Characteristic polynomial theory of two-stage phase shifting algorithms

Two-stage phase shifting algorithms make possible to directly recover the sum or the difference of the optical phase of two different fringe patterns. These algorithms can be built by combining the known phase shifting algorithms in a non-linear way. In this work, we associate a two-dimensional characteristic polynomial to each two-stage phase shifting algorithm. This enables us to qualitatively compare their behaviour against the main systematic error sources, by means of an analysis protocol like that used for phase shifting algorithms. We show that this tool allows to understand the propagation of properties from precursor phase shifting algorithms to new evaluation algorithms built from them. As an experimental application, a wavefront distortion evaluation in differential phase-shifting interferometry is presented.     

Distorted wave response of ultrasonic annular stator incorporating non-uniform geometry

The traveling wave ultrasonic stator is normally fabricated with teeth. The tooth geometry improves the driving speed, but it creates natural frequency splitting and mode contamination, especially a distorted traveling wave. A dynamic model of a stepped-plate periodic stator is developed to examine the distortion. The stator is treated as an annular supported by a thin mid plate, and the support stiffness is formulated by using equivalent energy principle. The effects of the tooth and mid plate on the natural frequency and vibration mode are examined by using the perturbation method. The rules governing the frequency splitting, frequency perturbation as well as mode contamination are also identified. The traveling wave response and elliptical trace on stator surface are obtained by using the mode superposition method and they are proved to be distorted due to the tooth geometry. The response at the repeated doublets becomes coupled forward and backward traveling waves, but that at the split doublets becomes coupled forward traveling, standing and backward traveling waves. The results indicate that the tooth mass instead of the stiffness decreases the vibration amplitude and driving speed of the dominant wave, but their effects are different at the repeated and split doublets. Inspection of the model implies that the distortion can be suppressed by using a suitable combination of the wavenumber, tooth count, tooth height and occupying fraction. Numerical calculations are carried out to demonstrate the tooth geometry effect on the transient waveform, driving speed and elliptical trace. The optimization of the tooth geometry that can help achieve a purer traveling wave is discussed.     

Quantum‐Chemical and Electrochemical Investigation of the Electrochemical Windows of Halogenated Carborate Anions

The range of electrochemical stability of a series of weakly coordinating halogenated (Hal=F, Cl, Br, I) 1‐carba‐closo‐dodecaborate anions, [1‐R‐CB₁₁X₅Y₆]^? (R=H, Me; X=H, Hal, Me; Y=Hal), has been established by using quantum chemical calculations and electrochemical methods. The structures of the neutral and dianionic radicals, as well as the anions, have been optimized by using DFT calculations at the PBE0/def2‐TZVPP level. The calculated structures are in good agreement with existing experimental data and with previous calculations. Their gas‐phase ionization energies and electron affinities were calculated based on their optimized structures and were compared with experimental (cyclic and square‐wave) voltammetry data. Electrochemical oxidation was performed in MeCN at room temperature and in liquid sulfur dioxide at lower temperatures. All of the anions show a very high resistance to the onset of oxidation (2.15–2.85 V versus Fc^0/+), with only a minor dependence of the oxidation potential on the different halogen substituents. In contrast, the reduction potentials in MeCN are strongly substituent dependent (?1.93 to ?3.32 V versus Fc^0/+). The calculated ionization energies and electron affinities correlate well with the experimental redox potentials, which provide important verification of the thermodynamic validity of the mostly irreversible redox processes that are observed for this series. The large electrochemical windows that are afforded by these anions indicate their suitability for electrochemical applications, for example, as supporting electrolytes.     

Geometric analysis of anharmonic downward distortion following paths

A mathematical aspect of the anharmonic downward distortion following (ADDF) path is discussed. The ADDF method is utilized as an automated reaction path search method, which can explore transition state geometries on a potential energy surface from a potential minimum. We show that the maximum number of the ADD stationary paths intersecting the potential minimum is 2^{f + 1} ? 2 , where f denotes the degree of freedom of the system. We also show that the bifurcation of the ADD stationary path is essential to detect all the transition states connected from a given minimum. The ADDF computation is demonstrated for a H₂O molecule in which pitchfork bifurcation is observed.     

Analysis of Non-innocence of Phosphaquinodimethane Ligands when Charge and Aromaticity Come into Play

Several phosphaquinodimethanes and their M(CO)₅ complexes (M=Cr, Mo, W) and model derivatives have been theoretically investigated regarding the quest of non-innocence. Computed structural and electronic properties of the P-Me/NH₂ substituted phosphaquinodimethanes and tungsten complexes revealed an interesting non-innocent ligand behaviour for the radical anion complexes with distonic ion character and a strong rearomatization of the middle phenyl ring. The latter was further probed taking also geometric aromaticity (HOMA) and quinoid distortion parameters (HOMQc) into account, as well as NICS(1). Furthermore, the effect of the P-substitution was investigated for real (or plausible) complexes and their free ligands focusing on the resulting aromaticity at the middle phenyl ring and vertical one-electron redox processes. The best picture of ligand engagement in redox changes was provided by representing NICS(1) values versus HOMA and the new geometric distortion parameter HOMQc8.     

