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${rcl} \partial_tu_{\varepsilon}(t,x)&=&\dfrac12\Delta_xu_{\varepsilon}(t,x)+{\varepsilon}^{-\gamma}V\left(\dfrac{x}{{\varepsilon}}\right)u_{\varepsilon}(t,x),\,(t,x)\in(0,+\infty)\times{\mathbb R}^d, \\ u_{\varepsilon}(0,x)&=&u_0(x),\,x\in{\mathbb R}^d, $\begin{array}{rcl} \partial_tu_{\varepsilon}(t,x)&=&\dfrac12\Delta_xu_{\varepsilon}(t,x)+{\varepsilon}^{-\gamma}V\left(\dfrac{x}{{\varepsilon}}\right)u_{\varepsilon}(t,x),\,(t,x)\in(0,+\infty)\times{\mathbb R}^d, \\ u_{\varepsilon}(0,x)&=&u_0(x),\,x\in{\mathbb R}^d, \end{array} 相似文献
96.
97.
Weglarz WP Tanasiewicz M Kupka T Skórka T Sułek Z Jasiński A 《Solid state nuclear magnetic resonance》2004,25(1-3):84-87
A 3D spin-echo (3D SE) pulse sequence was used on a 4.7 T research MRI system to produce images of extracted human first molar tooth placed in CuSO4 water solution. The maximal resolution achieved was 35 x 63 x 300 microm3 in read and two phase directions, respectively. The high-intensity signal from water in solution together with the lack of signal from mineralized tooth tissue produce very good contrast allowing to visualize topography of outer and inner surfaces of the tooth. The 3D MR data were median filtered, binarized and then divided into separate segments corresponding to the inner tooth cavities and the hard tooth tissue. The topography of the root canals was visualized and the canals volume was calculated. The presented technique may be used for quantitative analysis of the root canal cavities shape and volume. The results of such an analysis may be applied for estimation of the quality of the impressional mapping methods in restorative dentistry or as an alternative non-impressional 3D mapping method. 相似文献
98.
Caleb J. Hiller Dr. Chi Chung Lee Dr. Martin T. Stiebritz Lee A. Rettberg Prof. Dr. Yilin Hu 《Chemistry (Weinheim an der Bergstrasse, Germany)》2019,25(10):2389-2395
Nitrogenase utilizes an ATP-dependent reductase to deliver electrons to its catalytic component to enable two important reactions: the reduction of N2 to NH4+, and the reduction of CO to hydrocarbons. The two nitrogenase-based reactions parallel the industrial Haber–Bosch and Fischer–Tropsch processes, yet they occur under ambient conditions. As such, understanding the enzymatic mechanism of nitrogenase is crucial for the future development of biomimetic strategies for energy-efficient production of valuable chemical commodities. Mechanistic investigations of nitrogenase has long been hampered by the difficulty to trap substrates and intermediates relevant to the nitrogenase reactions. Recently, we have successfully captured CO on the Azotobacter vinelandii V-nitrogenase via two approaches that alter the electron fluxes in a controlled manner: one approach utilizes an artificial electron donor to trap CO on the catalytic component of V-nitrogenase in the resting state; whereas the other employs a mismatched reductase component to reduce the electron flux through the system and consequently accumulate CO on the catalytic component of V-nitrogenase. Here we summarize the major outcome of these recent studies, which not only clarified the catalytic relevance of the one-CO (lo-CO) and multi-CO (hi-CO) bound states of nitrogenase, but also pointed to a potential competition between N2 and CO for binding to the same pair of reactive Fe sites across the sulfur belt of the cofactor. Together, these results highlight the utility of these strategies in poising the cofactor at a well-defined state for substrate- or intermediate-trapping via controlled alteration of electron fluxes, which could prove beneficial for further elucidation of the mechanistic details of nitrogenase-catalyzed reactions. 相似文献
99.
Dr. Markus Hiller Thomas Sittel Prof. Dr. Hubert Wadepohl Prof. Dr. Markus Enders 《Chemistry (Weinheim an der Bergstrasse, Germany)》2019,25(45):10668-10677
Combination of three radical anionic Ph-BIAN ligands (Ph-BIAN=bis-(phenylimino)-acenaphthenequinone) with lanthanoid ions leads to a series of homoleptic, six-coordinate complexes of the type Ln(Ph-BIAN)3. Magnetic coupling data were measured by paramagnetic solution NMR spectroscopy. Combining 1H NMR with 2H NMR of partially deuterated compounds allowed a detailed study of the magnetic susceptibility anisotropies over a large temperature range. The observed chemical shifts were separated into ligand- and metal-centered contributions by comparison with the Y analogue (diamagnetic at the metal). The metal-centered contributions of the complexes with the paramagnetic ions could then be separated into pseudocontact and Fermi contact shifts. The latter is large within the Ph-BIAN scaffold, which shows that magnetic coupling is significant between the lanthanide ion and the radical ligand. Pseudocontact shifts were further correlated to structural data obtained from X-ray diffraction experiments. Ligand-field parameters were determined by fitting the temperature dependence of the observed magnetic susceptibility anisotropies. The electronic structure determined by this approach shows, that the Er and Tm analogues are candidates for single molecule magnets (SMM). These results demonstrate the possibilities for the application of NMR spectroscopy in investigations of paramagnetic systems in general and single molecule magnets in particular. 相似文献
100.
An application of electromagnetic devices of the motional type (i.e. eddy-current dampers) to improve the dynamic stability of a cantilever pipe discharging fluid is proposed. When the flow velocity reaches a critical value, this system loses stability through the flutter. A contactless damping device is used. This actuator is made of a conducting plate attached to the pipe that moves together with it within the perpendicular magnetic field that is generated by the controlled electromagnets. During the motion the eddy currents in the plate and a resultant drag force of a viscous character are generated. First, an optimal control problem that aims to stabilise the system with the optimal rate of decrease of the system’s energy is posed and solved. Then a state-feedback parametrization of the obtained optimal control, which can be used in a closed-loop scheme is proposed. The effectiveness of the designed optimal controller is validated by making a comparison with the corresponding passive solutions on the specially designed and constructed experimental test stand of a pipe conveying air. 相似文献 |