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1.
We propose to reduce the (spectral) condition number of a given linear system by adding a suitable diagonal matrix to the system matrix, in particular by shifting its spectrum. Iterative procedures are then adopted to recover the solution of the original system. The case of real symmetric positive definite matrices is considered in particular, and several numerical examples are given. This approach has some close relations with Riley's method and with Tikhonov regularization. Moreover, we identify approximately the aforementioned procedure with a true action of preconditioning. 相似文献
2.
Dengfeng LI 《Frontiers of Mathematics in China》2022,17(4):501
This paper introduces an open conjecture in time-frequency analysis on the linear independence of a finite set of time-frequency shifts of a given L2 function. Firstly, background and motivation for the conjecture are provided. Secondly, the main progress of this linear independence in the past twenty five years is reviewed. Finally, the partial results of the high dimensional case and other cases for the conjecture are briefly presented. 相似文献
3.
Jun Xu Victor V. Terskikh Yueying Chu Anmin Zheng Yining Huang 《Magnetic resonance in chemistry : MRC》2020,58(11):1082-1090
Metal–organic frameworks (MOFs) are a class of important porous materials with many current and potential applications. Their applications almost always involve the interaction between host framework and guest species. Therefore, understanding of host–guest interaction in MOF systems is fundamentally important. Solid-state NMR spectroscopy is an excellent technique for investigating host–guest interaction as it provides information complementary to that obtained from X-ray diffraction. In this work, using MOF α-Mg3(HCOO)6 as an example, we demonstrated that 13C chemical shift tensor of organic linker can be utilized to probe the host–guest interaction in MOFs. Obtaining 13C chemical shift tensor components (δ11, δ22, and δ33, where δ11 ≥ δ22 ≥ δ33) in this MOF is particularly challenging as there are six coordinatively equivalent but crystallographically non-equivalent carbons in the unit cell with very similar local coordination environment. Two-dimensional magic-angle-turning experiments were employed to measure the 13C chemical shift tensors of each individual crystallographically non-equivalent carbon in three microporous α-Mg3(HCOO)6 samples with different guest species. The results indicate that the δ22 component (with its direction approximately being co-planar with the formate anion and perpendicular to the C−H bond) is more sensitive to the adsorbate molecules inside the MOF channel due to the weak C−H···O hydrogen bonding or the ring current effect of benzene. The 13C isotropic chemical shift, on the other hand, seems much less sensitive to the subtle changes in the local environment around formate linker induced by adsorption. The approach described in this study may be used in future studies on host–guest interaction within MOFs. 相似文献
4.
Leah B. Casabianca 《Magnetic resonance in chemistry : MRC》2020,58(7):611-624
The nuclear magnetic resonance (NMR) chemical shift is extremely sensitive to molecular geometry, hydrogen bonding, solvent, temperature, pH, and concentration. Calculated magnetic shielding constants, converted to chemical shifts, can be valuable aids in NMR peak assignment and can also give detailed information about molecular geometry and intermolecular effects. Calculating chemical shifts in solution is complicated by the need to include solvent effects and conformational averaging. Here, we review the current state of NMR chemical shift calculations in solution, beginning with an introduction to the theory of calculating magnetic shielding in general, then covering methods for inclusion of solvent effects and conformational averaging, and finally discussing examples of applications using calculated chemical shifts to gain detailed structural information. 相似文献
5.
利用单相机所采集的图像实现了对光滑高反射表面面形的直接检测.首先利用相机获取参考平面在标准平面镜中的镜像,然后通过参考平面上的点与归一化成像平面上图像点之间的密集折返对应关系,求得待测镜面的深度距离,从而实现对高反射表面面形的测量.通过光线追迹将该测量过程转化为求解物空间中关于两对应光线束之间的相交问题.以相位为载体获取面形梯度分布,求得该表面的法向量场,并求解相应的反射光线束.通过光线追迹对该光线束与相应入射光线束求“交点”检测高反射表面.对标准平面镜进行实验检测,测量得到的面形平面度为0.19 mm.采用传统方法与本文所提方法对汽车后视镜进行检测,所得检测结果对应点之间的平均距离为0.15 mm,验证了本文方法检测镜面面形的有效性. 相似文献
6.
