Necessary and sufficient optimality conditions for mathematical programs with equilibrium constraints

In this paper we consider a mathematical program with equilibrium constraints (MPEC) formulated as a mathematical program with complementarity constraints. Various stationary conditions for MPECs exist in literature due to different reformulations. We give a simple proof to the M-stationary condition and show that it is sufficient for global or local optimality under some MPEC generalized convexity assumptions. Moreover, we propose new constraint qualifications for M-stationary conditions to hold. These new constraint qualifications include piecewise MFCQ, piecewise Slater condition, MPEC weak reverse convex constraint qualification, MPEC Arrow-Hurwicz-Uzawa constraint qualification, MPEC Zangwill constraint qualification, MPEC Kuhn-Tucker constraint qualification, and MPEC Abadie constraint qualification.     

A Class of Quadratic Programs with Linear Complementarity Constraints

We consider a class of quadratic programs with linear complementarity constraints (QPLCC) which belong to mathematical programs with equilibrium constraints (MPEC). We investigate various stationary conditions and present new and strong necessary and sufficient conditions for global and local optimality. Furthermore, we propose a Newton-like method to find an M-stationary point in finite steps without MEPC linear independence constraint qualification. The research of this author is partially supported by NSERC, and Research Grand Council of Hong Kong.     

Enhanced Karush–Kuhn–Tucker condition and weaker constraint qualifications

In this paper we study necessary optimality conditions for nonsmooth optimization problems with equality, inequality and abstract set constraints. We derive the enhanced Fritz John condition which contains some new information even in the smooth case than the classical enhanced Fritz John condition. From this enhanced Fritz John condition we derive the enhanced Karush–Kuhn–Tucker condition and introduce the associated pseudonormality and quasinormality condition. We prove that either pseudonormality or quasinormality with regularity on the constraint functions and the set constraint implies the existence of a local error bound. Finally we give a tighter upper estimate for the Fréchet subdifferential and the limiting subdifferential of the value function in terms of quasinormal multipliers which is usually a smaller set than the set of classical normal multipliers. In particular we show that the value function of a perturbed problem is Lipschitz continuous under the perturbed quasinormality condition which is much weaker than the classical normality condition.     

Boundary of Anosov dynamics and evolution equations for surfaces

We show that a compact surface of genus greater than one, without focal points and a finite number of bubbles (“good” shaped regions of positive curvature) is in the closure of Anosov metrics. Compact surfaces of nonpositive curvature and genus greater than one are in the closure of Anosov metrics, by Hamilton's work about the Ricci flow. We generalize this fact to the above surfaces without focal points admitting regions of positive curvature using a “magnetic” version of the Ricci flow, the so‐called Ricci Yang‐Mills flow.     

Using chemical probes to investigate the sub-inhibitory effects of azithromycin

The antibacterial drug azithromycin has clinically beneficial effects at sub-inhibitory concentrations for the treatment of conditions characterized by chronic Pseudomonas aeruginosa infection, such as cystic fibrosis. These effects are, in part, the result of inhibition of bacterial biofilm formation. Herein, the efficient synthesis of azithromycin in 4 steps from erythromycin and validation of the drug's ability to inhibit biofilm formation at sub-MIC (minimum inhibitory concentration) values are reported. Furthermore, the synthesis of immobilized and biotin-tagged azithromycin analogues is described. These chemical probes were used in pull-down assays in an effort to identify azithromycin's binding partners in vivo. Results from these assays revealed, as expected, mainly ribosomal-related protein binding partners, suggesting that this is the primary target of the drug. This was further confirmed by studies using a P. aeruginosa strain containing plasmid-encoded ermC, which expresses a protein that modifies 23S rRNA and so blocks macrolide entry to the ribosome. In this strain, no biofilm inhibition was observed. This work supports the hypothesis that the sub-inhibitory effects of azithromycin are mediated through the ribosome. Moreover, the synthesis of these chemical probes, and proof of their utility, is of value in global target identification in P. aeruginosa and other species.     

Quality assurance in research laboratories

During the last decade, it has become increasingly important that researchers demonstrate that research is conducted to the highest standards. The implementation of quality assurance for research laboratories will enable all fields of research and development to be judged impartially. There are no specific standards for research laboratories but where possible, existing standards can be adapted. This review is structured around two approaches. The first considers research to be a logical extension of testing, and it is assumed that testing standards can be applied methodically to each step in a research project. The second advocates a flexible approach, with research-specific criteria for assessing quality. The important papers published on this topic have been reviewed. The conclusions are that the general quality management approach, encompassed by the ISO 9000 series of standards with the emphasis on customer satisfaction and ‘fitness for purpose’, is suitable for implementing quality assurance in research laboratories.     

Patterned polyfluorene surfaces by functionalization of nanoimprinted polymeric features

A new procedure is described for surface grafting polymer brushes by step-growth polymerization from initiator-embedded polymeric thin films and micron- and nanometer-scale patterns. An imprint lithographic process, nanocontact molding, was used to prepare thin patterned cross-linked polyacrylate network films on silicon wafers that incorporated 4-bromostyrene in the networks. These networks present reactive 4-bromophenyl functionality at the surface that act as attachment sites for the subsequent Ni(0)- mediated step-growth condensation polymerization of 2,7-dibromo-9,9-dihexylfluorene The step-growth polymerization medium consisted of 2,7-dibromo-9,9-dihexylfluorene, Ni(0)-catalyst, and bipyridine in a toluene/dimethylformamide solvent mixture. The resulting growth of polydihexylfluorene brushes from the patterned surface was monitored by contact angle, optical spectrometry, surface profilometry and AFM. Brush growth was conducted from patterned features ranging from 100 microm to 100 nm in width and 50 nm in height. The optical and fluorescence behavior of the polyfluorene brushes was similar to that of thin polyfluorene films made by spin coating.     

Film growth precursor development for metal nitrides. Synthesis, structure, and volatility of molybdenum(VI) and tungsten(VI) complexes containing bis(imido)metal fragments and various nitrogen donor ligands

The molybdenum and tungsten complexes W2(NtBu)4(pz)4(pzH).(C6H14)0.5 (pz = pyrazolate), M(NtBu)2(Me2pz)2(Me2pzH)2 (Me2pz = 3,5-dimethylpyrazolate), M(NtBu)2(tBu2pz)2 (tBu2pz = 3,5-di-tert-butylpyrazolate), M2(NtBu)4(Me2pz)2Cl2, W(NtBu)2(C2N3(iPr)2)2py2, M(NtBu)2-(CN4CF3)2py2, and W(NtBu)2(PhNNNPh)2 were prepared by various synthetic routes from the starting materials Mo(NtBu)2Cl2, W(NtBu)2(NHtBu)2, and W(NtBu)2Cl2py2. These new complexes were characterized by spectral and analytical methods and by X-ray crystal structure determinations. The volatilities and thermal stabilities were evaluated to determine the potential of the new complexes for use in thin film growth of metal nitride films. Mo(NtBu)2(tBu2pz)2 and W(NtBu)2(tBu2pz)2 were found to have the optimum combination of volatility and thermal stability for application in atomic layer deposition thin film growth procedures.