Superconvergence of a two‐grid method for fourth‐order dispersive‐dissipative wave equations

In this paper, the superconvergence analysis of a two‐grid method (TGM) with low‐order finite elements is presented for the fourth‐order dispersive‐dissipative wave equations for a second order fully discrete scheme. The superclose estimates in the H¹‐norm on the two grids are obtained by the combination technique of the interpolation and Ritz projection. Then, with the help of the interpolated postprocessing technique, the global superconvergence properties are deduced. Finally, numerical results are provided to show the performance of the proposed TGM for conforming bilinear element and nonconforming element, respectively. It shows that the TGM is an effective method to the problem considered of our paper compared with the traditional Galerkin finite element method (FEM).     

Unconditionally Superclose Analysis of a New Mixed Finite Element Method for Nonlinear Parabolic Equation

This paper develops a framework to deal with the unconditional superclose analysis of nonlinear parabolic equation. Taking the finite element pair $Q_{11}/Q_{01} × Q_{10}$ as an example, a new mixed finite element method (FEM) is established and the $τ$ -independent superclose results of the original variable $u$ in $H^1$-norm and the flux variable $\mathop{q} \limits ^{\rightarrow}= −a(u)∇u$ in $L^2$-norm are deduced ($τ$ is the temporal partition parameter). A key to our analysis is an error splitting technique, with which the time-discrete and the spatial-discrete systems are constructed, respectively. For the first system, the boundedness of the temporal errors is obtained. For the second system, the spatial superclose results are presented unconditionally, while the previous literature always only obtain the convergent estimates or require certain time step conditions. Finally, some numerical results are provided to confirm the theoretical analysis, and show the efficiency of the proposed method.     

The regulation of biothiol-responsive performance and bioimaging application of benzo[c][1,2,5]oxadiazole dyes

The different oxidation states of sulphur atom play a significant role on functional materials. In this work, a aryl-thioether and its sulphone substituted benzo[c][1,2,5]oxadiazole dyes were synthesized and utilized to determine thiol-containing amino acids. The result of selectivity experiments showed they detected the cysteine and homocysteine under physiological condition with negligible interference from other amino acids. In comparison to the thioether dye, the sulphone-based dye exhibited much faster response time for Cys and Hcy. However, the sulphone restricted its thiol-reactivity and bioimaging performance in living cells. By reducing the oxidation state of sulphur atom, we amazedly found that the sulfoxide-based dye still maintained high selectivity ultrafast response time for Cys/Hcy under physiological condition. It was worth mentioning that it also had high reactivity and good bioimaging performance that sulfone compounds did not have.     

Influence of magnetic powders on the tribological performance of a novel magnetic brake material

By adding magnetic powders into matrix material, it has been proved to be a creative approach to improve tribological properties of brake materials. In this paper, a novel magnetic brake material with Nd–Fe–B and nano-Fe₃O₄ was developed, and the influential mechanism of these two magnetic powders and their content on the friction and wear performance was deeply discussed. Firstly, some experiments were carried out to investigate the tribological performance and influential mechanisms of four groups of brake pad samples with different magnetic powders. Furthermore, based on these results, further experiments for investigating the influence that Nd–Fe–B contents have on the tribological properties were conducted. According to the theoretical analysis about experiments, it was concluded that nano-Fe₃O₄ is beneficial to promote the formation of friction film and has certain lubricant effects. However, Nd–Fe–B has double effects on the formation of friction film. It will have positive effects when its content is less than a certain value. Otherwise, it will destroy the structure of friction film. Conclusively, it is believed that this study will be significantly valuable and meaningful for developing new brake materials and improving safety reliability of mechanical brakes.     

A Luminescent Hypercrosslinked Conjugated Microporous Polymer for Efficient Removal and Detection of Mercury Ions

A hypercrosslinked conjugated microporous polymer (HCMP‐1) with a robustly efficient absorption and highly specific sensitivity to mercury ions (Hg²⁺) is synthesized in a one‐step Friedel–Crafts alkylation of cost‐effective 2,4,6‐trichloro‐1,3,5‐triazine and dibenzofuran in 1,2‐dichloroethane. HCMP‐1 has a moderate Brunauer–Emmett–Teller specific surface (432 m² g⁻¹), but it displays a high adsorption affinity (604 mg g⁻¹) and excellent trace efficiency for Hg²⁺. The π–π* electronic transition among the aromatic heterocyclic rings endows HCMP‐1 a strong fluorescent property and the fluorescence is obviously weakened after Hg²⁺ uptake, which makes the hypercrosslinked conjugated microporous polymer a promising fluorescent probe for Hg²⁺ detection, owning a super‐high sensitivity (detection limit 5 × 10⁻⁸ mol L⁻¹).

     

A NEW NONCONFORMING MIXED FINITE ELEMENT SCHEME FOR THE STATIONARY NAVIER-STOKES EQUATIONS

In this article, a new stable nonconforming mixed finite element scheme is proposed for the stationary Navier-Stokes equations, in which a new low order CrouzeixRaviart type nonconforming rectangular element is taken for approximating space for the velocity and the piecewise constant element for the pressure. The optimal order error estimates for the approximation of both the velocity and the pressure in L2-norm are established, as well as one in broken H1-norm for the velocity. Numerical experiments are given which are consistent with our theoretical analysis.     

Simultaneous Determination of Ebastine and Its Active Metabolite (Carebastine) in Human Plasma Using LC–MS–MS

A sensitive and rapid LC–MS–MS method was developed for the simultaneous determination of ebastine and carebastine in human plasma. Solid-phase extraction was used to isolate the compounds from the biological matrix followed by separation on a Symmetry C18 column under isocratic conditions. The mobile phase was 10 mM ammonium formate in water/acetonitrile (40:60, v/v). Detection was carried out using a triple-quadrupole mass spectrometer in positive electrospray ionization and multiple reaction monitoring mode. The method was fully validated over the concentration range of 0.1–10 ng mL^?1 for ebastine and 0.2–200 ng mL^?1 for carebastine in human plasma, respectively. The lower limit of quantification (LLOQ) was 0.1 ng mL^?1 for ebastine and 0.2 ng mL^?1 for carebastine. For ebastine and carebastine inter- and intra-day precision (CV%) and accuracy values were all within ±15% and 85–115%, respectively. The extraction recovery was on average 60.0% for ebastine and 60.3% for carebastine.     

非线性抛物型积分微分方程非协调三角形Carey元的收敛性分析

将非协调三角形Carey元应用于二维空间中的非线性抛物型积分微分方程.通过一些新的特殊方法和技巧,给出了有限元解的最优L<'2>模和能量模误差估计.     

Stabilized mixed finite element methods for the Navier‐Stokes equations with damping

In this paper, the stabilized mixed finite element methods are presented for the Navier‐Stokes equations with damping. The existence and uniqueness of the weak solutions are proven by use of the Brouwer fixed‐point theorem. Then, optimal error estimates for the H¹‐norm and L²‐norm of the velocity and the L²‐norm of the pressure are derived. Moreover, on the basis of the optimal L²‐norm error estimate of the velocity, a stabilized two‐step method is proposed, which is more efficient than the usual stabilized methods. Finally, two numerical examples are implemented to confirm the theoretical analysis.