Upper semicontinuity result for the solution mapping of a mixed parametric generalized vector quasiequilibrium problem with moving cones

In this paper, we give sufficient conditions for the upper semicontinuity property of the solution mapping of a parametric generalized vector quasiequilibrium problem with mixed relations and moving cones. The main result is proven under the assumption that moving cones have local openness/local closedness properties and set-valued maps are cone-semicontinuous in a sense weaker than the usual sense of semicontinuity. The nonemptiness and the compactness of the solution set are also investigated.     

New Scalarizing Approach to the Stability Analysis in Parametric Generalized Ky Fan Inequality Problems

This paper gives sufficient conditions for the upper and lower semicontinuities of the solution mapping of a parametric mixed generalized Ky Fan inequality problem. We use a new scalarizing approach quite different from traditional linear scalarization approaches which, in the framework of the stability analysis of solution mappings of equilibrium problems, were useful only for weak vector equilibrium problems and only under some convexity and strict monotonicity assumptions. The main tools of our approach are provided by two generalized versions of the nonlinear scalarization function of Gerstewitz. Our stability results are new and are obtained by a unified technique. An example is given to show that our results can be applied, while some corresponding earlier results cannot.     

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.     

A backward parabolic equation with a time-dependent coefficient: Regularization and error estimates

We consider the problem of determining the temperature u(x,t)$u(x,t)$, for (x,t)∈[0,π]×[0,T)$(x,t)\in [0,\pi ]\times [0,T)$ in the parabolic equation with a time-dependent coefficient. This problem is severely ill-posed, i.e., the solution (if it exists) does not depend continuously on the given data. In this paper, we use a modified method for regularizing the problem and derive an optimal stability estimation. A numerical experiment is presented for illustrating the estimate.     

Inverse Problems for Multidimensional Heat Equations by Measurements at a Single Point on the Boundary

In this article we recover a coefficient in a multidimensional inverse problem for a heat equation. We show that a sequence of measurements taken at the same point on the boundary but at different times is enough to determine the coefficient uniquely. We provide an identifiability algorithm for both Dirichlet and Neumann lateral boundary conditions and we examine the smoothness of the recovered coefficient.     

Solution/Ammonolysis Syntheses of Unsupported and Silica-Supported Copper(I) Nitride Nanostructures from Oxidic Precursors

Herein we describe an alternative strategy to achieve the preparation of nanoscale Cu₃N. Copper(II) oxide/hydroxide nanopowder precursors were successfully fabricated by solution methods. Ammonolysis of the oxidic precursors can be achieved essentially pseudomorphically to produce either unsupported or supported nanoparticles of the nitride. Hence, Cu₃N particles with diverse morphologies were synthesized from oxygen-containing precursors in two-step processes combining solvothermal and solid−gas ammonolysis stages. The single-phase hydroxochloride precursor, Cu₂(OH)₃Cl was prepared by solution-state synthesis from CuCl₂·2H₂O and urea, crystallising with the atacamite structure. Alternative precursors, CuO and Cu(OH)₂, were obtained after subsequent treatment of Cu₂(OH)₃Cl with NaOH solution. Cu₃N, in the form of micro- and nanorods, was the sole product formed from ammonolysis using either CuO or Cu(OH)₂. Conversely, the ammonolysis of dicopper trihydroxide chloride resulted in two-phase mixtures of Cu₃N and the monoamine, Cu(NH₃)Cl under similar experimental conditions. Importantly, this pathway is applicable to afford composite materials by incorporating substrates or matrices that are resistant to ammoniation at relatively low temperatures (ca. 300 °C). We present preliminary evidence that Cu₃N/SiO₂ nanocomposites (up to ca. 5 wt.% Cu₃N supported on SiO₂) could be prepared from CuCl₂·2H₂O and urea starting materials following similar reaction steps. Evidence suggests that in this case Cu₃N nanoparticles are confined within the porous SiO₂ matrix.     

Effect of the shear layer on the etching behavior of 6060 aluminum extrusion alloys

The occurrence of preferential grain etching (PGE) during alkaline etching of aluminum extrusion alloys from the 6XXX series is often linked to the presence of certain impurity elements such as zinc, causing an undesired etching appearance. In the presented work, an additional culprit in this context is identified, which has not been investigated yet. A clear relation between PGE and the presence of a subsurface shear layer is identified for extruded Al 6060 alloys containing 0.02 and 0.06 wt% Zn. This shear layer can be distinguished from the bulk of the metal by its difference in crystallographic texture as visualized by electron backscatter diffraction (EBSD). For the Zn enriched alloy, the <111>//ND grains are etched away faster than grains with other orientations, resulting in the grainy appearance typical for PGE. Independent of the Zn content in the alloy, once the shear layer is removed and <111>//ND grains are practically absent on the new surface, the depths variations caused by preferential etching disappear. Instead, the surface of the alloy is attacked uniformly by the caustic etch bath.     

“Printing” DNA Strand Patterns on Small Molecules with Control of Valency,Directionality, and Sequence

The incorporation of synthetic molecules as corner units in DNA structures has been of interest over the last two decades. In this work, we present a facile method for generating branched small molecule‐DNA hybrids with controllable valency, different sequences, and directionalities (5′–3′) using a “printing” process from a simple 3‐way junction structure. We also show that the DNA‐imprinted small molecule can be extended asymmetrically using polymerase chain reaction (PCR) and can be replicated chemically. This strategy provides opportunities to achieve new structural motifs in DNA nanotechnology and introduce new functionalities to DNA nanostructures.     

Inhibitory Effects of Cucurbitane-Type Triterpenoids from Momordica charantia Fruit on Lipopolysaccharide-Stimulated Pro-Inflammatory Cytokine Production in Bone Marrow-Derived Dendritic Cells

The bitter melon, Momordica charantia L., was once an important food and medicinal herb. Various studies have focused on the potential treatment of stomach disease with M. charantia and on its anti-diabetic properties. However, very little is known about the specific compounds responsible for its anti-inflammatory activities. In addition, the in vitro inhibitory effect of M. charantia on pro-inflammatory cytokine production by lipopolysaccharide (LPS)-stimulated bone marrow-derived dendritic cells (BMDCs) has not been reported. Phytochemical investigation of M. charantia fruit led to the isolation of 15 compounds (1−15). Their chemical structures were elucidated spectroscopically (one- and two-dimensional nuclear magnetic resonance) and with electrospray ionization mass spectrometry. The anti-inflammatory effects of the isolated compounds were evaluated by measuring the production of the pro-inflammatory cytokines interleukin IL-6, IL-12 p40, and tumor necrosis factor α (TNF-α) in LPS-stimulated BMDCs. The cucurbitanes were potent inhibitors of the cytokines TNF-α, IL-6, and IL-12 p40, indicating promising anti-inflammatory effects. Based on these studies and in silico simulations, we determined that the ligand likely docked in the receptors. These results suggest that cucurbitanes from M. charantia are potential candidates for treating inflammatory diseases.