Positive ground state solutions for Schrödinger–Poisson system with critical nonlocal term in ℝ3

This paper is dedicated to studying the following Schrödinger–Poisson system $$\left\{\begin{array}{ll}-\mathrm{\Delta }u+V(x)u-K(x)\varphi |u{|}^{3}u=a(x)f(u),& x\in {ℝ}^3,\\ -\mathrm{\Delta }\varphi =K(x)|u{|}^5,& x\in {ℝ}^3.\end{array}\right.$$ Under some different assumptions on functions V(x), K(x), a(x) and f(u), by using the variational approach, we establish the existence of positive ground state solutions.     

共产主义实现过程的数学刻画

指出了极限蕴含着理想与现实的统一,以此刻画了共产主义的实现过程——人类社会可以无限地趋近共产主义.把人类社会视为一个系统,提出了它的两条基本公理.借助于公理法,利用逻辑推理论证了劳动将逐渐成为人们的第一需要、劳动创造财富、人类的思想觉悟可以逐渐达到共产主义人生观等重要结论.     

Theory of chemical bonds in metalloenzymes XXII: a concerted bond-switching mechanism for the oxygen–oxygen bond formation coupled with one electron transfer for water oxidation in the oxygen-evolving complex of photosystem II

ABSTRACT

QM(UB3LYP)/MM(AMBER) calculations were performed for the locations of the transition structure (TS) of the oxygen–oxygen (O–O) bond formation in the S₄ state of the oxygen-evolving complex (OEC) of photosystem II (PSII). The natural orbital (NO) analysis of the broken-symmetry (BS) solutions was also performed to elucidate the nature of the chemical bonds at TS on the basis of several chemical indices defined by the occupation numbers of NO. The computational results revealed a concerted bond switching (CBS) mechanism for the oxygen–oxygen bond formation coupled with the one-electron transfer (OET) for water oxidation in OEC of PSII. The orbital interaction between the σ-HOMO of the Mn(IV)₄–O₍₅₎ bond and the π*-LUMO of the Mn(V)₁=O₍₆₎ bond plays an important role for the concerted O–O bond formation for water oxidation in the CaMn₄O₆ cluster of OEC of PSII. One electron transfer (OET) from the π-HOMO of the Mn(V)₁=O₍₆₎ bond to the σ*-LUMO of the Mn(IV)₄–O₍₅₎ bond occurs for the formation of electron transfer diradical, where the generated anion radical [Mn(IV)₄–O₍₅₎]^-? part is relaxed to the ?Mn(III)₄?…?O₍₅₎^- structure and the cation radical [O₍₆₎=Mn(V)₁]⁺ ? part is relaxed to the ⁺O₍₆₎–Mn(IV)₁? structure because of the charge-spin separation for the electron-and hole-doped Mn–oxo bonds. Therefore, the local spins are responsible for the one-electron reductions of Mn(IV)₄->Mn(III)₄ and Mn(V)₁->Mn(IV)₁. On the other hand, the O₍₅₎^- and O₍₆₎⁺ sites generated undergo the O–O bond formation in the CaMn₄O₆ cluster. The Ca(II) ion in the cubane- skeleton of the CaMn₄O₆ cluster assists the above orbital interactions by the lowering of the orbital energy levels of π*-LUMO of Mn(V)₁=O₍₆₎ and σ*-LUMO of Mn(IV)₄–O₍₅₎, indicating an important role of its Lewis acidity. Present CBS mechanism for the O–O bond formation coupled with one electron reductions of the high-valent Mn ions is different from the conventional radical coupling (RC) and acid-base (AB) mechanisms for water oxidation in artificial and native photosynthesis systems. The proton-coupled electron transfer (PC-OET) mechanism for the O–O bond formation is also touched in relation to the CBS-OET mechanism.     

宁波市公共自行车服务满意度评价模型构建研究

以宁波市公共自行车为例，将因子分析法与二项logistic法相结合，对采集的1 688份居民满意度有效问卷展开分析。利用因子分析法筛选出6个因子，利用二项logistic法剔除并筛选出5个有效因子构建公共自行车服务满意度评价模型，合理评估当前宁波市公共自行车服务满意度。同时，利用随机抽取并不参与建模的5%问卷样本对评价模型进行校验，以确保模型的准确性与合理性。该研究有助于合理评价当前宁波市居民对公共自行车的服务满意度，同时适用于对未来一段时间内公共自行车服务满意度的预测。     

冷轧带钢局部高点卷取过程起筋控制的建模与仿真

为了研究带钢局部高点卷取起筋的控制方法，利用三维弹塑性变形基本理论，并引入带钢塑性流动因子，建立了弹塑性卷取应力和起筋量模型.基于应力函数假设、S. Timoshenko最小功原理和伽辽金虚位移法建立了起筋带钢的应力场分布和可用于在线计算的起筋临界卷取张力设定模型.仿真结果表明：局部高点在径向累积叠加所引起的带钢张力不均匀分布和轴向压应力是导致带钢起筋的主要原因；起筋量随局部高点高度、卷径和卷取张力增加而增大，薄带钢比厚带钢起筋量增幅明显；临界卷取张力随卷径、带钢厚度和局部高点高度增大而减小.     

Recent trends in capillary and micro-chip electrophoretic instrumentation for field-analysis

Technical advances in the development of field-deployable capillary and microchip electrophoretic instruments and reports of their deployment between 2013 and 2017 were reviewed. Strategies and considerations in the design of the injection, separation and detection hardware, chemistry and associated infrastructure were discussed from an in-field perspective, with portability, robustness and automation/“ease of use” featuring as key requirements. Integration of functionality is important for adequate in-field performance. Progress was made towards the use of multiple channel devices for increased throughput and/or resolving power, mixing devices for on-line/in-line sample derivatization, battery operation and temperature control. The strengths and weaknesses of the various approaches described in the literature are discussed from the perspective of in-field operation. An overview of the applications of the field electrophoretic instruments is provided, including environmental science and planetary investigation.     

两个DEA的逆问题的解法的探讨

文[1]提出了两个DEA的逆问题，并用搜索法来解．而本文根据所证的定理，对每个问题一般只要解二、三个线性规划问题就能得到答案．     

N-烯丙基-N''''-(对苯磺酸钠)硫脲的合成及分析应用进展

本文评述了一种新的硫脲试剂N-烯丙基-N'-(对苯磺酸钠)硫脲的合成、性质及其在定性分析、光度分析、电化学分析中的应用进展,展望了今后的研究方向.引用文献20篇.     

产品竞争力的分析方法

为了提高产品的市场竞争力，必须采取一定的方法对产品进行竞争力分析。本文提出了一种实用的、基于客户价值的产品竞争力分析方法，该方法通过产品量化的客户感知价值和客户感知成本的组合比较，确定了产品的相对竞争力。     

采场人员可靠性模糊综合分析

针对采场人—机—环境可靠性系统中,人是最主要的也是最脆弱的这一特点,根据可靠性理论,应用模糊数学理论与层次分析法,建立了一种新型的系统可靠性模糊数学分析模型,对采场人员可靠性进行综合分析和评价。该分析方法能够对采场人员系统可靠性给以直观、定量的描述。最后,以某磷矿为例,验证了模型的合理性。