《Tetrahedron letters》2019,60(24):1582-1586
Rh(II)-catalyzed decomposition of certain cyclic α-diazocarbonyl compounds in the presence of cyclic ethers has been shown to give bicyclic ring expansion products. These are thought to arise from a [1,4]-alkyl shift toward the carbonyl oxygen atom and are in contrast with the recently observed spirocyclic products of a Stevens-type [1,2]-alkyl shift within the postulated oxonium ylide intermediate. Quantum chemical calculations performed at the B3LYP/6-31G* level of theory showed that the former reaction pathway (toward fused bicycles) is kinetically preferred. 相似文献
7.
Back Cover: Reactions of Group 4 Metallocenes with Monosubstituted Acetonitriles: Keteniminate Formation versus CC Coupling (Chem. Eur. J. 8/2015) 下载免费PDF全文
8.
ABSTRACTA novel BODIPY-based dye with highly emissive character was configured by Sonogashira coupling and routinely characterized by NMR and MS technology. The emission of dye was investigated in solution/film/solid and shows intensive emission. In solution, the emission peak appeared around 510 nm with little influence by the polar environment. The terthiophene plays an effective antenna effect, harvesting the light and transferring the energy to BODIPY. The pseudo Stoke's shift enlarged to ~170 nm in solution. In film, the emission peak shifted to 563 nm in polycarbonate matrix. And it shifted further to 585 nm in solid due to the highly twisted structure, which avoided closely regular-tight packing. The dye rendered an intense fluorescence, good optothermal stability, and high fluorescence quantum yield (0.55). The solid emission showed highly red emission with Commission Internationale de L'Eclairage (CIE) coordinates of (X = 0.69, Y = 0.31). Thus, the synthesized dye is idea candidate for emitting materials. 相似文献
9.
Tahya Bamine Edouard Boivin Christian Masquelier Laurence Croguennec Elodie Salager Dany Carlier 《Magnetic resonance in chemistry : MRC》2020,58(11):1109-1117
7Li, 31P, and 19F solid-state nuclear magnetic resonance (NMR) spectroscopy was used to investigate the local arrangement of oxygen and fluorine in LiVPO4F1-yOy materials, interesting as positive electrode materials for Li-ion batteries. From the evolution of the 1D spectra versus y, 2D 7Li radiofrequency-driven recoupling (RFDR) experiments combined, and a tentative signal assignment based on density functional theory (DFT) calculations, it appears that F and O are not randomly dispersed on the bridging X position between two X–VO4–X octahedra (X = O or F) but tend to segregate at a local scale. Using DFT calculations, we analyzed the impact of the different local environments on the local electronic structure. Depending on the nature of the VO4X2 environments, vanadium ions are either in the +III or in the +IV oxidation state and can exhibit different distributions of their unpaired electron(s) on the d orbitals. Based on those different local electronic structures and on the computed Fermi contact shifts, we discuss the impact on the spin transfer mechanism on adjacent nuclei and propose tentative signal assignments. The O/F clustering tendency is discussed in relation with the formation of short VIVO vanadyl bonds with a very specific electronic structure and possible cooperative effect along the chain. 相似文献
10.
肝损伤是影响公众健康的重大问题之一, 已经引起了人们越来越多的关注. 而过表达的过氧化亚硝酸盐(ONOO?)在肝损伤等疾病的发病机制中起着重要作用, 被认为是一种与早期肝损伤密切相关的生物活性分子. 因此, 为了探究ONOO?在肝损伤过程中的作用, 开发可以实现肝损伤过程中ONOO?高选择性和实时检测的分析方法具有重要意义. 本文报道了一种具有大斯托克斯位移的远红光至近红外(FR-NIR)ONOO?荧光探针. 由于该探针具有大的斯托克斯位移, 可以有效消除光谱重叠和自吸收的干扰, 从而显著提高成像的信噪比. 此外, 该探针对ONOO?具有高的灵敏度(检出限为25.8 nmol/L)和良好的选择性, 被成功用于药物诱导肝损伤过程中ONOO?信号的成像检测. 相似文献