The wavelength-dependent and frequency-dependent dielectric function of wurtzite-GaN is cMculated totally from fundamental parameters such as the lattice constant using Waiter＇s ab initio model. The errors occurring ...The wavelength-dependent and frequency-dependent dielectric function of wurtzite-GaN is cMculated totally from fundamental parameters such as the lattice constant using Waiter＇s ab initio model. The errors occurring in the cMculation are carefully reduced by/inear interpolation of energy data. The Kramers-Kronig transform of the real part of greater range is obtained by extrapolation of the reM part. The calculation is time-consuming but meaningful The long-wave results are similar to the experimental data of the photon and are useful for related investigation of properties of wide-gap semiconductors such as electron scattering like the Auger recombination and impact ionization.展开更多
After posing the axiom of linear algebra, the author develops how this allows the calculation of arbitrary base powers, which provides an instantaneous calculation of powers in a particular base such as base ten;first...After posing the axiom of linear algebra, the author develops how this allows the calculation of arbitrary base powers, which provides an instantaneous calculation of powers in a particular base such as base ten;first of all by developing the any base calculation of these powers, then by calculating triangles following the example of the “arithmetical” triangle of Pascal and showing how the formula of the binomial of Newton is driving the construction. The author also develops the consequences of the axiom of linear algebra for the decimal writing of numbers and the result that this provides for the calculation of infinite sums of the inverse of integers to successive powers. Then the implications of these new forms of calculation on calculator technologies, with in particular the storage of triangles which calculate powers in any base and the use of a multiplication table in a very large canonical base are discussed.展开更多
The nonuniform sampling method in hologram plane is proposed to reconstruct objects on multi-plane simultaneously. The hologram is nonuniformly sampled by decomposing it into several parts with various sampling rates....The nonuniform sampling method in hologram plane is proposed to reconstruct objects on multi-plane simultaneously. The hologram is nonuniformly sampled by decomposing it into several parts with various sampling rates. The hologram is calculated based on the nonuniform fast Fourier transform （NUFFT） algorithm. In the experiment, we load this nonuniformly sampled hologram on phases-only spatial light modulator （SLM）, and by illumination with collimated light objects with different sampling rates are reconstructed at different distant planes simultaneously. Both of the numerically simulation and optical experiments are performed to demonstrate the feasibility of our method. The experiment also shows that our proposed nonuniform sampled hologram for multi-plane objects is calculated by only one step, better than conventional method that needs several steps of calculation proportional to the numbers of object planes.展开更多
The electronic structures of 17 perchlorofluoroolefins and perfluoroolefins were calculated using the MNDO method.Based on these calculations combined with the perturbation theory,a good structure-reactivity relations...The electronic structures of 17 perchlorofluoroolefins and perfluoroolefins were calculated using the MNDO method.Based on these calculations combined with the perturbation theory,a good structure-reactivity relationship of perchlorofluoroolefins has been established.In the case of internal ole- fins,the direction of nucleophilic attack is governed not only by the perturbation energy of the ground state,but also by the stability of the anionic intermediate and the activation energy of the reaction.展开更多
基金Supported by the National Key Research and Development Program of China under Grant No 2016YFB0400102the National Basic Research Program of China under Grant Nos 2012CB3155605,2013CB632804,2014CB340002 and 2015CB351900+7 种基金the National Natural Science Foundation of China under Grant Nos 61574082,61210014,61321004,61307024 and 51561165012the High Technology Research and Development Program of China under Grant No 2015AA017101the Tsinghua University Student Research Training Projects under Grant No 1611T0157the Tsinghua University Initiative Scientific Research Program under Grant Nos 2013023Z09N and 2015THZ02-3the Open Fund of the State Key Laboratory on Integrated Optoelectronics under Grant No IOSKL2015KF10the CAEP Microsystem and THz Science and Technology Foundation under Grant No CAEPMT201505the Science Challenge Project under Grant No JCKY2016212A503the Guangdong Province Science and Technology Program under Grant No 2014B010121004
文摘The wavelength-dependent and frequency-dependent dielectric function of wurtzite-GaN is cMculated totally from fundamental parameters such as the lattice constant using Waiter＇s ab initio model. The errors occurring in the cMculation are carefully reduced by/inear interpolation of energy data. The Kramers-Kronig transform of the real part of greater range is obtained by extrapolation of the reM part. The calculation is time-consuming but meaningful The long-wave results are similar to the experimental data of the photon and are useful for related investigation of properties of wide-gap semiconductors such as electron scattering like the Auger recombination and impact ionization.
文摘After posing the axiom of linear algebra, the author develops how this allows the calculation of arbitrary base powers, which provides an instantaneous calculation of powers in a particular base such as base ten;first of all by developing the any base calculation of these powers, then by calculating triangles following the example of the “arithmetical” triangle of Pascal and showing how the formula of the binomial of Newton is driving the construction. The author also develops the consequences of the axiom of linear algebra for the decimal writing of numbers and the result that this provides for the calculation of infinite sums of the inverse of integers to successive powers. Then the implications of these new forms of calculation on calculator technologies, with in particular the storage of triangles which calculate powers in any base and the use of a multiplication table in a very large canonical base are discussed.
基金supported by the National"973"Program of China(Nos.2013CB328803 and 2013CB328804)the National"863"Program of China (Nos.2012AA03A302 and 2013AA013904)the Aeronautical Science Foundation of China(No.20125169021)
文摘The nonuniform sampling method in hologram plane is proposed to reconstruct objects on multi-plane simultaneously. The hologram is nonuniformly sampled by decomposing it into several parts with various sampling rates. The hologram is calculated based on the nonuniform fast Fourier transform （NUFFT） algorithm. In the experiment, we load this nonuniformly sampled hologram on phases-only spatial light modulator （SLM）, and by illumination with collimated light objects with different sampling rates are reconstructed at different distant planes simultaneously. Both of the numerically simulation and optical experiments are performed to demonstrate the feasibility of our method. The experiment also shows that our proposed nonuniform sampled hologram for multi-plane objects is calculated by only one step, better than conventional method that needs several steps of calculation proportional to the numbers of object planes.
基金Part Ⅶ was published in Tetrahedron Letter,31,1307 (1990).
文摘The electronic structures of 17 perchlorofluoroolefins and perfluoroolefins were calculated using the MNDO method.Based on these calculations combined with the perturbation theory,a good structure-reactivity relationship of perchlorofluoroolefins has been established.In the case of internal ole- fins,the direction of nucleophilic attack is governed not only by the perturbation energy of the ground state,but also by the stability of the anionic intermediate and the activation energy of the reaction.
