Asymptotically exact a posteriori local discontinuous Galerkin error estimates for the one‐dimensional second‐order wave equation

In this article, we analyze a residual‐based a posteriori error estimates of the spatial errors for the semidiscrete local discontinuous Galerkin (LDG) method applied to the one‐dimensional second‐order wave equation. These error estimates are computationally simple and are obtained by solving a local steady problem with no boundary condition on each element. We apply the optimal L² error estimates and the superconvergence results of Part I of this work [Baccouch, Numer Methods Partial Differential Equations 30 (2014), 862–901] to prove that, for smooth solutions, these a posteriori LDG error estimates for the solution and its spatial derivative, at a fixed time, converge to the true spatial errors in the L²‐norm under mesh refinement. The order of convergence is proved to be , when p‐degree piecewise polynomials with are used. As a consequence, we prove that the LDG method combined with the a posteriori error estimation procedure yields both accurate error estimates and superconvergent solutions. Our computational results show higher convergence rate. We further prove that the global effectivity indices, for both the solution and its derivative, in the L²‐norm converge to unity at rate while numerically they exhibit and rates, respectively. Numerical experiments are shown to validate the theoretical results. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1461–1491, 2015     

Control of the Electronic Ground State on an Electron‐Transfer Copper Site by Second‐Sphere Perturbations

The Cu_A center is a dinuclear copper site that serves as an optimized hub for long‐range electron transfer in heme–copper terminal oxidases. Its electronic structure can be described in terms of a σ_u* ground‐state wavefunction with an alternative, less populated ground state of π_u symmetry, which is thermally accessible. It is now shown that second‐sphere mutations in the Cu_A containing subunit of Thermus thermophilus ba₃ oxidase perturb the electronic structure, which leads to a substantial increase in the population of the π_u state, as shown by different spectroscopic methods. This perturbation does not affect the redox potential of the metal site, and despite an increase in the reorganization energy, it is not detrimental to the electron‐transfer kinetics. The mutations were achieved by replacing the loops that are involved in protein–protein interactions with cytochrome c, suggesting that transient protein binding could also elicit ground‐state switching in the oxidase, which enables alternative electron‐transfer pathways.     

Cross-Link-Functionalized Nanoparticles for Rapid Excretion in Nanotheranostic Applications

Most NIR-IIb fluorophores are nanoparticle-based probes with long retention (≈1 month or longer) in the body. Here, we applied a novel cross-linked coating to functionalize core/shell lead sulfide/cadmium sulfide quantum dots (PbS/CdS QDs) emitting at ≈1600 nm. The coating was comprised of an amphiphilic polymer followed by three crosslinked amphiphilic polymeric layers (P³ coating), imparting high biocompatibility and >90 % excretion of QDs within 2 weeks of intravenous administration. The P³-QDs were conjugated to an engineered anti-CD8 diabody (Cys-diabody) for in vivo molecular imaging of CD8+ cytotoxic T lymphocytes (CTLs) in response to anti-PD-L1 therapy. Two-plex molecular imaging in combination with down-conversion Er nanoparticles (ErNPs) was performed for real-time in vivo monitoring of PD-L1 positive tumor cells and CTLs with cellular resolution by non-invasive NIR-IIb light sheet microscopy. Imaging of angiogenesis in the tumor microenvironment and of lymph nodes deep in the body with a signal-to-background ratio of up to ≈170 was also achieved using P³-QDs.     

Photocontrolled Release of the Anticancer Drug Chlorambucil with Caged Harmonic Nanoparticles

While chemotherapy is one of the most used treatments in oncology, the systemic administration of chemotherapeutics generally results in undesired damages to healthy tissues and cells, side effects such as severe nausea and leukopenia, and reduced efficacy due to multidrug resistance and poor target accessibility. The limitations of conventional chemotherapy formulation have prompted the development of alternative nanomaterials-based strategies to achieve targeted and stimuli sensitive payload delivery to reach optimal local drug concentration at tumor sites. In this study, the anticancer drug chlorambucil (Clb) was conjugated to the surface of silica coated lithium niobate (LNO) harmonic nanoparticles (HNPs) using a photocaging tether based on coumarin-4-yl methyl derivative. Upon laser pulsed femtosecond irradiation at 790 nm, the second harmonic emission from the metal oxide core induced the efficient release of Clb, with concomitant contribution from the nonlinear absorption of the coumarin (CM)-based moiety.     

