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《Journal of Pure and Applied Algebra》2019,223(11):4677-4688
In this paper, we prove a conjecture by T. Suzuki, which says if a smooth Fano manifold satisfies some positivity condition on its Chern characters, then it can be covered by rational N-folds. We prove this conjecture by using purely combinatorial properties of Bernoulli numbers. 相似文献
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ABSTRACTThis study computes the potential energy curves of the X1Σ+, A1Π, B1Δ, C1Σ+, and D1Π states of AlO+ cation and the transition dipole moments between them. The orders of the rotationless radiative lifetimes are 10–100?μs for the A1Π state, 1–1000?ms for the B1Δ state, 10?ns for the first well and 100?ns for the second well of the C1Σ+ state, and 1?μs for the D1Π state. Emissions of the B1Δ–A1Π and D1Π–C1Σ+ systems are so weak that they are hardly measured via spectroscopy, the emissions of the C1Σ+–X1Σ+, C1Σ+–A1Π, and D1Π–X1Σ+ systems are so strong that they can be detected readily, and emissions of the A1Π–X1Σ+ and D1Π–A1Π systems can be observed through spectroscopy only by a significant effort. There is a strong great similarity between spontaneous emissions of the A1Π–X1Σ+ system of the AlO+ cation and the A2Π–X2Σ+ system of the AlO radical. The emissions of the A2Π–X2Σ+ system of the AlO radical have been measured in outer space Therefore, it is highly possible that the emissions of the A1Π–X1Σ+ system of the AlO+ cation can be detected in the astrophysical media. 相似文献
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Two novel 2′-hydroxychalcone derivatives (i.e., M1 and M2) are explored in this work. We mainly focus on investigating the effects of photoexcitation on hydrogen bonds and on the excited-state intramolecular proton transfer (ESIPT) process. On the basis of calculations of electrostatic potential surface and intramolecular interactions, we verify the formation of hydrogen bond O1 H2···O3 in both S0 and S1 states. Exploring the ultraviolet–visible spectra in the liquid phase, our simulated results reappear in the experimental phenomenon. Analyzing molecular geometry and infrared stretching vibrational spectra, we confirm O1 H2···O3 is strengthened for both M1 and M2 in the S1 state. We further confirm that charge redistribution facilitates ESIPT tendency. Constructing potential energy curves, we find the ultrafast ESIPT behavior for M1, which is because of the deficiency of side hydroxyl moiety comparing with M2. This work makes a reasonable affiliation of the ESIPT mechanism for M1 and M2. We wish this paper could facilitate understanding these two novel systems and promote their applications. 相似文献
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Cavitation erosion is caused in solids exposed to strong pressure waves developing in an adjacent fluid field. The knowledge of the transient distribution of stresses in the solid is important to understand the cause of damaging by comparisons with breaking points of the material. The modeling of this problem requires the coupling of the models for the fluid and the solid. For this purpose, we use a strategy based on the solution of coupled Riemann problems that has been originally developed for the coupling of 2 fluids. This concept is exemplified for the coupling of a linear elastic structure with an ideal gas. The coupling procedure relies on the solution of a nonlinear equation. Existence and uniqueness of the solution is proven. The coupling conditions are validated by means of quasi‐1D problems for which an explicit solution can be determined. For a more realistic scenario, a 2D application is considered where in a compressible single fluid, a hot gas bubble at low pressure collapses in a cold gas at high pressure near an adjacent structure. 相似文献