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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
76.
77.
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
78.
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79.
Oussama Graja Bacem Zghal Kajetan Dziedziech Fakher Chaari Adam Jablonski Tomasz Barszcz Mohamed Haddar 《Comptes Rendus Mecanique》2019,347(1):49-61
Planetary gearboxes are widely used in industrial machines. They usually work in harsh environments giving rise to damages and high maintenance costs. Condition monitoring is a key action allowing one to detect the presence of such damage ensuring healthy running conditions. The knowledge of the dynamic behavior of such a gearbox can be achieved using modeling tools as a primary step before conditioning the monitoring subject. In addition, modeling a gear set can help in the stage of design in order to optimize physical and geometric parameters of the system. Therefore, in this work, a two-dimensional lumped parameter model is adopted to build all vibration sources. The time-varying mesh stiffness is approximated as a square wave form. A novel mathematical formulation is proposed to model the amplitude modulation phenomenon due to the rotational motion of the planets around the center of the gearbox. Finally, the overall vibration signal is concluded as a summation of all vibration components influenced by the modulation function. 相似文献
80.
Tomasz Nienałtowski Paweł Szczepanik Paweł Małecki Dr. Dorota Czajkowska-Szczykowska Dr. Stefan Czarnocki Dr. Jolanta Pawłowska Dr. Anna Kajetanowicz Prof. Karol Grela 《Chemistry (Weinheim an der Bergstrasse, Germany)》2020,26(67):15708-15717
A large-scale synthesis of known Ru olefin metathesis catalyst VII featuring an unsymmetrical N-heterocyclic carbene (NHC) ligand with one 2,5-diisopropylphenyl (DIPP) and one thiophenylmethylene N-substituent is reported. The optimised procedure does not require column chromatography in any step and allows for preparation of up to 0.5 kg batches of the catalyst from simple precursors. The application profile of the obtained catalyst was studied in environmentally friendly dimethyl carbonate (DMC). Although VII exhibited low efficiency in cross-metathesis (CM) with electron-deficient partners, good to excellent results were noted for substrates featuring easy to isomerise C−C double bonds. This includes polyfunctional substrates of medicinal chemistry interest, such as analogues of psychoactive 5F-PB-22 and NM-2201 and two PDE5 inhibitors—Sildenafil and Vardenafil. Finally, a larger scale ring-closing metathesis (RCM) of a Vardenafil derivative was conducted in DMC, allowing for straightforward isolation of the expected product (23 g) in high yield and with low Ru contamination level (7.7 ppm). 相似文献
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