The coupled-cluster formalism – a mathematical perspective

ABSTRACT

The Coupled-Cluster (CC) theory is one of the most successful high precision methods used to solve the stationary Schrödinger equation. In this article, we address the mathematical foundation of this theory with focus on the advances made in the past decade. Rather than solely relying on spectral gap assumptions (non-degeneracy of the ground state), we highlight the importance of coercivity assumptions – Gårding type inequalities – for the local uniqueness of the CC solution. Based on local strong monotonicity, different sufficient conditions for a local unique solution are suggested. One of the criteria assumes the relative smallness of the total cluster amplitudes (after possibly removing the single amplitudes) compared to the Gårding constants. In the extended CC theory the Lagrange multipliers are wave function parameters and, by means of the bivariational principle, we here derive a connection between the exact cluster amplitudes and the Lagrange multipliers. This relation might prove useful when determining the quality of a CC solution. Furthermore, the use of an Aubin–Nitsche duality type method in different CC approaches is discussed and contrasted with the bivariational principle.     

Response surface methodology toward the optimization of high-energy carotenoid extraction from Aristeus antennatus shrimp

High-energy assisted extraction techniques, like ultrasound assisted extraction (UAE) and microwave assisted extraction (MAE), are widely applied over the last years for the recovery of bioactive compounds such as carotenoids, antioxidants and phenols from foods, animals and herbal natural sources. Especially for the case of xanthophylls, the main carotenoid group of crustaceans, they can be extracted in a rapid and quantitative way with the use of UAE and MAE.     

Evolution of Local Structural Ordering and Chemical Distribution upon Delithiation of a Rock Salt–Structured Li1.3Ta0.3Mn0.4O2 Cathode

Lithium‐rich disordered rock‐salt oxides have attracted great interest owing to their promising performance as Li‐ion battery cathodes. While experimental and theoretical efforts are critical in advancing this class of materials, a fundamental understanding of key property changes upon Li extraction is largely missing. In the present study, single‐crystal synthesis of a new disordered rock‐salt cathode material, Li_1.3Ta_0.3Mn_0.4O₂ (LTMO), and its use as a model compound to investigate Li concentration–driven evolution of local cationic ordering, charge compensation, and chemical distribution are reported. Through the combined use of 2D and 3D X‐ray nanotomography, it is shown that Li removal accompanied by oxygen oxidation is correlated with the development of morphological defects such as particle cracking. Chemical heterogeneity, quantified by subparticle level distribution of Mn valence state, is minimal during Mn redox, which drastically increases upon the formation of cracks during oxygen redox. Density functional theory and bond valence sum mismatch calculations reveal the presence of local short‐range ordering in the pristine oxide, which gradually disappears along with the extraction of Li. The study suggests that with cycling the transformation into true cation–disordered state can be expected, which likely impacts the voltage profile and obtainable energy density of the oxide cathodes.     

基于时空的弱点状运动目标检测技术

如何在复杂背景下持续有效地检测目标位置,一直是研究者们需要面对的主要挑战。本文在研究红外点状移动目标特征的基础上,根据目标无纹理,无形状的特性,提出一种改进的形态学目标增强算法,并利用目标连续时空不变性检测目标。首先,建立多尺度的图像金字塔,在每层上采用改进的形态学算法快速、粗糙定位小目标。然后进一步的根据目标在时空上的位置相关性,提出基于目标运动特征分析的精确检测方法。得到精确稳定的检测结果。最后实验结果表明与经典的形态学检测算法及其他算法相比,该技术能更有效地检测弱小目标,具有更高的鲁棒性。     

Graph-based video fingerprinting using double optimal projection

A double optimal projection method that involves projections for intra-cluster and inter-cluster dimensionality reduction are proposed for video fingerprinting. The video is initially set as a graph with frames as its vertices in a high-dimensional space. A similarity measure that can compute the weights of the edges is then proposed. Subsequently, the video frames are partitioned into different clusters based on the graph model. Double optimal projection is used to explore the optimal mapping points in a low-dimensional space to reduce the video dimensions. The statistics and geometrical fingerprints are generated to determine whether a query video is copied from one of the videos in the database. During matching, the video can be roughly matched by utilizing the statistics fingerprint. Further matching is thereafter performed in the corresponding group using geometrical fingerprints. Experimental results show the good performance of the proposed video fingerprinting method in robustness and discrimination.     

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.     

基于压电陶瓷动态信息的结构裂纹识别方法

利用压电陶瓷的动态特性和压电系统的动态信息,对铝梁的裂纹损伤进行了分析研究。随着梁裂纹尺寸的增加,压电陶瓷片的导钠幅值下降,且系统固有频率减小。利用导钠幅值的变化和系统的动态信息,可以对裂纹的位置和尺寸大小进行识别。实验证明该方法的有效性。     

差分跳频通信系统的特点及性能

文章介绍了一种新型的短波跳频通信技术——差分跳频,分析了差分跳频技术区别于常规跳频技术的主要特点。针对按序列检测的信号接收方法,对差分跳频通信系统在AWGN信道下的性能进行了理论分析,同时做出相应的计算机仿真,证实了差分跳频通信技术和按序列检测方法的结合,使通信系统在AWGN信道下的性能得到了比较显著的提升。     

相关条件下基于N-P准则的分布式检测理论研究

本文针对并行网络、二元局部判决的情况,研究了在相关条件下基于N-P准则的分布式检测融合算法,给出了在联合概率密度已知和未知两种情况下的最优融合规则的理论推导及相应的解决方案,并在实验仿真的基础上,得到了部分有益的结论。     

网络安全事件的关联分析方法的比较研究

随着当前攻击手段和技术的日益复杂化,一次入侵事件往往需要多个步骤才能完成,这些步骤都是彼此相关的。但是传统的入侵检测集中于检测底层的入侵或异常,所检测到的结果也仅仅是一次完整入侵的一部分,所以不能将不同的报警结合起来以发现入侵的逻辑步骤或者入侵背后的攻击策略。关联分析技术将不同分析器上产生的报警进行融合与关联分析,极大地减少了报警的数量,降低了入侵检测的误报率,并且适当的减少了入侵检测的漏报率。文中在对网络安全事件关联分析方法的系统结构进行分析后,着重介绍了当前比较流行的几种网络安全事件关联分析方法,最后对各种方法进行了比较研究。