Characterization of vector strict global minimizers of order 2 in differentiable vector optimization problems under a new approximation method

In this paper, a new approximation method is introduced to characterize a so-called vector strict global minimizer of order 2 for a class of nonlinear differentiable multiobjective programming problems with (F,ρ)-convex functions of order 2. In this method, an equivalent vector optimization problem is constructed by a modification of both the objectives and the constraint functions in the original multiobjective programming problem at the given feasible point. In order to prove the equivalence between the original multiobjective programming problem and its associated F-approximated vector optimization problem, the suitable (F,ρ)-convexity of order 2 assumption is imposed on the functions constituting the considered vector optimization problem.     

High-Efficiency Liquid Chromatography Using Sub-2?��m Columns at Elevated Temperature for the Analysis of Sulfonamides in Wastewater

Efficiency in HPLC can be enhanced by increasing the column length and/or decreasing the particle size. The use of high temperature in HPLC has emerged as a valuable tool to overcome the increase in column backpressure when using small packing particles, as it allows for reduction in mobile phase viscosity. In this study, high plate count was obtained by coupling sub-2 ??m columns at elevated temperature to reduce the viscosity of the mobile phase, thus reducing the column backpressure. At 80 °C, up to three columns of 15 cm × 4.6 mm I.D. packed with 1.8 ??m particles could be coupled generating ~84,000 theoretical plates for the last eluting compound. The number of theoretical plates was increased on average by a factor of ~3.6 when three columns were coupled at 80 °C compared with one column at 30 °C. The relationships between separation efficiency and column length were examined using Van Deemter plots constructed at 30 °C and 80 °C for different column lengths. The advantages of using coupled columns in combination with elevated temperature for the environmental analysis were illustrated using test mixtures comprised of eight sulfonamides separated on one column at 30 °C and three coupled columns at 80 °C by isocratic elution. Sample clean up was carried out by employing solid-phase extraction (SPE) using Oasis HLB cartridges. The method developed was validated based on parameters such as linearity, precision, accuracy, detection and quantification limits. Recoveries generally ranged from 71.7 to 99% (with the exception of sulfanilamide), with standard deviations not higher than 4.7%. The detection limits of the method ranged from 0.6?C2 ??g L^?1, while limits of quantification were in the range 2?C6.7 ??g L^?1 with UV detection.     

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.     

Boundary Solutions of Differential Inclusions and Recovering the Initial Data

The solutions of differential inclusions staying at the boundary of attained sets are investigated using the contingent cones to attained sets. The possibility of recovering the starting point and the time which elapsed since the beginning is shown when some fragments of an attained set are known.     

Parallel implementation of the p‐version of the finite element method for elliptic equations on a shared‐memory architecture

An implementation of the p‐version of the finite element method for solving two‐dimensional linear elliptic problems on a shared‐memory parallel computer is analyzed. The idea is to partition the problem among the available processors and perform computations corresponding to different elements in parallel. The parallelization is based on a domain decomposition technique using the Lagrange multipliers. The numerical experiments carried out on the Sequent system indicate very high performance of the mixed finite element algorithm in terms of attained speedups. This revised version was published online in August 2006 with corrections to the Cover Date.     

Chloride interference with non-stoichiometric copper sulphide copper(II)-selective electrodes : Part 2. Exact determination of the chloride interference region

A general equation for calculating the limit of the ligand interference region with the non-stoichiometric copper sulphide single-crystal electrode is described. The critical ligand concentration can be computed for a preselected maximal error in copper(II) ion determinations. The effect of the composition of the electrode material is discussed. The experimental results for the chloride interference show good agreement with theoretical predictions.     

Dilithium tetrabromonickelate (II) as a source of soft nucleophilic bromide : Reaction with epoxides

Dilithium tetrabromonickelate (II) in THF serves as a source of “soft” nucleophilic bromide and reacts regioselectively with epoxides to give bromohydrins in high yield.     

The mass gap for Higgs models on a unit lattice

An isomorphism is established between eertain compact and noncompact formulations of Abelian gauge theory on a lattice. For weak coupling, the mass gap predicted by the Higgs mechanism is then established.