Quadratic properties of least-squares solutions of linear matrix equations with statistical applications

Assume that a quadratic matrix-valued function \(\psi (X) = Q - X^{\prime }PX\) is given and let \(\mathcal{S} = \left\{ X\in {\mathbb R}^{n \times m} \, | \, \mathrm{trace}[\,(AX - B)^{\prime }(AX - B)\,] = \min \right\} \) be the set of all least-squares solutions of the linear matrix equation \(AX = B\). In this paper, we first establish explicit formulas for calculating the maximum and minimum ranks and inertias of \(\psi (X)\) subject to \(X \in {\mathcal S}\), and then derive from the formulas the analytic solutions of the two optimization problems \(\psi (X) =\max \) and \(\psi (X)= \min \) subject to \(X \in \mathcal{S}\) in the Löwner partial ordering. As applications, we present a variety of results on equalities and inequalities of the ordinary least squares estimators of unknown parameter vectors in general linear models.     

Quantum reaction dynamics of C(1D) + HD → CH(CD) + D(H) on the ground state potential energy surface

We present accurate quantum dynamic calculations of the reaction C(¹D) + HD on the latest version of the potential energy surface [Zhang et al., J. Chem. Phys. 140, 234301 (2014)]. Using a Chebyshev real wave packet method with full Coriolis coupling, we obtain the initial state‐specified ( ) reaction probabilities, integral cross sections, and rate constants. The resulting probabilities display oscillatory structures due to numerous long‐lived resonances supported by the deep potential well. The calculated rate constants and CD/CH product branching ratio at room temperature are in reasonably good agreement with the experimental measurements.     

Fuzzy logic modifications of the Analytic Hierarchy Process

The Analytic Hierarchy Process (AHP) is a measurement methodology based on pair-wise comparisons that relies on judgment to derive priority scales. During its implementation, one constructs hierarchies, then makes judgments or performs measurements on pairs of elements with respect to a criterion to derive preference scales, which are then synthesized throughout the structure to select the preferred alternative.One of the areas where the AHP finds application is in the subjective phases of risk assessment (RA), where it is used to structure and prioritize diverse risk factors, including the judgments of experts. Since fuzzy logic (FL) has been shown to be an effective tool for accommodating human experts and their communication of linguistic variables, there has been research aimed at modeling the fuzziness in the AHP (FAHP), and recently the focus of some of that modeling has been with respect to RA.The literature discusses more than one FAHP model, which raises the question as to which are the prominent models and what are their characteristics. In response to this question, we examine three of the most influential FAHP models. The article proceeds as follows. It begins with a brief overview of the AHP and its limitations when confronted with a fuzzy environment. This is followed by a discussion of FL modifications of the AHP. A RA-based likelihood score example is used throughout. The article ends with a commentary on the findings.     

Removal of Cu(II) Contamination from Aqueous Solution by Ethylenediamine@β-Zeolite Composite

The low cost β-zeolite and ethylenediamine modified β-zeolite (EDA@β-zeolite) were prepared by self-assembly method and used for Cu(II) removal from contaminated aqueous solution. Removal ability of β-zeolite toward Cu(II) was greatly improved after ethylenediamine (EDA) modification, the removal performance was greatly affected by environmental conditions. XPS results illustrated that the amide group played important role in the removal process by forming complexes with Cu(II). The EDA@β-zeolite showed desirable recycling ability. The finding herein suggested that the proposed composite is a promising and suitable candidate for the removal of Cu(II) from contaminated natural wastewater and aquifer.     

Diboron Bonds Between BX3 (X=H,F, CH3) and BYZ2 (Y=H,F; Z=CO,N2, CNH)

The ability of B atoms on two different molecules to engage with one another in a noncovalent diboron bond is studied by ab initio calculations. Due to electron donation from its substituents, the trivalent B atom of BYZ₂ (Z=CO, N₂, and CNH; Y=H and F) has the ability to in turn donate charge to the B of a BX₃ molecule (X=H, F, and CH₃), thus forming a B⋅⋅⋅B diboron bond. These bonds are of two different strengths and character. BH(CO)₂ and BH(CNH)₂, and their fluorosubstituted analogues BF(CO)₂ and BF(CNH)₂, engage in a typical noncovalent bond with B(CH₃)₃ and BF₃, with interaction energies in the 3–8 kcal/mol range. Certain other combinations result in a much stronger diboron bond, in the 26–44 kcal/mol range, and with a high degree of covalent character. Bonds of this type occur when BH₃ is added to BH(CO)₂, BH(CNH)₂, BH(N₂)₂, and BF(CO)₂, or in the complexes of BH(N₂)₂ with B(CH₃)₃ and BF₃. The weaker noncovalent bonds are held together by roughly equal electrostatic and dispersion components, complemented by smaller polarization energy, while polarization is primarily responsible for the stronger ones.     

