Pullback attractors for nonautonomous 2D Bénard problem in some unbounded domains

In this paper, we study the 2D Bénard problem, a system with the Navier–Stokes equations for the velocity field coupled with a convection–diffusion equation for the temperature, in an arbitrary domain (bounded or unbounded) satisfying the Poincaré inequality with nonhomogeneous boundary conditions and nonautonomous external force and heat source. The existence of a weak solution to the problem is proved by using the Galerkin method. We then show the existence of a unique minimal finite‐dimensional pullback D_σ‐attractor for the process associated to the problem. Copyright © 2013 John Wiley & Sons, Ltd.     

Characterization and antimicrobial activity of silver nanoparticles prepared by a thermal decomposition technique

Recently, there has been an increasing need of efficient synthetic protocols using eco-friendly conditions including low costs and green chemicals for production of metal nanoparticles. In this work, silver nanoparticles (silver NPs) with average particle size about 10 nm were synthesized by using a thermal decomposition technique. Unlike the colloidal chemistry method, the thermal decomposition method developed has advantages such as the high crystallinity, single-reaction synthesis, and easy dispersion ability of the synthesized NPs in organic solvents. In a modified synthesis process, we used sodium oleate as a capping agent to modify the surface of silver NPs because the oleate has a C₁₈ tail with a double bond in the middle, therefore, forming a kink which is to be effective for aggregative stability. Importantly, the as-synthesized silver NPs have demonstrated strong antimicrobial effects against various bacteria and fungi strains. Electron microscopic studies reveal physical insights into the interaction and bactericidal mechanism between the prepared silver NPs and tested bacteria in question. The observed excellent antibacterial and antifungal activity of the silver NPs make them ideal for disinfection and biomedicine applications.     

On the convex hull of the multiform numerical range

Let A ₁,…,A_m be nxn hermitian matrices. Definine

W(A ₁,…,A_m )={(xA₁x ^?,…xA_mx ^?):x?C ⁿ ,xx ^?=1}. We will show that every point in the convex hull of W(A ₁,…,A_m ) can be represented as a convex combination of not more than k(m,n) points in W(A ₁,…,A_m ) where k(m,n)=min{n,[√m]+δ _n ² _m+1}.     

The First Attempt on the Stochastic Calculus on Time Scale

The aim of this article is to study the Doob–Meyer decomposition theorem, ?-stochastic integration and Ito's formula for stochastic processes defined on time scale. The obtained results can be considered as a first attempt on the stochastic calculus on time scale.     

Ultrahigh‐Density Plasmonic‐Nanoparticle‐Sensitized Semiconductor Photocatalysts Profit from Cooperative Light Harvesting and Charge Separation Processes: Experiments,Simulations, and Multifunctional Plasmonics

Here, a controlled synthesis of remarkable 3D photocatalysts is presented that is composed of ultrahigh‐density unaggregated plasmonic Au nanoparticles (AuNPs) chemically bound to vertically aligned ZnO nanorod arrays (ZNA) through bifunctional molecular linkers. Experimental probes and electromagnetic simulations of electron transfer and localized plasmonic coupling processes are exploited to gain insight into the underlying light‐irradiation‐induced interactions in the 3D ZNA–AuNPs photocatalysts. Highly dense AuNPs on ZNA surfaces act as sinks for the storage of UV‐generated electrons, which promote the separation of charge carriers and create numerous photocatalytic reaction centers. Furthermore, 3D finite‐difference time domain simulation indicates that significant visible light confinement and enhancement around the ZNA–AuNPs interfacial plasmon “hot spots” contribute to efficient conversion of light energy to electron‐hole pairs. Significantly, in comparison with the bare ZNA, the 10‐nm‐sized AuNPs‐decorated ZNA exhibits 10.6‐fold enhanced photoreaction rate in the entire UV–vis region. Moreover, various novel hybrid structures based on the plasmonic AuNPs and diverse nanostructures (films, powdered nanorods, mesoporous, and nanotubes) or functional materials (multiferroic BiFeO₃, CuInGaSe₂ absorber layers, and photoactive TiO₂) are successfully constructed using the present synthesis methodology. It may stimulate the progress in materials science toward the synthesis of multifunctional plasmonic heterostructures or devices.     

On Some Quasilinear Elliptic Systems with Singular and Sign-Changing Potentials

Using variational methods, we study the existence and nonexistence of nontrivial weak solutions for the quasilinear elliptic system $$\left\{\begin{array}{ll}- {\rm div}(h_1(|\nabla u|^2)\nabla u) = \frac{\mu}{|x|^2}u + \lambda F_u(x, u, \upsilon)\quad {\rm in}\,\Omega,\\- {\rm div}(h_2(|\nabla \upsilon|^2)\nabla \upsilon) = \frac{\mu}{|x|^2}\upsilon + \lambda F_\upsilon(x,u,\upsilon)\quad {\rm in}\,\Omega,\\u = \upsilon = 0 \qquad \qquad \qquad \qquad \qquad \qquad {\rm in}\, \partial\Omega, \end{array}\right.$$ where \({\Omega \subset \mathbb{R}^N,N \geq 3}\) , is a bounded domain containing the origin with smooth boundary \({\partial \Omega ; h_i, i = 1, 2}\) , are nonhomogeneous potentials; \({(F_u, F_v) = \nabla F}\) stands for the gradient of a sign-changing C ¹-function \({F : \Omega \times \mathbb{R}^2 \to \mathbb{R}}\) in the variable \({{w = (u, v) \in \mathbb{R}^2}}\) ; and λ and μ are parameters.     

Oxidized Xanthan Gum Crosslinked NOCC: Hydrogel System and Their Biological Stability from Oxidation Levels of the Polymer

Dynamic hydrogel systems from N,O-carboxymethyl chitosan (NOCC) are investigated in the past years, which has facilitated their widespread use in many biomedical engineering applications. However, the influence of the polymer's oxidation levels on the hydrogel biological properties is not fully investigated. In this study, chitosan is converted into NOCC and introduced to react spontaneously with oxidized xanthan gum (OXG) to form several injectable hydrogels with controlled degradability. Different oxidation levels of xanthan gum, as well as NOCC/OXG volume ratios, are trialed. The infrared spectroscopy spectra verify chemical modification on OXG and successful crosslinking. With increasing oxidation levels, more dialdehyde groups are introduced into the OXG, resulting in changes in physical properties including gelation, swelling, and self-healing efficiency. Under different volume ratios, the hydrogel shows a stable structure and rigidity with higher mechanical properties, and a slower degradation rate. The shear-thinning and self-healing properties of the hydrogels are confirmed. In vitro assays with L929 cells show the biocompatibility of all formulations although the use of a high amount of OXG15 and OXG25 limited the cell proliferation capacity. Findings in this study suggested a suitable amount of OXG at different oxidation levels in NOCC hydrogel systems for tissue engineering applications.     

K bar -Hyperon Interactions and Possible S-Wave Resonances

Using one-hadron-exchange potentials which describe consistently the baryon–baryon (NN, YN and YY) and meson–baryon (π N and KN) interactions, we discuss properties of the S-wave K ^bar -hyperon interactions. Solving the coupled-channel πΞ-K ^bar Λ-K ^bar Σ problem, we obtain the possible existence of an S-wave resonance (a quasibound state of K ^bar Λ) below the K ^bar Λ threshold. A K ^bar Ξ bound state with I = 0 is also predicted.