In this article we show that there exists an analogue of the Fourier duality technique in the setting a series of shift-invariant spaces.Really,every a series shift-invariant spaceΣ^𝑛𝑖=1𝑉x...In this article we show that there exists an analogue of the Fourier duality technique in the setting a series of shift-invariant spaces.Really,every a series shift-invariant spaceΣ^𝑛𝑖=1𝑉𝜙𝑖𝑖with a stable generator^𝑛𝑖=1𝜙𝑖is the range space of a bounded one-to-one linear operator𝑇𝑇between𝐿𝐿2(0,1)and𝐿𝐿2(R).We show regular and irregular sampling formulas inΣ𝑛𝑛𝑖𝑖=1𝑉𝑉𝜙𝜙𝑖𝑖are obtained by transforming.展开更多
In this paper, we investigated the influence of sample temperature on the expansion dynamics and the optical emission spectroscopy of laser-induced plasma, and Ge was selected as the test sample. The target was heated...In this paper, we investigated the influence of sample temperature on the expansion dynamics and the optical emission spectroscopy of laser-induced plasma, and Ge was selected as the test sample. The target was heated from room temperature（22 °C） to 300 °C, and excited in atmospheric environment by using a Q-Switched Nd：YAG pulse laser with the wavelength of 1064 nm. To study the plasma expansion dynamics, we observed the plasma plume at different laser energies（5.0, 7.4 and 9.4 mJ）and different sample temperatures by using time-resolved image. We found that the heated target temperature could accelerate the expansion of plasma plume. Moreover, we also measured the effect of target temperature on the optical emission spectroscopy and signal-to-noise ratio.展开更多
文摘In this article we show that there exists an analogue of the Fourier duality technique in the setting a series of shift-invariant spaces.Really,every a series shift-invariant spaceΣ^𝑛𝑖=1𝑉𝜙𝑖𝑖with a stable generator^𝑛𝑖=1𝜙𝑖is the range space of a bounded one-to-one linear operator𝑇𝑇between𝐿𝐿2(0,1)and𝐿𝐿2(R).We show regular and irregular sampling formulas inΣ𝑛𝑛𝑖𝑖=1𝑉𝑉𝜙𝜙𝑖𝑖are obtained by transforming.
基金support by National Natural Science Foundation of China(Grant Nos.11674128,11504129,and 11474129)Jilin Province Scientific and Technological Development Program,China(Grant No.20170101063JC)the Thirteenth Five-Year Scientific and Technological Research Project of the Education Department of Jilin Province,China(2016,No.400)
文摘In this paper, we investigated the influence of sample temperature on the expansion dynamics and the optical emission spectroscopy of laser-induced plasma, and Ge was selected as the test sample. The target was heated from room temperature（22 °C） to 300 °C, and excited in atmospheric environment by using a Q-Switched Nd：YAG pulse laser with the wavelength of 1064 nm. To study the plasma expansion dynamics, we observed the plasma plume at different laser energies（5.0, 7.4 and 9.4 mJ）and different sample temperatures by using time-resolved image. We found that the heated target temperature could accelerate the expansion of plasma plume. Moreover, we also measured the effect of target temperature on the optical emission spectroscopy and signal-to-noise ratio.