Nb掺杂调控CoSeS多级纳米结构用于增强析氢反应

电催化析氢(HER)是清洁制氢的一种有效途径,对于氢经济和氢能产业的发展具有重要意义.金属掺杂是提高电催化剂本征活性的有效方法,导电基底的采用也有利于电荷传输和催化性能的整体提高.尽管已有关于硒化物作为HER催化剂的相关报道,但是合成条件有限、导电性、本征活性的影响,其电催化性能仍有提升的空间.此外,在酸性电解液中的腐蚀和氧化极大限制了催化剂性能的发挥.基于此,本文以氮掺杂碳球为载体,采用金属Nb掺杂、非金属硫硒化物协同以及表面碳包覆的三重策略,将掺杂元素Nb和活性位中心元素Co封装到氮掺杂碳纳米球内并进行连续的硫硒化反应,成功构筑多级纳米结构(Nb-CoSeS@NC)以提高其电催化析氢性能.碳球可为活性位的生长和分散提供足够的空间,同时有效防止活性金属的腐蚀和分解,并阻止金属纳米颗粒的团聚.硫化过程实现了非金属硫元素的掺杂,对于提高硒化物的催化活性和导电性都有重要作用.通过扫描电镜(SEM)、透射电镜(TEM)、X射线衍射(XRD)、拉曼光谱、X射线光电子能谱(XPS)及电催化性能测试,详细研究了Nb-CoSeS@NC独特的纳米结构和电催化制氢性能,并分析了构效关系.XRD结果发现,引入Nb后Co9Se8和CoSe的特征峰移向更高的角度,表明其晶格体积的减小,有助于电荷传输.同时,氮掺杂碳球(NC)在26°可以观察到无定型碳的峰,而石墨碳的D带和G带强度比约为1.05,均表明NC中缺陷的存在,这可以进一步提高碳材料的导电性.SEM和TEM表征显示,催化剂为直径120 nm的均匀的纳米核壳结构,壳层约为30 nm,无明显的团聚和破碎,这是催化剂具有高稳定性的重要原因.表面的褶皱保证了大的活性比表面积,可以大大增加活性位点的数量.同时,催化剂与NC之间的紧密结合可以降低电子传输的阻抗进而改善其稳定性和析氢性能.分析高分辨率的TEM结果发现,Nb掺杂后,Nb-CoSeS@NC中Co₉Se₈的(222)晶面由0.301 nm减小至0.184 nm,与XRD结果相符.XPS表征揭示了引入Nb之后的电子效应.与CoSeS@NC相比,Nb的掺杂使Co 2p向更低的结合能移动,而Se 3d则移向高结合能移动,这是由于Nb导致了更强的电子相互作用.在0.5 M的H₂SO₄中测试催化剂的析氢性能,Nb-CoSeS@NC仅需115 mV的过电位便可以实现10 mA cm^-2的电流密度,Tafel斜率为43 mV dec^-1,优于CoSeS@NC等其他对比样品,且优于大多数掺杂型硒化物电催化剂.经过12 h稳定性测试,电流密度未见明显降低,表明该多级结构催化剂的优异稳定性.Nb-CoSeS@NC提高活性可归因为Nb的掺杂增强了催化剂的电子相互作用,有助于提高的其本征导电性.Nb、Co正离子可以形成氢化物-受体中心,可能会削弱S-H键和Se-H键,并促进H-H键的形成,因此,多元掺杂产生的协同效应可以有效促进HER过程.此外,坚固的氮掺杂纳米碳壳为活性位点的分散提供了足够的空间和优异的电荷传输性能,同时降低了金属活性位腐蚀的可能性.     

Promotion Effect of Gold on Mo/ZSM-5 Catalyst for the Catalytic Cracking of Light Diesel Oil to Increase Propylene Production

Kinetics and Catalysis - Using a modified deposition-precipitation method, a series of Au–Mo/ZSM-5 catalysts with different Au loadings were prepared. The XRD, nitrogen adsorption-desorption,...     

QUALITATIVE ANALYSIS OF DYNAMICAL BEHAVIOR FOR AN IMPERFECT INCOMPRESSIBLE NEO-HOOKEAN SPHERICAL SHELL

IntroductionIn applications, it is commonly considered that the phenomena of cavity formation,growth and run-through of adjacent cavities occur in materials as precursors to failure. Thesephenomena are mainly due to instability of materials. On the other …     

北斗双星/SINS组合导航系统滤波模型的一致性研究

北斗双星定位系统（简称双星定位）是我国自行建立的一种定位系统.根据北斗双星定位系统采用有源定位的特点,介绍了北斗双星与SINS组合的最优预测模型,该方法利用了双星定位系统提供的滞后定位信息对组合系统进行最优预测,进而校正惯导;同时为验证该滤波方法对状态估计的一致性,文中重点研究了滤波器一致性的准则,并给出了检验的统计量.理论研究和试验仿真证明,文中介绍的滤波器与系统是匹配的,具有较高的滤波性能和精度.