Based on the independent, continuous and mapping (ICM) method and homogenization method, a research model is constructed to propose and deduce a theorem and corollary from the invariant between the weight filter function and the corresponding stiffness filter function of the form of power function. The efficiency in searching for optimum solution will be raised via the choice of rational filter functions, so the above mentioned results are very important to the further study of structural topology optimization. 相似文献
We characterize the completeness and frame/basis property of a union of under-sampled windowed exponentials of the form
$$ {\mathcal{F}}(g): =\bigl\{ e^{2\pi i n x}: n\ge 0\bigr\} \cup \bigl\{ g(x)e^{2\pi i nx}: n< 0\bigr\} $$
for \(L^{2}[-1/2,1/2]\) by the spectra of the Toeplitz operators with the symbol \(g\). Using this characterization, we classify all real-valued functions \(g\) such that \({\mathcal{F}}(g)\) is complete or forms a frame/basis. Conversely, we use the classical non-harmonic Fourier series theory to determine all \(\xi \) such that the Toeplitz operators with the symbol \(e^{2\pi i \xi x}\) is injective or invertible. These results demonstrate an elegant interaction between frame theory of windowed exponentials and Toeplitz operators. Finally, we use our results to answer some open questions in dynamical sampling, and derivative samplings on Paley-Wiener spaces of bandlimited functions.
Two cycloaddition methods were applied to chiral protected aminocyclopentenes 2 and 9 and provided novel bicyclic products 3 and 4 in good yields. The explanation for the observed stereochemistry was based on the sterically encumbered β-face forcing the cycloadditions to occur on the α-face of the cyclopentene ring. The stereochemistry of 4 was confirmed by X-ray of the fumarate salt 10 and showed the trans-relationship between the newly formed ring and the chiral –NHBoc group. 相似文献
Macrocystis pyrifera is one important marine macro-algae, while its residues produced by industrial alginate extraction is a hot potato. To figure out whether its residue is suitable for pyrolysis for biofuel, the pyrolytic characteristics and kinetics of macro-algae M. pyrifera residue was investigated using thermogravimetric method from 50 to 800 °C in an inert argon atmosphere at different heating rates of 5, 10, 20, and 30 °C min?1. The activation energy and pre-exponential factor was calculated by Flynn–Wall–Ozawa, Kissinger–Akahira–Sunose, and Popescu methods, and the kinetic mechanism was deduced by Popescu method. The results showed that the primary devolatilization stage of M. pyrifera residue can be described by Jander function $ \left(\left[ {1 - \left( {1 - \alpha } \right)^{1/3} } \right]^{2}\right) $. The average activation energy of M. pyrifera residue was 222.4 kJ mol?1. The results suggested that the experimental results and kinetic parameters provided useful information for the design of pyrolytic processing system using M. pyrifera residue as feedstock. 相似文献
In this study, the objective was to investigate the degradation behavior of Esomeprazole under different recommended stress conditions according to International Conference on Harmonization of Technical Requirements for Registration of Pharmaceuticals for Human Use [1] by HPLC. Our research showed that the effect of mobile phase species on separation was significant for the determination of Esomeprazole and its related compounds. Successful separation of the drug from its related impurities and degradation products formed under different stress conditions was achieved using ammonium acetate buffer/ACN by a gradient elution. Compared with phosphate buffer/ACN, ammonium acetate buffer/ACN under same pH and gradient showed a great improvement in resolution due to the change of elution order. The drug was subjected to stress conditions including acidic, alkaline, oxidative, photolytic, and thermal conditions. Extensive degradation occurred in acidic and oxidative conditions, while mild degradation was observed in alkaline and photolytic conditions. Besides, it turned out the drug was extremely stable under thermal condition. The stability‐indicating LC–UV method was validated with respect to linearity, precision, accuracy, specificity, and robustness. The LC–MS method was also adopted for the characterization of degradation products. Based on the m/z values and fragmentation patterns, the degradation pathway of the drug has been proposed. 相似文献