A quaternion QR algorithm

Summary This paper extends the Francis QR algorithm to quaternion and antiquaternion matrices. It calculates a quaternion version of the Schur decomposition using quaternion unitary similarity transformations. Following a finite step reduction to a Hessenberg-like condensed form, a sequence of implicit QR steps reduces the matrix to triangular form. Eigenvalues may be read off the diagonal. Eigenvectors may be obtained from simple back substitutions. For serial computation, the algorithm uses only half the work and storage of the unstructured Francis QR iteration. By preserving quaternion structure, the algorithm calculates the eigenvalues of a nearby quaternion matrix despite rounding errors.     

Boundary Value Problems with Local Generalized Nevanlinna Functions in the Boundary Condition

For a class of abstract λ-dependent boundary value problems where a local variant of generalized Nevanlinna functions appears in the boundary condition, linearizations are constructed and their local spectral properties are investigated.     

Local field enhancements on gold and silver nanostructures for aperture near field spectroscopy

Optical properties of silver and gold semi-continuous films near the percolation threshold are investigated by scanning near field optical microscopy (SNOM) operating in the collection/transmission mode. The electromagnetic enhanced fields, due to plasmon-polariton localizations, are observed and the intensity distribution is shown to present high intensity variations that increase with the wavelength. The local fields are also demonstrated to be polarization dependent. The intensity distribution is investigated as function of the incident wavelength both for gold and silver films. The calculated probability distribution function (PDF) exhibits an exponential decay for large enhancement factors and is proved to be wavelength dependent.     

On the separation of stress-induced and texture-induced birefringence in acoustoelasticity

In this paper we develop a simple micromechanical model of a prestressed polycrystalline aggregate, in which the texture-induced and stress-induced anisotropies of the aggregate are precisely defined; here the word texture always refers to the texture of the aggregate at the given prestressed configuration, not to that of a perhaps fictitious natural state of the aggregate. We use this model to derive, for a prestressed orthotropic aggregate of cubic crystallites, a birefringence formula which shows explicitly the effects of the orthotropic texture on the acoustoelastic coefficients. From this formula we observe that, generally speaking, we cannot separate the total birefringence into two distinct parts, one reflecting purely the influence of stress on the birefringence, and the other encompassing all the effects of texture. The same formula, on the other hand, provides for each material specific quantitative criteria under which the separation of stress-induced and texture-induced birefringence would become meaningful in an approximate sense.     

两个相邻建筑物周围风环境的数值模拟

高层建筑物及其群体周围所引起的风环境问题正日益受到人们的重视。本文用数值模拟方法对两幢串列布置高层建筑周围的流场进行了模拟，讨论了建筑物高度、间距比等因素对风环境特性的影响。为了与两个相邻建筑物的流场进行比较，本文同时计算了单个建筑物周围流动的分布情况。数值模拟结果对揭示高层建筑群区域内再生风载荷的形成机理提供了一定的分析方法，为城市规划和高层建筑住宅小区设计提供了一定的理论参考和依据。     

回火温度对40Cr钢疲劳裂纹萌生寿命的影响

用系统分析的方法，通过三点弯曲疲劳试验，以数值描述的方式，在线跟踪了40Cr钢及其在三种回火温度下疲劳裂纹萌生过程的疲劳损伤，实验结果表明：随着回火处理温度的提高，40Cr钢的疲劳裂纹萌生寿命都有不同程度的提高．但裂纹萌生寿命在低于450℃的温度范围里，随着回火温度的提高，裂纹萌生寿命有明显的提高，在450℃至580℃范围内，随回火温度的上升，裂纹萌生寿命则没有明显的增加．     

水工混凝土S-N和P-S-N曲线特性研究

在已知混凝土静压强度分布的基础上使用S－N曲线模型推导出一种疲劳寿命满足的分布，并对水工混凝土做了大量的等幅抗压疲劳试验。通过分析发现，实验数据能较好地符合该分布，同时得出了该种混凝土的S－N曲线和P－S－N曲线。     

Synthesis of Carbon/Sulfur Nanolaminates by Electrochemical Extraction of Titanium from Ti2SC

Herein we electrochemically and selectively extract Ti from the MAX phase Ti₂SC to form carbon/sulfur (C/S) nanolaminates at room temperature. The products are composed of multi‐layers of C/S flakes, with predominantly amorphous and some graphene‐like structures. Covalent bonding between C and S is observed in the nanolaminates, which render the latter promising candidates as electrode materials for Li‐S batteries. We also show that it is possible to extract Ti from other MAX phases, such as Ti₃AlC₂ , Ti₃SnC₂ , and Ti₂GeC, suggesting that electrochemical etching can be a powerful method to selectively extract the “M” elements from the MAX phases, to produce “AX” layered structures, that cannot be made otherwise. The latter hold promise for a variety of applications, such as energy storage, catalysis, etc.     

Substrate‐Tuned Catalysis of the Radical S‐Adenosyl‐L‐Methionine Enzyme NosL Involved in Nosiheptide Biosynthesis

NosL is a radical S‐adenosyl‐L ‐methionine (SAM) enzyme that converts L ‐Trp to 3‐methyl‐2‐indolic acid, a key intermediate in the biosynthesis of a thiopeptide antibiotic nosiheptide. In this work we investigated NosL catalysis by using a series of Trp analogues as the molecular probes. Using a benzofuran substrate 2‐amino‐3‐(benzofuran‐3‐yl)propanoic acid (ABPA), we clearly demonstrated that the 5′‐deoxyadenosyl (dAdo) radical‐mediated hydrogen abstraction in NosL catalysis is not from the indole nitrogen but likely from the amino group of L ‐Trp. Unexpectedly, the major product of ABPA is a decarboxylated compound, indicating that NosL was transformed to a novel decarboxylase by an unnatural substrate. Furthermore, we showed that, for the first time to our knowledge, the dAdo radical‐mediated hydrogen abstraction can occur from an alcohol hydroxy group. Our study demonstrates the intriguing promiscuity of NosL catalysis and highlights the potential of engineering radical SAM enzymes for novel activities.     

DFT‐Aided Vibrational Circular Dichroism Spectroscopy Study of (−)‐S‐cotinine

The implementation of a strategy comprising the use of vibrational circular dichroism spectroscopy and DFT calculations allows determination of the solution‐state conformational distribution in (?)‐S‐cotinine, giving further proof of the extra conformer‐discriminating potential of this experimental technique, which may offer unique molecular fingerprints of subtly dissimilar molecular conformers of chiral samples. Natural bond orbital electronic structure calculations of the rotational barrier height between the two main conformers of the species indicate that hyperconjugative effects are the key force governing the conformational equilibrium. The negligible effect of the solvent’s polarity over both structure and conformational energy profile supports this result.