In this paper, we study the Cauchy problem for the Benjamin-Ono-Burgers equation \({\partial _t}u - \epsilon \partial _x^2u + {\cal H}\partial _x^2u + u{u_x} = 0\), where \({\cal H}\) denotes the Hilbert transform operator. We obtain that it is uniformly locally well-posed for small data in the refined Sobolev space \({\tilde H^\sigma }(\mathbb{R})\,\,(\sigma \geqslant 0)\), which is a subspace of L2(ℝ). It is worth noting that the low-frequency part of \({\tilde H^\sigma }(\mathbb{R})\) is scaling critical, and thus the small data is necessary. The high-frequency part of \({\tilde H^\sigma }(\mathbb{R})\) is equal to the Sobolev space Hσ (ℝ) (σ ⩾ 0) and reduces to L2(ℝ). Furthermore, we also obtain its inviscid limit behavior in \({\tilde H^\sigma }(\mathbb{R})\) (σ ⩾ 0).
Effective analysis and forecasting of carbon prices, which is an essential endeavor for the carbon trading market, is still considered a difficult task because of the nonlinearity and nonstationarity inherent in carbon prices. Previous studies have failed at the analysis and interval prediction of carbon prices and are limited to point forecasts. Therefore, an improved carbon price analysis and forecasting system that consists of an analysis module and a forecasting module is established in this study; more importantly, the forecasting module includes point forecasting and interval forecasting as well. Aimed at investigating the characteristics of the carbon price series, a chaotic analysis based on the maximum Lyapunov exponent is performed, the determination of appropriate distribution functions based on our newly proposed hybrid optimization algorithm is conducted, and different distribution functions are effectively designed in the analysis module. Furthermore, in the point forecasting model, the phase space reconstruction technique is applied to reconstruct the sequences decomposed by variational mode decomposition due to the chaotic characteristics of the carbon price series, and the reconstructed sequences are considered as the optimal input–output variables of the forecasting model. Then, an adaptive neuro-fuzzy inference system model is trained by the newly proposed hybrid optimization algorithm, which is developed for the first time in the domain of carbon price point forecasting. Moreover, based on the results of point forecasting and the distribution function of the carbon price series determined by the analysis module, the interval forecasting results can be obtained and implemented to provide more reliable information for decision making. Empirical results based on the carbon price data of the European Union Emissions Trading System and Shenzhen of China demonstrate that the proposed system achieves better results than other benchmark models in point forecasting as well as interval forecasting. 相似文献
Ion funnel is a new-style ion guider which can reduce spatial divergence and energy dispersity of the transmission ions by using radio frequency (RF) electric field to confine the ions radially and the direct current (DC) axial electric field to move the ions toward the exit, and thus it can greatly increase the ion transmission efficiency and improve the sensitivity of the mass spectrometry. Since ion funnel was invented in 1997, it has attracted a close attention of mass spectrometry scientists all over the world. Ion funnel has been used in various kinds of mass spectrometry, and built a bridge with high efficiency ion transmission between low vacuum ionization source and high vacuum mass analyzer. In this paper, the principle, technology development, and application progress of ion funnel are reviewed, and the future prospects are prospected. 相似文献
Research on Chemical Intermediates - In this paper, a one-pot and sustainable method for the preparation of Ag/ZnO nanocomposites in green polyethylene glycol-200 (PEG-200) was reported with silver... 相似文献