空间遥感测绘光学系统研究综述

将遥感技术应用到测绘当中是现代地质测绘技术的发展趋势,随着光学载荷分辨率的不断提高,遥感测绘已经成为社会发展和国民经济发展的重要保障。光学载荷决定了测绘空间遥感器的分辨率、测绘精度、卫星平台体积与重量,是遥感器的核心部分。本文对高成像质量透射光学系统、同轴三反光学系统、离轴三反系统等常用的空间遥感测绘光学系统的结构形式和光学性能分别进行了介绍,并对处于研发阶段的新型空间反射光学系统的结构形式和光学性能进行了展望。分析认为,根据不同的应用环境和技术指标,合理选用不同种类的遥感测绘光学系统,可以最大程度利用平台资源,满足遥感测绘需求。     

Hydrothermal synthesis and phase stability of Pb stabilized ZrO2 nanoparticles

The Pb doped metastable tetragonal ZrO₂ (t-ZrO₂:Pb) nanoparticles have been successfully synthesized by hydrothermal method. Pb ion doping has great effects on the phases, crystallite sizes and optical band gaps. Systematic structural characterization revealed that the introduction of Pb ion results in lattice expansion. The as-prepared t-ZrO₂:Pb with ca 4–6 nm in size has high specific surface area (>150 m²/g) and narrow particle size distributions. The diffuse reflectance spectra investigated that the band gap shifts from ultraviolet (E_g = 5.19 eV) for pure ZrO₂ to the visible region for t-ZrO₂:Pb and the gap can be effectively adjusted with the content of Pb in nanocrystals. Through thermal treatment, Pb ion doped in ZrO₂ crystals was excluded with increasing temperature. At 800 °C, the three t-ZrO₂:Pb samples of ZPO-2, ZPO-3 and ZPO-4 still contained the pure tetragonal phase, in which Pb content were not reduced to zero, while the transformation from tetragonal to monoclinic phase occurred due to zero Pb content in ZPO-1. The reason to this transformation and stabilized mechanism of Pb ion in ZrO₂ were discussed.     

High Compression‐Induced Conductivity in a Layered Cu–Br Perovskite

We show that the onset pressure for appreciable conductivity in layered copper‐halide perovskites can decrease by ca. 50 GPa upon replacement of Cl with Br. Layered Cu–Cl perovskites require pressures >50 GPa to show a conductivity of 10^?4 S cm^?1, whereas here a Cu–Br congener, (EA)₂CuBr₄ (EA=ethylammonium), exhibits conductivity as high as 2×10^?3 S cm^?1 at only 2.6 GPa, and 0.17 S cm^?1 at 59 GPa. Substitution of higher‐energy Br 4p for Cl 3p orbitals lowers the charge‐transfer band gap of the perovskite by 0.9 eV. This 1.7 eV band gap decreases to 0.3 eV at 65 GPa. High‐pressure X‐ray diffraction, optical absorption, and transport measurements, and density functional theory calculations allow us to track compression‐induced structural and electronic changes. The notable enhancement of the Br perovskite's electronic response to pressure may be attributed to more diffuse Br valence orbitals relative to Cl orbitals. This work brings the compression‐induced conductivity of Cu‐halide perovskites to more technologically accessible pressures.     

GDP vs. LDP: A Survey from the Perspective of Information-Theoretic Channel

The existing work has conducted in-depth research and analysis on global differential privacy (GDP) and local differential privacy (LDP) based on information theory. However, the data privacy preserving community does not systematically review and analyze GDP and LDP based on the information-theoretic channel model. To this end, we systematically reviewed GDP and LDP from the perspective of the information-theoretic channel in this survey. First, we presented the privacy threat model under information-theoretic channel. Second, we described and compared the information-theoretic channel models of GDP and LDP. Third, we summarized and analyzed definitions, privacy-utility metrics, properties, and mechanisms of GDP and LDP under their channel models. Finally, we discussed the open problems of GDP and LDP based on different types of information-theoretic channel models according to the above systematic review. Our main contribution provides a systematic survey of channel models, definitions, privacy-utility metrics, properties, and mechanisms for GDP and LDP from the perspective of information-theoretic channel and surveys the differential privacy synthetic data generation application using generative adversarial network and federated learning, respectively. Our work is helpful for systematically understanding the privacy threat model, definitions, privacy-utility metrics, properties, and mechanisms of GDP and LDP from the perspective of information-theoretic channel and promotes in-depth research and analysis of GDP and LDP based on different types of information-theoretic channel models.     

有限深水域中三维频域自由面格林函数及其导数的计算方法

三维频域自由面格林函数及其偏导数的数值计算是海洋结构物水动力分析的难点.本文对有限水深格林函数及其偏导数的数值算法作出两点改进:①对原函数的级数表达式进行变形,提出适用于数值计算的形式,解决高频率情况下级数解的计算失真问题;②对Gauss-Laguerre积分法作出改进,解决高频率大水深情况下积分解的数值溢出问题.计算...