Optimality and duality for nonsmooth multiobjective programming problems with V-r-invexity

In the paper, we consider a class of nonsmooth multiobjective programming problems in which involved functions are locally Lipschitz. A new concept of invexity for locally Lipschitz vector-valued functions is introduced, called V-r-invexity. The generalized Karush–Kuhn–Tuker necessary and sufficient optimality conditions are established and duality theorems are derived for nonsmooth multiobjective programming problems involving V-r-invex functions (with respect to the same function η).     

Synthesis and EPR Studies of 2′‐Deoxyuridines with Alkynyl,Rodlike Linkages

Sonogashira coupling of diacetyl 5‐ethynyl‐2′‐deoxyuridine with diacetyl 5‐iodo‐2′‐deoxyuridine gave the acylated ethynediyl‐linked 2′‐deoxyuridine dimer ( 3 b ; 63 %), which was deprotected with ammonia/methanol to give ethynediyl‐linked 2′‐deoxyuridines ( 3 a ; 79 %). Treatment of 5‐ethynyl‐2′‐deoxyuridine ( 1 a ) with 5‐iodo‐2′‐deoxyuridine gave the furopyrimidine linked to 2′‐deoxyuridine (78 %). Catalytic oxidative coupling of 1 a (O₂, CuI, Pd/C, N,N‐dimethylformamide) gave butadiynediyl‐linked 2′‐deoxyuridines ( 4 ; 84 %). Double Sonogashira coupling of 5‐iodo‐2′‐deoxyuridine with 1,4‐diethynylbenzene gave 1,4‐phenylenediethynediyl‐bridged 2′‐deoxyuridines ( 5 ; 83 %). Cu‐catalyzed cycloisomerization of dimers 4 and 5 gave their furopyrimidine derivatives. One‐electron addition to 1 a , 3 a , and 4 gave the anion radical, the EPR spectra of which showed that the unpaired electron is largely localized at C6 of one uracil ring (17 G doublet) at 77 K. The EPR spectra of the one‐electron‐oxidized derivatives of ethynediyl‐ and butadiynediyl‐linked uridines 3 a and 4 at 77 K showed that the unpaired electron is delocalized over both rings. Therefore, structures 3 a and 4 provide an efficient electronic link for hole conduction between the uracil rings. However, for the excess electron, an activation barrier prevents coupling to both rings. These dimeric structures could provide a gate that would separate hole transfer from electron transport between strands in DNA systems. In the crystal structure of acylated dimer 3 b , the bases were found in the anti position relative to each other across the ethynyl link, and similar anti conformation was preserved in the derived furopyrimidine–deoxyuridine dinucleoside.     

5,5‐Di­methoxy‐2‐phenoxy‐1,3,2‐dioxaphosphorinane 2‐oxide

In the title compound, C₁₁H₁₅O₆P, the six‐membered dioxa­phospho­rinane ring of the cyclic phosphate triester exists in a distorted chair conformation, with the phenoxy group in an axial position. The phenyl ring and both methoxy groups are in a trans–gauche orientation with respect to the 1,3,2‐di­oxa­phospho­rinane ring. In the phosphate group, a significant deformation from the ideal tetrahedral shape is observed. The crystal structure is stabilized by a three‐dimensional network of C—H⋯O interactions.     

Effects of serum proteins on corrosion behavior of ISO 5832–9 alloy modified by titania coatings

Stainless steel ISO 5832–9 type is often used to perform implants which operate in protein-containing physiological environments. The interaction between proteins and surface of the implant may affect its corrosive properties. The aim of this work was to study the effect of selected serum proteins (albumin and γ-globulins) on the corrosion of ISO 5832–9 alloy (trade name M30NW) which surface was modified by titania coatings. These coatings were obtained by sol–gel method and heated at temperatures of 400 and 800 °C. To evaluate the effect of the proteins, the corrosion tests were performed with and without the addition of proteins with concentration of 1 g L^?1 to the physiological saline solution (0.9 % NaCl, pH 7.4) at 37 °C. The tests were carried out within 7 days. The following electrochemical methods were used: open circuit potential, linear polarization resistance, and electrochemical impedance spectroscopy. In addition, surface analysis by optical microscopy and X-ray photoelectron spectroscopy (XPS) method was done at the end of weekly corrosion tests. The results of corrosion tests showed that M30NW alloy both uncoated and modified with titania coatings exhibits a very good corrosion resistance during weekly exposition to corrosion medium. The best corrosion resistance in 0.9 % NaCl solution is shown by alloy samples modified by titania coating annealed at 400 °C. The serum proteins have no significant effect onto corrosion of investigated biomedical steel. The XPS results confirmed the presence of proteins on the alloy surface after 7 days of immersion in protein-containing solutions.     

