On Efficiency Conditions for Nonsmooth Vector Equilibrium Problems with Equilibrium Constraints

In this article, necessary conditions of Fritz John type for weak efficient solutions of a nonsmooth vector equilibrium problem involving equilibrium constraints (VEPEC) in terms of the Clarke subdifferentials are established. Under constraint qualifications which are suitable for (VEPEC), necessary conditions of Kuhn-Tucker type for efficiency are derived. Under assumptions on generalized convexity of data, sufficient conditions for efficiency are developed. Some applications to vector variational inequalities and vector optimization problems with equilibrium constraints are also given.     

Equidistribution of Periodic Points for Modular Correspondences

Let T be an exterior modular correspondence on an irreducible locally symmetric space X. We show that the isolated fixed points of the power T ⁿ are equidistributed with respect to the invariant measure on X as n tends to infinity. A similar statement is given for general sequences of modular correspondences.     

Broken circuit complexes and hyperplane arrangements

We study Stanley–Reisner ideals of broken circuit complexes and characterize those ones admitting linear resolutions or being complete intersections. These results will then be used to characterize hyperplane arrangements whose Orlik–Terao ideal has the same properties. As an application, we improve a result of Wilf on upper bounds for the coefficients of the chromatic polynomial of a maximal planar graph. We also show that for a matroid with a complete intersection broken circuit complex, the supersolvability of the matroid is equivalent to the Koszulness of its Orlik–Solomon algebra.     

pH‐sensing nanostar probe using surface‐enhanced Raman scattering (SERS): theoretical and experimental studies

Local pH environment has been considered to be a potential biomarker for tumor diagnosis because solid tumors contain highly acidic environments. A pH‐sensing nanoprobe based on surface‐enhanced Raman scattering (SERS) using nanostars under near‐infrared excitation has been developed for potential biomedical applications. To theoretically investigate the effect of protonation state on SERS spectra of p‐mercaptobenzoic acid (pMBA), we used the density functional theory (DFT) with the B3LYP functional to calculate Raman vibrational spectra of pMBA‐Au/Ag complex in both protonated and deprotonated states. Vibrational spectral bands were assigned with DFT calculation and used to investigate SERS spectral changes observed from experiment when varying pH value between five and nine. The SERS peak position of pMBA at ~1580 cm⁻¹ was identified to be a novel pH‐sensing index, which has small but noticeable downshift with pH increase. This phenomenon is confirmed and well‐explained with theoretical simulation. The study demonstrates that SERS is a sensitive tool to monitor minor structural changes due to local pH environment, and DFT calculations can be used to investigate Raman spectra changes associated with minor differences in molecular structure. Copyright © 2013 John Wiley & Sons, Ltd.     

Anticyanobacterial phenolic constituents from the aerial parts of Eupatorium fortunei Turcz

Four thymol derivatives and two phenolic compounds were isolated from the aerial parts of Eupatorium fortunei. The new structures were elucidated to be 7,8,9-trihydroxythymol (1), and 8,10-didehydro-7,9-dihydroxythymol (2) by means of MS and NMR analysis. The known compounds were identified as 8,9,10-trihydroxythymol (3), 10-acetoxy-8,9-dihydroxythymol (4), o-coumaric acid (5) and 4-(2-hydroxyethyl)benzaldehyde (6). Compound 3 showed strongest inhibitory effect on the growth of Microcystis aeruginosa in comparison with CuSO₄.     

Shape‐directed platinum nanoparticle synthesis: nanoscale design of novel catalysts

Platinum‐based catalytic materials have received significant attention, particularly in the shape and size control of faceted materials for catalysis. More recently, there has been a rapid increase in the number of reports of successful preparations in this field; however, a fundamental understanding of controlled growth towards catalytic material design is essential for future implementation and broad application. In this review, we provide an overview of the recent findings reported since 2009, focusing on methods for shape control as well as the effects of exposed surface facets on select catalytic reactions. Copyright © 2013 John Wiley & Sons, Ltd.