In this article we consider the asymptotic behavior of extreme distribution with the extreme value index γ>0 . The rates of uniform convergence for Fréchet distribution are constructed under the second-order regular variation condition.
In this paper,we study a second-order accurate and linear numerical scheme for the nonlocal CahnHilliard equation.The scheme is established by combining a modified Crank-Nicolson approximation and the Adams-Bashforth extrapolation for the temporal discretization,and by applying the Fourier spectral collocation to the spatial discretization.In addition,two stabilization terms in different forms are added for the sake of the numerical stability.We conduct a complete convergence analysis by using the higher-order consistency estimate for the numerical scheme,combined with the rough error estimate and the refined estimate.By regarding the numerical solution as a small perturbation of the exact solution,we are able to justify the discrete?^(∞)bound of the numerical solution,as a result of the rough error estimate.Subsequently,the refined error estimate is derived to obtain the optimal rate of convergence,following the established?∞bound of the numerical solution.Moreover,the energy stability is also rigorously proved with respect to a modified energy.The proposed scheme can be viewed as the generalization of the second-order scheme presented in an earlier work,and the energy stability estimate has greatly improved the corresponding result therein.
This survey article illustrates many important current trends and perspectives for the field and their applications, of interest to researchers in modern algebra, mathematical logic and discrete mathematics. It covers a number of directions, including completeness theorem and compactness theorem for hyperidentities;the characterizations of the Boolean algebra of n-ary Boolean functions and the bounded distributive lattice of n-ary monotone Boolean functions;the functional representations of finitely-generated free algebras of various varieties of lattices via generalized Boolean functions, etc.
目的:研究单眼屈光参差性弱视患者对一阶光栅锐度和二阶纹理敏感度的感知能力。方法:收集2018-01/2022-12于我院确诊的单眼屈光参差性弱视儿童715例715眼作为弱视组,另选取矫正视力正常儿童745例745眼作为正常对照组。分别检测最佳矫正视力(BCVA)、一阶光栅锐度和(或)二阶纹理敏感度,并分析不同程度弱视患者对一阶光栅锐度和二阶纹理敏感度的感知能力。结果:弱视组与正常对照组一阶光栅锐度(11.58±6.10 vs 20.27±3.47,P<0.001)、二阶纹理敏感度(0.33±0.16 vs 0.12±0.04,P<0.001)均有明显差异,且轻中度弱视患者与重度弱视患者一阶光栅锐度(12.10±6.23 vs 8.13±3.70,P<0.001)和二阶纹理敏感度(0.32±0.16 vs 0.37±0.17,P<0.05)均有明显差异。结论:单眼屈光参差性弱视患者大脑皮层一阶视觉通路和二阶视觉通路均存在不同程度的损伤,重度弱视患者较轻中度弱视患者损伤更为严重。
