A posteriori error analysis of a quadratic finite volume method for nonlinear elliptic problems

In this article, we construct and analyze a residual-based a posteriori error estimator for a quadratic finite volume method (FVM) for solving nonlinear elliptic partial differential equations with homogeneous Dirichlet boundary conditions. We shall prove that the a posteriori error estimator yields the global upper and local lower bounds for the norm error of the FVM. So that the a posteriori error estimator is equivalent to the true error in a certain sense. Numerical experiments are performed to illustrate the theoretical results.     

Injectable and self-healing hydrogels with tissue adhesiveness and antibacterial activity as wound dressings for infected wound healing

The design of wound dressings with excellent self-healing ability, adequate adhesion, good biocompatibility, and potential antibacterial ability is of great significance for the healing of infected wounds arising from human activities. Herein, a series of multi-functional hydrogel dressings, poly(ionized isocyanoethyl methacrylate-glutamine)/poly(hexamethylene guanidine) (iG_x/PHMG_y) hydrogels, were obtained through homopolymerization of fully ionized isocyanoethyl methacrylate-glutamine (iIEM-Gln) in the presence of poly(hexamethylene guanidine) (PHMG), in which strong hydrogen bonds were formed among urea groups in the P (iIEM-Gln) chain to form a stable hydrogel network. The prepared iG_x/PHMG_y hydrogels exhibited adequate self-healing ability and tissue adhesion, which could be firmly adhered to the wound surface and remained intact during application. In addition, the presence of PHMG imparted good antibacterial activity to the hydrogels for the effective promotion of the wound healing in S. aureus infected skin wound on mice. Overall, this multi-functional hydrogel provides a facile and effective strategy for the design of infected wound dressings, and may show great potential in clinical applications.     

Understanding the solubility and crystallization of molybdenum in high-sodium borosilicate glasses: effect of lanthanum oxide

Journal of Radioanalytical and Nuclear Chemistry - The simplified 8-oxide system (SiO2-B2O3-Na2O-Al2O3-CaO-TiO2-MoO3-La2O3) has been prepared under two types of cooling methods, and analyzed with...     

Macroscopic Polarization Change of Mononuclear Valence Tautomeric Cobalt Complexes Through the Use of Enantiopure Ligand

The crystallization of a complex having electron transfer properties in a polar space group can induce the polarization switching of a crystal in a specific direction, which is attractive for the development of sensors, memory devices, and capacitors. Unfortunately, the probability of crystallization in a polar space group is usually low. Noticing that enantiopure compounds crystallize in Sohncke space groups, this paper reports a strategy for the molecular design of non-ferroelectric polarization switching crystals based on the use of intramolecular electron transfer and chirality. In addition, this paper describes the synthesis of a mononuclear valence tautomeric (VT) cobalt complex bearing an enantiopure ligand. The introduction of enantiomer enables the crystallization of the complex in the polar space group (P2₁). The polarization of the crystals along the b-axis direction is not canceled out and the VT transition is accompanied by a change in the macroscopic polarization of the polar crystal. Polarization switching via electron transfer is realized at around room temperature.     

Preparation of C30 concrete and its adsorption performance for Cs(I)

Journal of Radioanalytical and Nuclear Chemistry - The preparation of C30 concrete for a cavernous waste repository under construction in China and its Cs(I) adsorption performance were...     

Examples of compactλ-hypersurfaces in Euclidean spaces

In this paper,we first construct compact embeddedλ-hypersurfaces with the topology of torus which are calledλ-torus in Euclidean spaces?n^+1.Then,we give many compact immersedλ-hypersurfaces in Euclidean spaces?n^+1.     

Direct Synthesis of Adipic Esters and Adiponitrile via Photoassisted Cobalt-Catalyzed Alkene Hydrodimerization

The direct hydrodimerization of acrylates and acrylonitrile offers a general streamlined access to industrially important intermediates to nylon 6,6. However, a practical catalytic method for this process has thus far underdeveloped owing to the challenges in regioselectivity and environmental compatibility of applied reagents. Here, we report a cobalt-catalyzed tail-to-tail hydrodimerization of activated alkenes driven by a visible-light photoredox catalysis at ambient temperature, which is applicable to both adipates and adiponitrile synthesis from potentially renewable feedstocks. This protocol utilizes half equivalent of hantzsch ester as a recyclable two-electron and two-proton donor with the assistance of catalytic amount of base as a proton shuttle, and has been shown to be highly regioselective and efficient for hydrodimerizing various activated alkenes to 1,4-difunctionalized butane derivatives.     

On order-preserving and order-reversing mappings defined on cones of convex functions

In this paper,we first show that for a Banach space X,there is a fully order-reversing mapping T from conv(X)(the cone of all the extended real-valued lower semicontinuous proper convex functions defined on X) onto itself if and only if X is reflexive and linearly isomorphic to its dual X~*.Then we further prove the following generalized Artstein-Avidan-Milman representation theorem:For every fully order-reversing mapping T:conv(X)→conv(X),there exist a linear isomorphism U:X→X~*,x_0~*,φ_0∈X~*,α0 and r_0∈R so that(Tf)(x)=α(Ff)(Ux+x_0~*)+φ_0,x+r_0,■x∈X where T:conv(X)→conv(X~*) is the Fenchel transform.Hence,these resolve two open questions.We also show several representation theorems of fully order-preserving mappings defined on certain cones of convex functions.For example,for every fully order-preserving mapping S:semn(X)→ semn(X),there is a linear isomorphism U:X→ X so that(Sf)(x)=f(Ux),■f∈semn(X),x∈X where semn(X) is the cone of all the lower semicontinuous seminorms on X.     

Adaptive finite-time prescribed performance control for stochastic nonlinear systems with unknown virtual control coefficients

Nonlinear Dynamics - This paper is devoted to the adaptive finite-time prescribed performance control (FTPPC) for stochastic nonlinear systems with unknown virtual control coefficients (UVCCs),...