 18 molar ratios, the CmA induced bilayer thickness decrease shows a minimum and the lipid surface area increase a maximum at the alkyl chain length m = 9. The obtained results are discussed in the context of a structural perturbation model of the cut-off effect in biological potencies of surfactants which occurs when increasing the alkyl substituent chain length above the critical value.