Along with the development of industry and the improvement of people’s living standards, peoples’ demand on resources has greatly increased, causing energy crises and environmental pollution. In recent years, photocatalytic technology has shown great potential as a low-cost, environmentally-friendly, and sustainable technology, and it has become a hot research topic. However, current photocatalytic technology cannot meet industrial requirements. The biggest challenge in the industrialization of photocatalyst technology is the development of an ideal photocatalyst, which should possess four features, including a high photocatalytic efficiency, a large specific surface area, a full utilization of sunlight, and recyclability. In this review, starting from the photocatalytic reaction mechanism and the preparation of the photocatalyst, we review the classification of current photocatalysts and the methods for improving photocatalytic performance; we also further discuss the potential industrial usage of photocatalytic technology. This review also aims to provide basic and comprehensive information on the industrialization of photocatalysis technology.
In this paper, we are concerned with the existence, multiplicity and concentration of positive ground state solutions for the semilinear Schrödinger-Poisson systemwhere ε > 0 is a small parameter, f is a continuous, superlinear and subcritical nonlinearity, and λ = 0 is a real parameter. Suppose that a(x) has at least one global minimum and b(x) has at least one global maximum. We prove that there are two families of positive solutions for sufficiently small ε > 0, of which one is concentrating on the set of minimal points of a and the other on the sets of maximal points of b. Moreover, we obtain some sufficient conditions for the nonexistence of positive ground state solutions.Mathematics Subject Classification. 35J61 · 35J50 · 35Q55 · 49J40.
In this paper, we study the existence, nonexistence and mass concentration of L2-normalized solutions for nonlinear fractional Schrödinger equations. Comparingwith the Schrödinger equation, we encounter some new challenges due to the nonlocal nature of the fractional Laplacian. We first prove that the optimal embedding constant for the fractional Gagliardo–Nirenberg–Sobolev inequality can be expressed by exact form, which improves the results of [17, 18]. By doing this, we then establish the existence and nonexistence of L2-normalized solutions for this equation. Finally, under a certain type of trapping potentials, by using some delicate energy estimates we present a detailed analysis of the concentration behavior of L2-normalized solutions in the mass critical case.
Polytetrafluoroethylene (PTFE) is polymerized by tetrafluoroethylene, which has high corrosion resistance, self-lubrication and high temperature resistance. However, due to the large expansion coefficient, high temperature will gradually weaken the intermolecular bonding force of PTFE, which will lead to the enhancement of permeation absorption and the limitation of the application range of fluoroplastics. In order to improve the performance of PTFE, the modified polytetrafluoroethylene, filled by carbon materials and aramid fiber with different scales, is prepared through the compression and sintering. Moreover, the mechanical properties and wear resistance of the prepared composite materials are tested. In addition, the influence of different types of filler materials and contents on the properties of PTFE is studied. According to the experiment results, the addition of carbon fibers with different scales reduces the tensile and impact properties of the composite materials, but the elastic modulus and wear resistance are significantly improved. Among them, the wear rate of 7 μm carbon fiber modified PTFE has decreased by 70%, and the elastic modulus has increased by 70%. The addition of aramid fiber filler significantly reduces the tensile and impact properties of the composite, but its elastic modulus and wear resistance are significantly improved. Among them, the wear rate of the modified composite material with 3% alumina particles and 5% aramid pulp decreased by 68%, and the elastic modulus increased by 206%.
In this paper, we are concerned with a class of Schrödinger-Poisson systems with the asymptotically linear or asymptotically 3-linear nonlinearity. Under some suitable assumptions on V , K, a, and f , we prove the existence, nonexistence, and asymptotic behavior of solutions via variational methods. In particular, the potential V is allowed to be sign-changing for the asymptotically linear case. C 2016 AIP Publishing LLC.
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