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991.
Chia-Ou Chang Guo-En Chang Chan-Shin Chou Wen-Tien Chang Chien Po-Chih Chen 《International Journal of Solids and Structures》2008,45(24):6114-6132
In this paper the natural frequencies and the associated mode shapes of in-plane free vibration of a single-crystal silicon ring are analyzed. It is found that the Si(1 1 1) ring is two-dimensionally isotropic in the (1 1 1) plane for elastic constants but three-dimensionally anisotropic, while the Si(1 0 0) ring is fully anisotropic. Hamilton’s principle is used to derive the equations of vibration, which is a set of partial differential equations with coefficients being periodic in polar variable. Expressing the radial and tangential displacements in sinusoidal form with non-predetermined amplitudes, and through the integration with respect to the circumferential variable, the original governing equations in partial differential form can be converted into the amplitude equations in ordinary differential form. The exact expressions for frequencies and mode shapes are obtained. It is found that for Si(1 0 0) rings the frequencies of a pair of modes, which are equal for an isotropic ring, split due to the anisotropic effect only for the second in-plane vibration mode. The phenomena of frequency splitting and degenerate modes can be proved either based on the conservation of averaged mechanical energy or by the concept of crystallographic symmetry groups. When the single-crystal silicon is replaced by the polycrystalline silicon, which is isotropic in elastic constants, the derived equations for frequencies correctly predict the vanishing of the phenomenon of frequency splitting. 相似文献
992.
The title compound 2 was readily prepared by MCPBA oxidation of the sulfide 1. Thermal desulfonylation of 2 gave the sulfoxide‐substituted diene 3. The Diels‐Alder reactions of 3 with various dienophiles gave the cyclized products 4‐9 in good yields. The regiochemistry was found to be dominated by the phenylsulfinyl group, but could be reversed by the presence of a Lewis acid. Deprotonation of 2 by BuLi, followed by the reaction with alkyl halides, gave the substituted 2‐sulfolenes 10. A synthetic application of 10 was demonstrated by converting 10e to the bicyclic product 11. 相似文献
993.
In this research, an experimental short-range visible light communication link using red-, green-, and blue-based light-emitting diodes (LEDs) for portable micro-projector applications is presented. A Reconfigurable design of a post-equalizer aimed to improve the inherent narrow modulation bandwidth of red-, green-, and blue-based LEDs has been experimentally implemented, and its effectiveness with optical filters at the receiver is investigated. Reflective liquid-crystal-on-silicon-based micro-projection architecture, widely used in portable micro-projectors, was set up to evaluate the proposed visible light communication system. The measurement results demonstrated that a significant aggregative bandwidth improvement of 162 MHz as well as an aggregative data transmission rate of nearly 400 Mb/s can be achieved by using a non-return-to-zero–on-off keying (NRZ–OOK) modulation scheme based on only one polarization state of incident light without any offline signal processing. 相似文献
994.
995.
Though the B(a)cklund transformation on time-like surfaces with constant mean curvature surfaces in R2,1 has been obtained,it is not easy to obtain corresponding surfaces because the procedure of solving the related integrable system cannot be avoided when the B(a)cklund transformation is used.For sake of this,in this article,some special work is done to reform the B(a)cklund transformation to a recursion formula,by which we can construct time-like surfaces with constant mean curvature form known ones just by quadrature procedure. 相似文献
996.
The Ramanujan Journal - Let F be a number field, and let $$F^{{\text {cyc}}}$$ be obtained by adjoining to F all the roots of unity. We show that as E ranges over all elliptic curves defined over... 相似文献
997.
998.
Chu-En Chou Yi-An Chen Yi-Ching Lin Shih-Chieh Kao Chieh-Yu Chang Yen-Ku Wu 《中国化学会会志》2020,67(12):2198-2203
Described is a formal synthesis of racemic schulzeines B and C that intercepts intermediates developed by Gurjar and co-workers. The synthetic sequence features an annulative coupling of a ketimine and acrylic acid enabling the construction of the benzoquinolizidine nucleus in a highly convergent manner. We also examined a continuous-flow version of the thermal aza-annulation, which proved less practical as compared to the batch processes. 相似文献
999.
1000.
During the course of investigating the anticancer activities of new compounds, we have synthesized a series of novel cyclic N-hydroxyurea derivatives and several carbamate intermediates1–3. Infrared absorption, nuclear magnetic resonance, and electronic absorption spectra were examined in order to confirm the identities and to study the molecular structure of these compounds. 相似文献