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.     

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),...     

Polyhydrido Copper Nanoclusters with a Hollow Icosahedral Core: [Cu30H18{E2P(OR)2}12] (E=S or Se; R=nPr,iPr or iBu)

Although atomically precise polyhydrido copper nanoclusters are of prime interest for a variety of applications, they have so far remained scarce. Herein, this work describes the synthesis of a dithiophosphate-protected copper(I) hydride-rich nanocluster (NC), [Cu₃₀H₁₈{S₂P(OnPr)₂}₁₂] ( 1_H ), fully characterized by various spectroscopic methods and single-crystal X-ray diffraction. The X-ray structure of 1_H reveals an unprecedented central Cu₁₂ hollow icosahedron. Six faces of this icosahedron are capped by Cu₃ triangles, the whole Cu₃₀ core being wrapped by twelve dithiophosphate ligands and the whole cluster has ideal S₆ symmetry. The locations of the 18 hydrides in 1_H were ascertained by a single-crystal neutron diffraction study. They are composed of three types: capping μ₃-H, interstitial μ₄-H (seesaw) and μ₅-H ligands (square pyramidal), in good agreement with the DFT simulations. The numbers of hydrides and ligand resonances in the ¹H NMR spectrum of 1_H are in line with their coordination environment in the solid state, retaining the S₆ symmetry in solution. Furthermore, two new Se-protected polyhydrido copper nanoclusters, [Cu₃₀H₁₈{Se₂P(OR)₂}₁₂] ( 2_H : R=iPr 3_H : R=iBu) were synthesized from their sulfur relative 1_H via ligand displacement reaction and their X-ray structures feature the exceptional case where both the NC shape and size are fully conserved during the course of ligand exchange. DFT and TD-DFT calculations allow understanding the bonding and optical properties of clusters 1_H – 3_H . In addition, the reaction of 1_H with [Pd(PPh₃)₂Cl₂] in the presence of terminal alkynes led to the formation of new bimetallic Cu−Pd alloy clusters [PdCu₁₄H₂{S₂P(OnPr)₂}₆(C≡CR)₆] ( 4 : R=Ph; 5 : R = C₆H₄F).     

Purification of low-abundance lysozyme in egg white via free-flow electrophoresis with gel-filtration chromatography

As an effective separation tool, free-flow electrophoresis has not been used for purification of low-abundance protein in complex sample matrix. Herein, lysozyme in complex egg white matrix was chosen as the model protein for demonstrating the purification of low-content peptide via an FFE coupled with gel fitration chromatography (GFC). The crude lysozyme in egg while was first separated via free-flow zone electrophoresis (FFZE). After that, the fractions with lysozyme activity were condensed via lyophilization. Thereafter, the condensed fractions were further purified via a GFC of Sephadex G50. In all of the experiments, a special poly(acrylamide- co-acrylic acid) (P(AM-co-AA)) gel electrophoresis and a mass spectrometry were used for identification of lysozyme. The conditions of FFZE were optimized as follows: 130 μL/min sample flow rate, 4.9 mL/min background buffer of 20 mM pH 5.5 Tris-Acetic acid, 350 V, and 14 °C as well as 2 mg/mL protein content of crude sample. It was found that the purified lysozyme had the purity of 80% and high activity as compared with its crude sample with only 1.4% content and undetectable activity. The recoveries in the first and second separative steps were 65% and 82%, respectively, and the total recovery was about 53.3%. The reasons of low recovery might be induced by diffusion of lysozyme out off P(AM-co-AA) gel and co-removing of high-abundance egg ovalbumin. All these results indicated FFE could be used as alternative tool for purification of target solute with low abundance.     

A study on small-world brain functional networks altered by postherpetic neuralgia

Understanding the effect of postherpetic neuralgia (PHN) pain on brain activity is important for clinical strategies. This is the first study, to our knowledge, to relate PHN pain to small-world properties of brain functional networks. Functional magnetic resonance imaging (fMRI) was used to construct functional brain networks of the subjects during the resting state. Sixteen patients with PHN pain and 16 (8 males, 8 females for both groups) age-matched controls were studied. The PHN patients exhibited decreased local efficiency along with non-significant changes of global efficiency in comparison with the healthy controls. Moreover, regional nodal efficiency was found to be significantly affected by PHN pain in the areas related to sense (postcentral gyrus, inferior parietal gyrus and thalamus), memory/affective processes (parahippocampal gyrus) and emotional activities (putamen). Significant correlation (p < 0.05) was also found between the nodal efficiency of putamen and pain intensity in PHN patients. Our results suggest that PHN modulates the local efficiency, and the small-world properties of brain networks may have potentials to objectively evaluate pain information in clinic.     

Built-in piezoelectric field improved photocatalytic performance of nanoflower-like Bi2WO6 using low-power white LEDs

Photocatalysis technology has been proved to be a potential strategy for removal of organic dyes, however high-power light sources are generally necessary to initiate photocatalytic reaction. In this work, we employed an excellent photocatalyst of Bi₂WO₆ with visible light harvest and meanwhile an intrinsic ferroelectricity, which realized the efficient degradation of organic dye via the synergetic photopiezocatalysis. Through coupling the illumination by a low-power (9 W) LED and the ultrasonic vibration (120 W) by an ultrasonic cleaner, the nanoflower-like Bi₂WO₆ composed of ultrathin nanosheets showed a much more enhanced photopiezocatalysis performance for purification of organic dye than the individual photocatalysis and piezocatalysis. Furthermore, the high mineralization efficiency and the good durability of the Bi₂WO₆ catalyst were demonstrated. The possible mechanism of photopiezocatalysis was finally proposed, where the ultrasound-induced piezoelectric field in Bi₂WO₆ drove photo-generated electrons and holes to diffuse along opposite directions, consequently promoting the separation efficiency of charge carriers. This work indicates that the synergetic photopiezocatalysis by coupling irradiation and ultrasonic vibration is a promising strategy to purify organic pollutants in wastewater.     

Enhanced Oral Absorption of Icaritin by Using Mixed Polymeric Micelles Prepared with a Creative Acid-Base Shift Method

The purpose of this study was to develop mixed polymeric micelles with high drug loading capacity to improve the oral bioavailability of icaritin with Soluplus^® and Poloxamer 407 using a creative acid-base shift (ABS) method, which exhibits the advantages of exclusion of organic solvents, high drug loading and ease of scaling-up. The feasibility of the ABS method was successfully demonstrated by studies of icaritin-loaded polymeric micelles (IPMs). The prepared IPMs were characterized to have a spherical shape with a size of 72.74 ± 0.51 nm, and 13.18% drug loading content. In vitro release tests confirmed the faster release of icaritin from IPMs compared to an oil suspension. Furthermore, bioavailability of icaritin in IPMs in beagle dogs displayed a 14.9-fold increase when compared with the oil suspension. Transcellular transport studies of IPMs across Caco-2 cell monolayers confirmed that the IPMs were endocytosed in their intact forms through macropinocytosis, clathrin-, and caveolae-mediated pathways. In conclusion, the results suggested that the mixed micelles of Soluplus^® and Poloxamer 407 could be a feasible drug delivery system to enhance oral bioavailability of icaritin, and the ABS method might be a promising technology for the preparation of polymeric micelles to encapsulate poorly water-soluble weakly acidic and alkaline drugs.