A new Fenchel dual problem in vector optimization

We introduce a new Fenchel dual for vector optimization problems inspired by the form of the Fenchel dual attached to the scalarized primal multiobjective problem. For the vector primal-dual pair we prove weak and strong duality. Furthermore, we recall two other Fenchel-type dual problems introduced in the past in the literature, in the vector case, and make a comparison among all three duals. Moreover, we show that their sets of maximal elements are equal.     

The Genuine Bernstein–Durrmeyer Operators Revisited

We present some direct and inverse results for the approximation by the genuine Bernstein–Durrmeyer operators U _n . We also consider iterates of U _n and discuss some convergence results towards the corresponding semigroup. Using the eigenstructure of the operators U _n we give new proofs of some known qualitative results and obtain new quantitative estimates concerning the convergence of iterates towards the semigroup.     

Evidence on single-molecule transport in electrostatically-gated molecular transistors

We show that, if adequately formulated for molecular electronics, the barrier picture can quantitatively reproduce the currents and describe the orbital gating in the molecular transistors fabricated by Song et al. [H. Song, Y. Kim, Y.H. Jang, H. Jeong, M.A. Reed, T. Lee, Nature 462 (2009) 1039]. Based on our results, we demonstrate (i) that the measured current represents the contribution of a single   molecule, and (ii) the linear dependence of the molecular orbital energy offset _εg${\epsilon }_g$ on the voltage _Vt$V_t$ at the Fowler–Nordheim minimum, validating thereby the transition voltage spectroscopy for the gated single molecule devices of Song et al.     

Why Ortho- and Para-Hydroxy Metabolites Can Scavenge Free Radicals That the Parent Atorvastatin Cannot? Important Pharmacologic Insight from Quantum Chemistry

The pharmaceutical success of atorvastatin (ATV), a widely employed drug against the “bad” cholesterol (LDL) and cardiovascular diseases, traces back to its ability to scavenge free radicals. Unfortunately, information on its antioxidant properties is missing or unreliable. Here, we report detailed quantum chemical results for ATV and its ortho- and para-hydroxy metabolites (o-ATV, p-ATV) in the methanolic phase. They comprise global reactivity indices, bond order indices, and spin densities as well as all relevant enthalpies of reaction (bond dissociation BDE, ionization IP and electron attachment EA, proton detachment PDE and proton affinity PA, and electron transfer ETE). With these properties in hand, we can provide the first theoretical explanation of the experimental finding that, due to their free radical scavenging activity, ATV hydroxy metabolites rather than the parent ATV, have substantial inhibitory effect on LDL and the like. Surprisingly (because it is contrary to the most cases currently known), we unambiguously found that HAT (direct hydrogen atom transfer) rather than SPLET (sequential proton loss electron transfer) or SET-PT (stepwise electron transfer proton transfer) is the thermodynamically preferred pathway by which o-ATV and p-ATV in methanolic phase can scavenge DPPH• (1,1-diphenyl-2-picrylhydrazyl) radicals. From a quantum chemical perspective, the ATV’s species investigated are surprising because of the nontrivial correlations between bond dissociation energies, bond lengths, bond order indices and pertaining stretching frequencies, which do not fit the framework of naive chemical intuition.     

Influence of Convective and Vacuum-Type Drying on Quality,Microstructural, Antioxidant and Thermal Properties of Pretreated Boletus edulis Mushrooms

Freshly harvested Boletus edulis mushrooms are subjected to rapid loss of quality due to the high moisture content and enzymatic activity. Drying time, quality characteristics, microstructural and thermal properties were studied in mushrooms ground to puree subjected to hot air drying (HAD), freeze drying (FD) and centrifugal vacuum drying (CVD). The influence of hot water blanching and UV-C pretreatments was additionally investigated. The rehydration ability of mushroom powders was improved by FD, especially without pretreatment or combined to UV-C exposure. The HAD and CVD, with no pretreatment or combined to UV-C, ensured good preservation of phenolics and antioxidant activity of dried mushrooms. The total difference in color of mushroom pigments extracted in acetone was lower in samples dried by CVD and higher in ones by FD. Blanching before HAD produced whiter product probably due to the reduced polyphenoloxidase activity. Scanning Electron Microscopy (SEM) analysis showed fewer physical changes in FD-samples. Heat-induced structural changes were noticed by Differential Scanning Calorimetry (DSC), Thermogravimetry (TG) and Derivative Thermogravimetry (DTG) analysis, in particular of biopolymers, confirmed by ATR-FTIR analysis. Based on our complex approach, the UV pretreatment of mushrooms could be a better alternative to water blanching. Centrifugal vacuum emerged as a new efficient drying method in terms of bioactive compounds, color and thermal stability, while FD led to better rehydration ability and microstructure.     

ChemInform Abstract: Beyond the Icosahedron: A Density Functional Theory Study of 14‐Atom Germanium Clusters.

ChemInform is a weekly Abstracting Service, delivering concise information at a glance that was extracted from about 200 leading journals. To access a ChemInform Abstract of an article which was published elsewhere, please select a “Full Text” option. The original article is trackable via the “References” option.     

Structural studies of tetrazoles. Crystal and molecular structure and ab initio calculations of 1-phenyl-1H-tetrazole-5-thiolate,as its [diaqua(18-crown-6)sodium] salt: An anionic tetrazole free of direct metal interactions

The structure of the anionic heterocycle obtained by deprotonation of 1-phenyl-1H-tetrazole-5-thione was determined by X-ray diffractometry. The counterion is [Na(18-crown-6)(H₂O)₂]⁺. There are no direct interactions between the metal and the tetrazole, while hydrogen bonds between sodium ion coordinated water molecules and neighboring azole anions give cohesion to the crystal. The thiotetrazolato ion displays extensive π-delocalization, with all members of the ring and the exocyclic sulfur contributing to it; however, no interannular conjugation between the phenyl and azole rings is found. The structure of the heterocycle is best described as a resonance hybrid. The geometric parameters of the metal-free tetrazole could be used as the input of ab initio MO calculations at the 6-31G*//3-21G* level, which supported the proposal that the negative charge is mainly concentrated on the N₄-C₅-S portion of the tetrazolate. Some small but significant and consistent bond length differences are found in the uncoordinated tetrazole with respect to metal-bonded analogues. The coordination behavior of the crown ether, with five oxygens bonded to sodium in the complex cation, is rare. © 1997 John Wiley & Sons, Inc.     

Multipolymers with Fischer-Tropsch olefins

Multipolymers consisting of ethylene, 1-heptene, 3-methylpentene and 4-methylpentene were prepared with a heterogeneous Ziegler-Natta catalyst. The polymers were prepared in such a way that the molar fraction of the comonomers remained the same. Copolymers of ethylene/1-heptene and ethylene/4-methylpentene were prepared in order to study the changes in polymer characteristics as one moves from an ethylene/linear alpha olefin copolymer through ethylene multipolymers to an ethylene/4-methylpentene copolymer. The mechanical, rheological and application properties showed expected trends.     

Fast Augmented Lagrangian Method in the convex regime with convergence guarantees for the iterates

Mathematical Programming - We present a trust-region steepest descent method for dynamic optimal control problems with binary-valued integrable control functions. Our method interprets the control...     

Heats of formation of organic molecules by ab initio methods: Thiaalkanes

The bond energy scheme for calculating heats of formation of organic molecules from ab initio data (6–31G*) has been extended to include 24 compounds containing sulfur in the sulfide oxidation state. The rms deviation from the experimental values for these compounds is 0.54 kcal/mol, which is approximately experimental error.