Existence of Three Weak Solutions for a Class of Quasi-Linear Elliptic Operators with a Mixed Boundary Value Problem Containing $p(\cdot )$-Laplacian in a Variable Exponent Sobolev Space

In this paper, we consider a mixed boundary value problem to a class of nonlinear operators containing $p(\cdot )$-Laplacian. More precisely, we are concerned with the problem with the Dirichlet condition on a part of the boundary and the Steklov boundary condition on an another part of the boundary. We show the existence of at least three weak solutions under some hypotheses on given functions and the values of parameters.     

Entropic uncertainty relation of a qubit-qutrit Heisenberg spin model and its steering

We investigate the quantum-memory-assisted entropic uncertainty relation (QMA-EUR) in a Heisenberg XYZ mixed-spin (1/2, 1) model. Coupling strength, Dzyaloshinskii-Moriya (DM) interaction and inhomogeneous magnetic field, respectively, contributing to QMA-EUR by a thermal entanglement in the hybrid-spin model are studied in detail. Furthermore, we compare the uncertainty of the bipartite hybrid model with those of qubit-qubit and qutrit-qutrit systems. Meanwhile, the effects of local PT-symmetric operation and weak measurement on the steering of entropic uncertainty are analyzed. We find that the local PT-symmetric operation can reduce the entropic uncertainty, and the entropic uncertainty can also be decreased by weak measurement reversal.     

From Quantum Probabilities to Quantum Amplitudes

The task of reconstructing the system’s state from the measurements results, known as the Pauli problem, usually requires repetition of two successive steps. Preparation in an initial state to be determined is followed by an accurate measurement of one of the several chosen operators in order to provide the necessary “Pauli data”. We consider a similar yet more general problem of recovering Feynman’s transition (path) amplitudes from the results of at least three consecutive measurements. The three-step histories of a pre- and post-selected quantum system are subjected to a type of interference not available to their two-step counterparts. We show that this interference can be exploited, and if the intermediate measurement is “fuzzy”, the path amplitudes can be successfully recovered. The simplest case of a two-level system is analysed in detail. The “weak measurement” limit and the usefulness of the path amplitudes are also discussed.     

基于像差特征分析的变焦光学系统装调

提出了一种基于像差特征分析的变焦系统共轴性装调方法。针对某型20倍变焦光学系统的装调,在分析变焦光学系统装调要求的基础上,通过采用光学定心加工技术,提高变焦系统各镜组内光学元件的同轴度;采用Zygo干涉仪,检测变焦系统在长短焦位置的像差特性分布;借助CodeV软件仿真计算各光学元件在系统中的公差灵敏度分布,并确定产生像差影响的敏感光学元件;在中心偏测量仪上,完成最终光学系统像质的调整。此外,还设计了一种变焦光学系统各动组间同轴度调试装置,对变焦相机主镜筒机械内孔轴线与直线导轨的平行性进行了精确测量,保证了动组组元光轴的同轴精度。装调结果表明:变焦系统成像质量有明显改善,像面一致性得到保证,长短焦轴上传递函数值分别优于技术要求值0.45和0.55,长短焦轴外0.7视场传递函数值优于0.25和0.35,实现了高精度装调,验证了该方法的可靠性。     

Determination of the arc-root position in a DC plasma torch

The behavior of an arc operated in the nontransferred mode with a conical-shaped cathode and a nozzle-shaped anode is studied by applying general tyro-dimensional conservation equations and auxiliary relations for the simulation of arc channel flows. The position of the arc-root attachment at the anode surface is determined by using Steenbeck's minimum principle, which postulates a minimum arc voltage for a given current and certain given boundary conditions. The overall effects of the anode-arc root on the plasma flow are, studied by comparing the results with those of the transferred mode of operation. Specific arc-channel diameters are chosen in the simulation in order to verify flit, numerical model through comparisons with experimental results. The results show that Steenbeck's minimum principle is useful for determining the position of the arc-root attachment at the anode surface. Application of this method for control of the arc-anode attachment may be valuable in the design and operation of plasma spray torches to avoid jet instabilities.     

弱酸HA与弱碱B-混合溶液缓冲能力分析*

计算了几个常见一元弱酸HA和一元弱碱B-混合溶液的pH,并对其缓冲能力进行了分析。结果表明,HA-B-溶液在一定的浓度条件下,具有一定的缓冲能力。当酸电离常数之比KHA/KHB接近1时,HA-B-溶液中主要存在HA-A-和HB-B- 2个缓冲对。随着KHA/KHB逐渐增大,B-的浓度越来越小,当KHA/KHB大于1 000时,HA-B-溶液主要存在的是HA-A-缓冲对。     

Z及logI对离子交换色谱中脲变溶菌酶分子构象变化的表征

以溶菌酶(Lys)为目标蛋白,用计量置换保留理论(SDT-R)中的参数Z和logI对弱阳离子交换色谱(WCX)中“准天然态”和脲变还原与非还原的两种变性状态的Lys的分子构象变化进行了表征。发现在流动相中含有脲时,蛋白的保留仍服从SDT理论,可以准确测定在特定脲浓度条件下Lys的Z及logI值。结果表明,3种分子构象状态的Lys的Z值均随脲浓度改变呈现不连续变化;“准天然态”Lys在同一脲浓度条件下的Z值比变性状态的大,logI比变性状态的小,而非还原变性态和“准天然态”Lys的Z和logI值比较接近。还     

CO2在Cu表面还原成碳氢化合物的DFT计算研究

应用密度泛函理论（DFT）反应能计算及最小能量路径分析研究了CO2在气相和电化学环境中于Cu(111)单晶表面的还原过程。气相中,CO2还原为碳氢化合物的反应路径可能为：CO2(g) + H* → COOH* → (CO +OH)* → CHO*;CHO + H* → CH2O* → (CH2 + O)*;CH2* + 2H* → CH4或2CH2* → C2H4。整个反应由CO2(g) + H* → COOH* → (CO +OH)*,(CO + H)* → CHO*和CH2O* → (CH2 + O)*等几个步骤联合控制。在-0.50V (vs RHE) 以正的电势下,CO2在Cu(111)表面电化学还原主要形成HCOO-和CO吸附物;随着电势逐渐负移,CO2加氢解离形成CO的反应越来越容易,CO成为主要产物;随电势进一步变负,形成碳氢化合物的趋势逐渐变强。与CO2的气相化学还原不同的是,电化学环境下CO质子化形成的CHO中间体倾向于解离形成CH,而在气相中CHO中间体则倾向于进一步质子化形成CH2O中间体。     

亲水单分散聚合物基质阳离子色谱柱的制备及其应用

以自制5.0 μm单分散大孔亲水交联聚甲基丙烯酸环氧丙酯微球为基质,合成一种新型弱酸性阳离子色谱填料.选用甲烷磺酸作淋洗液,在流速为1.0 mL/min时,对6种无机阳离子(Li+, Na+, NH+4, K+, Mg2+, Ca2+)和有机胺进行了良好分离.考察了淋洗液种类、浓度以及流速对6种无机阳离子分离的影响,选择了合适的色谱分离条件.测得6种离子在一定浓度范围内具有良好的线性关系和低的检出限.将其用于决明茶中阳离子的分析,4种离子在20 min内完全分离,各离子标准加入回收率在96%～107%之间.此色谱柱的分离效果与Dionex IonPacCS12A商品柱接近,但分析时间缩短了44 min.