Summary
Although the FeS2 is a promising electrocatalyst for hydrogen storage, the electronic and optical properties of the hydrogenated FeS2 are unclear. To solve these problems, we apply the ...first‐principles calculations to study the hydrogenated behavior, electronic and optical properties of H‐doped FeS2. The results show that the hydrogen is easy to store in cubic FeS2 compared to the orthorhombic FeS2. The reason is that the large interstice of cubic structure can enhance the interaction between H and FeS2. The narrow band gap of FeS2 improves the electronic transfer and enhances the catalytic activity. The hydrogenated FeS2 shows the strong electronic interaction between H and FeS2. The electronic structure shows that the hydrogenated FeS2 is attributed to the formation of H‐S and H‐Fe bonds. Finally, the adsorption spectrum affirms that the hydrogenated cubic FeS2 improves the electronic jump between the occupied state and the empty state.
The hydrogen prefers to store in cubic FeS2 compared to the orthorhombic FeS2.
The narrow band gap enhances the electronic transfer and catalytic activity of FeS2.
The hydrogenated cubic FeS2 improves the electronic transition between the occupied state and the empty state.
Abstract
The classical uncertainty principle works for smooth signal functions. In our work, we apply the Fourier transform derivatives for the study of uncertainty principle, so that the smoothness ...condition for the signal functions is not required. At first, the amplitude and phase derivatives of vector-valued signal functions based on the Fourier transform are defined. Then we obtain a strong form of the uncertainty principle.
We develop a systematic study of the superpositions of elliptic operators with different orders, mixing classical and fractional scenarios. For concreteness, we focus on the sum of the Laplacian and ...the fractional Laplacian, and we provide structural results, including existence, maximum principles (both for weak and classical solutions), interior Sobolev regularity and boundary regularity of Lipschitz type.
Abstract In the last two academical years, as part of the Italian Ministry plan PLS – “Piano Lauree Scientifiche” (Scientific Degree Plan), two courses for high school students and teachers ...consisting in some interdisciplinary and transversal online meetings have been proposed. They regarded the three principles of dynamics, the law of universal gravitation and Maxwell’s equations. “Variations” around these topics were also presented – of historical, philosophical and also of musical nature – to make the cultural setting of what has been discussed deeper and make it meaningful in the present. At the end of each course, students produced a video of few minutes with a personal reworking and rethinking of the meaning of one of the topics discussed.
In this paper, we define the two‐sided fractional Clifford–Fourier transform (FrCFT). Using its properties, we get some uncertainty principles of the FrCFT. Two parts are obtained. One part is a ...modified uncertainty principle. The uncertainty principle states a lower bound on the spreads of two specific transform domains. It is shown that only a Gaussian‐type signal minimizes the uncertainty. We also give a Heisenberg‐type uncertainty principle. The other part is a logarithmic uncertainty principle, which may be obtained from a sharp of Pitt's inequality.
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