(NH4)Bi2(IO3)2F5: An Unusual Ammonium‐Containing Metal Iodate Fluoride Showing Strong Second Harmonic Generation Response and Thermochromic Behavior

An ammonium‐containing metal iodate fluoride compound, (NH₄)Bi₂(IO₃)₂F₅, featuring a two‐dimensional double‐layered framework constructed by [BiO₂F₅]^6? and [BiO₄F₄]^9? polyhedra, as well as [IO₃]^? groups, was successfully synthesized. The well‐ordered alignment of these SHG‐active units leads to an extraordinary strong SHG response of 9.2 times that of KDP. Moreover, this compound possesses a large birefringence (Δn=0.0690 at 589.3 nm), a wide energy band gap (E_g=3.88 eV), and a high laser damage threshold (LDT; 40.2×AgGaS₂). In particular, thermochromic behavior was observed for the first time in this type of compound. Such multifunctional crystals will expand the application of nonlinear optical materials.     

Multifunctional Zn0.3Al0.4O4.5 crystals: An efficient photocatalyst for formaldehyde degradation and EBT adsorption

The Zn_0.3Al_0.4O_4.5 nanoparticles (ZnAlONPs) with size of 70–90 nm are used as an efficient photocatalyst for formaldehyde (HCHO) degradation and effective adsorbent for the removal of eriochrome black-T (EBT) dye from synthetic aqueous solution. Degradation of HCHO reactions were studied using TiO₂ (homemade), TiO₂ (P-25) and ZnAlONPs by irradiating under 18 W daylight lamp source for photocatalytic degradation. The HCHO degradation rate is about 67, 76 and 89% for TiO₂ (homemade), TiO₂ (P25) and ZnAlONPs during 2 h reaction, respectively at initial formaldehyde gas concentration of 20 ppm. Maximum adsorption capacity was optimized by changing the parameters such as pH, EBT concentration and adsorbent dosage. A  200 mg of ZnAlONPs are useable for quick removal of EBT (>95%). Langmuir isotherm model showed a maximum adsorption capacity of 90.90 mgg⁻¹. The ZnAlONPs could be successfully reused upto 5^th adsorption/desorption cycle for EBT dye removal from water samples.     

基于泰勒展开的二阶层次分析法初探

经典AHP常用于武器装备效能或能力评估,然而经典AHP采用线性加权模型,即通过底层指标效能线性加权得到顶层指标效能,对非线性体系往往会引入较大评估误差,易产生决策性错误。为解决这一问题,本文以底层指标效能值等于1/2为展开点,给出基于泰勒展开的二阶加权模型,对线性体系,二阶加权模型可退化为经典线性加权模型;推导出二阶AHP的数学表达式,给出二阶AHP效能评估步骤,构建二阶AHP的基本框架。算例表明,二阶AHP评估结果相比经典AHP更接近于解析解,产生决策性错误的机率远小于经典AHP。     

基于P89LPC922的Mifare卡预付费智能水表的设计与实现

介绍了一种低功耗智能水表的设计方案。该水表以Philips公司的低功耗单片机P89LPC922为控制芯片,配有电源电路、阀门驱动电路、计量电路、Mifare卡的读写电路、液晶显示等部分。根据该方案设计的水表已投入市场。     

Computational Aspect for Function-Valued Padé-Type Approximation

The computational problems of two special determinants are investigated. Those tion for computing Fredholm integral equation of the second kind. The main tool to be used in this paper is the well-known Schur complement theorem.