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.
Bare (unmodified) and crown ether (CE)-modified Fe3O4 magnetic nanoparticles (MNPs) were investigated for the rapid extraction of 226Ra from water samples. It involved synthesizing the MNPs, introducing them into the sample solutions, ultrasonicating and agitating the suspension, magnetically separating the nanoparticles from solution, and measuring the 226Ra content in the supernatant. Experimental parameters such as salt choice, salt concentration and pH were optimized to achieve maximum extraction of 226Ra onto the MNPs. 226Ra content was determined using a Hidex 300SL liquid scintillation counter with α/β separation capability, or a gamma spectrometric detection system. The bare Fe3O4 nanoparticles showed significant pH dependence for the extraction of 226Ra from an aqueous solution over a pH range of 2–10. They gave an extraction of 95 ± 1 and 98 ± 1 % at pH 9 in 0.1 M NaCl and 0.1 M NaClO4, respectively, whereas an extraction of 8–24 % was obtained, over the pH ranges from 2 to 5. The CE-modified MNPs yielded extraction efficiencies as high as 99 ± 1 % in the presence of 0.01 M picric acid at pH 4. This study demonstrates that the surface functionalization of Fe3O4 MNPs with suitable ligand modification can offer a selective mode of extraction for 226Ra in the presence of its daughter progenies. 相似文献
High-performance porous carbons derived from tea waste were prepared by hydrothermal treatment, combined together with KOH activation. The heat-treatment-processed materials possess an abundant hierarchical structure, with a large specific surface of 2235 m2 g−1 and wetting-complemental hydrophilicity for electrolytes. In a two-electrode system, the porous carbon electrodes’ built-in supercapacitor exhibited a high specific capacitance of 256 F g−1 at 0.05 A g−1, an excellent capacitance retention of 95.4% after 10,000 cycles, and a low leakage current of 0.014 mA. In our work, the collective results present that the precursor crafted from the tea waste can be a promising strategy to prepare valuable electrodes for high-performance supercapacitors, which offers a practical strategy to recycle biowastes into manufactured materials in energy storage applications. 相似文献
Target tracking technology that is based on aerial videos is widely used in many fields; however, this technology has challenges, such as image jitter, target blur, high data dimensionality, and large changes in the target scale. In this paper, the research status of aerial video tracking and the characteristics, background complexity and tracking diversity of aerial video targets are summarized. Based on the findings, the key technologies that are related to tracking are elaborated according to the target type, number of targets and applicable scene system. The tracking algorithms are classified according to the type of target, and the target tracking algorithms that are based on deep learning are classified according to the network structure. Commonly used aerial photography datasets are described, and the accuracies of commonly used target tracking methods are evaluated in an aerial photography dataset, namely, UAV123, and a long-video dataset, namely, UAV20L. Potential problems are discussed, and possible future research directions and corresponding development trends in this field are analyzed and summarized. 相似文献