Efficient Solvent‐Free Synthesis of Benzothiazine‐Fused Pyrrolo[3,4‐c]coumarins: Cycloaddition Reactions between Coumarin‐Based Dihydrobenzothiazoles and Isocyanides

A new and unusual synthesis of benzothiazine‐fused pyrrolo[3,4‐c]coumarins, involving the ring‐opening of coumarin‐based dihydrobenzothiazoles and subsequent [4+1] cycloaddition reaction with isocyanides, was described. Thus, simple heating of various 3‐(2,3‐dihydro‐2‐methylbenzo[d]thiazol‐2‐yl)coumarins with isocyanides produced the title compounds in good yields under solvent‐free conditions.     

Synthesis of Novel α‐(Acyloxy)‐α‐(quinolin‐4‐yl)acetamides by a Three‐Component Reaction between an Isocyanide,Quinoline‐4‐carbaldehyde,and Arenecarboxylic Acids

Novel α‐(acyloxy)‐α‐(quinolin‐4‐yl)acetamides were synthesized by the Passerini three‐component reaction between an isocyanide, quinoline‐4‐carbaldehyde, and arenecarboxylic acids in H₂O. The reactions were carried out in one pot at room temperature with quantitative yields.     

Mean value in invexity analysis

In this paper, a generalization of the mean value theorem is considered in the case of functions defined on an invex set with respect to η (which is not necessarily connected).     

The 2:1 cocrystal of benzamide and penta­fluoro­benzoic acid

The crystal structure of the title compound, benzamide–2,3,4,5,6‐penta­fluoro­benzoic acid (2/1), 2C₇H₇NO·C₇HF₅O₂, consists of centrosymmetric hexa­meric supermolecules composed of four amide and two carboxylic acid mol­ecules connected via O—H⋯O and N—H⋯O hydrogen bonds. No phen­yl–perfluoro­phenyl π–π stacking inter­actions are observed in this cocrystal.     

On the reactivity of platina‐β‐diketones: a straightforward synthesis of trans‐acetylchlorobis(phosphine)platinum(II) complexes and their reactivity

The platina‐β‐diketone [Pt₂{(COMe)₂H}₂(µ‐Cl)₂] ( 1 ) was found to react with monodentate phosphines to yield acetyl(chloro)platinum(II) complexes trans‐[Pt(COMe)Cl(PR₃)₂] (PR₃ = PPh₃, 2a ; P(4‐FC₆H₄)₃, 2b ; PMePh₂, 2c ; PMe₂Ph, 2d ; P(n‐Bu)₃, 2e ; P(o‐tol)₃, 2f ; P(m‐tol)₃, 2g ; P(p‐tol)₃, 2h ). In the reaction with P(o‐tol)₃ the methyl(carbonyl)platinum(II) complex [Pt(Me)Cl(CO){P(o‐tol)₃}] ( 3a ) was found to be an intermediate. On the other hand, treating 1 with P(C₆F₅)₃ led to the formation of [Pt(Me)Cl(CO){P(C₆F₅)₃}] ( 3b ), even in excess of the phosphine. Phosphine ligands with a lower donor capability in complexes 2 and the arsine ligand in trans‐[Pt(COMe)Cl(AsPh₃)₂] ( 2i ) proved to be subject to substitution by stronger donating phosphine ligands, thus forming complexes trans‐[Pt(COMe)Cl(L)L′] (L/L′ = AsPh₃/PPh₃, 4a ; PPh₃/P(n‐Bu)₃, 4b ) and cis‐[Pt(COMe)Cl(dppe)] ( 4c ). Furthermore, in boiling benzene, complexes 2a – 2c and 2i underwent decarbonylation yielding quantitatively methyl(chloro)platinum(II) complexes trans‐[Pt(Me)Cl(L)₂] (L = PPh₃, 5a ; P(4‐FC₆H₄)₃, 5b ; PMePh₂, 5c ; AsPh₃, 5d ). The identities of all complexes were confirmed by ¹H, ¹³C and ³¹P NMR spectroscopy. Single‐crystal X‐ray diffraction analyses of 2a ·2CHCl₃, 2f and 5b showed that the platinum atom is square‐planar coordinated by two phosphine ligands (PPh₃, 2a ; P(o‐tol)₃, 2f ; P(4F‐C₆H₄)₃, 5b ) in mutual trans position as well as by an acetyl ligand ( 2a, 2f ) and a methyl ligand ( 5b ), respectively, trans to a chloro ligand. Single‐crystal X‐ray diffraction analysis of 3b exhibited a square‐planar platinum complex with the two π‐acceptor ligands CO and P(C₆F₅)₃ in mutual cis position (configuration index: SP‐4‐3). Copyright © 2005 John Wiley & Sons, Ltd.