In this paper,we study unbounded complex symmetric Toeplitz operators on the Hardy space H2(D) and the Fock space g2.The technique used to investigate the complex symmetry of unbounded Toeplitz operators is different from that used to investigate the complex symmetry of bounded Toeplitz operators. 相似文献
Lithium ion batteries (LIBs) have broad applications in a wide variety of a fields pertaining to energy storage devices. In line with the increasing demand in emerging areas such as long-range electric vehicles and smart grids, there is a continuous effort to achieve high energy by maximizing the reversible capacity of electrode materials, particularly cathode materials. However, in recent years, with the continuous enhancement of battery energy density, safety issues have increasingly attracted the attention of researchers, becoming a non-negligible factor in determining whether the electric vehicle industry has a foothold. The key issue in the development of battery systems with high specific energies is the intrinsic instability of the cathode, with the accompanying question of safety. The failure mechanism and stability of high-specific-capacity cathode materials for the next generation of LIBs, including nickel-rich cathodes, high-voltage spinel cathodes, and lithium-rich layered cathodes, have attracted extensive research attention. Systematic studies related to the intrinsic physical and chemical properties of different cathodes are crucial to elucidate the instability mechanisms of positive active materials. Factors that these studies must address include the stability under extended electrochemical cycles with respect to dissolution of metal ions in LiPF6-based electrolytes due to HF corrosion of the electrode; cation mixing due to the similarity in radius between Li+ and Ni2+; oxygen evolution when the cathode is charged to a high voltage; the origin of cracks generated during repeated charge/discharge processes arising from the anisotropy of the cell parameters; and electrolyte decomposition when traces of water are present. Regulating the surface nanostructure and bulk crystal lattice of electrode materials is an effective way to meet the demand for cathode materials with high energy density and outstanding stability. Surface modification treatment of positive active materials can slow side reactions and the loss of active material, thereby extending the life of the cathode material and improving the safety of the battery. This review is targeted at the failure mechanisms related to the electrochemical cycle, and a synthetic strategy to ameliorate the properties of cathode surface locations, with the electrochemical performance optimized by accurate surface control. From the perspective of the main stability and safety issues of high-energy cathode materials during the electrochemical cycle, a detailed discussion is presented on the current understanding of the mechanism of performance failure. It is crucial to seek out favorable strategies in response to the failures. Considering the surface structure of the cathode in relation to the stability issue, a newly developed protocol, known as surface-localized doping, which can exist in different states to modify the surface properties of high-energy cathodes, is discussed as a means of ensuring significantly improved stability and safety. Finally, we envision the future challenges and possible research directions related to the stability control of next-generation high-energy cathode materials. 相似文献
Journal of Applied Mechanics and Technical Physics - A self-equilibrated stress field for an incompressible sphere is constructed based on a non-Euclidean continuum model. The... 相似文献
SARS-CoV-2 (severe acute respiratory syndrome coronavirus 2) has been causing an outbreak of a new type of pneumonia globally, and repeated outbreaks have already appeared. Among the studies on the spread of the COVID-19, few studies have investigated the repeated outbreaks in stages, and the quantitative condition of a controllable spread has not been revealed. In this paper, a brief compartmental model is developed. The effective reproduction number (ERN) of the model is interpreted by the ratio of net newly infectious individuals to net isolation infections to assess the controllability of the spread of COVID-19. It is found that the value of the ERN at the inflection point of the pandemic is equal to one. The effectiveness of the quarantine, even the treatment, is parametrized in various stages with Gompertz functions to increase modeling accuracy. The impacts of the vaccinations are discussed by adding a vaccinated compartment. The results show that the sufficient vaccinations can make the inflection point appear early and significantly reduce subsequent increases in newly confirmed cases. The analysis of the ERNs of COVID-19 in the United States, Spain, France, and Peru confirms that the condition of a repeated outbreak is to relax or lift the interventions related to isolation and quarantine interventions to a level where the ERN is greater than one.
The (2+1)-dimensional Boiti–Leon–Manna–Pempinelli (BLMP) equation is an important integrable model. In this paper, we obtain the breather molecule, the breather-soliton molecule and some localized interaction solutions to the BLMP equation. In particular, by employing a compound method consisting of the velocity resonance, partial module resonance and degeneration of the breather techniques, we derive some interesting hybrid solutions mixed by a breather-soliton molecule/breather molecule and a lump, as well as a bell-shaped soliton and lump. Due to the lack of the long wave limit, it is the first time using the compound degeneration method to construct the hybrid solutions involving a lump. The dynamical behaviors and mathematical features of the solutions are analyzed theoretically and graphically. The method introduced can be effectively used to study the wave solutions of other nonlinear partial differential equations. 相似文献
Boundary layers are omnipresent in fundamental kinetic experimental facilities and practical combustion engines, which can cause ambiguity and misleading results in kinetic target acquisition and even abnormal engine combustion. In this paper, using n-heptane as a representative large hydrocarbon fuel exhibiting pronounced low-temperature chemistry (LTC), two-dimensional numerical simulation is conducted to resolve the transient autoignition phenomena affected by a boundary layer. We focus on the ignition characteristics and the subsequent combustion mode evolution of a hot combustible mixture flowing over a colder flat plate in an isobaric environment. For cases with autoignition occurring within the boundary layer, similarity is observed in the first-stage ignition as manifested by a constant temperature at all locations. The first-stage ignition is found to be rarely affected by heat and radical loss within the boundary layer. While for the main ignition event, an obvious dependence of ignition process on boundary layer thickness is identified, where the thermal-chemical process exhibits similarity at locations with similar boundary layer thickness, and the main ignition tends to first occur within the boundary layer at the domain end and generates a C-shape reaction front. It is found that sequential spontaneous autoignition is the dominant subsequent combustion mode at high-pressure conditions. At low to intermediate pressures, auto-ignition assisted flame propagation is nevertheless the dominant mode for combustion evolution. This research identifies novel features of autoignition and the subsequent combustion mode evolution affected by a cold, fully developed boundary layer, and provides useful guidance to the interpretation of abnormal combustion and combustion mode evolution in boundary layer flows. 相似文献