数学季刊

楼与群Ⅱ

周国晖 , 黎景辉

2020, 35(3): 221-254. doi:10.13371/j.cnki.chin.q.j.m.2020.03.001

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This is the second part of a pedagogical introduction to the theory of buildings of Jacques Tits. We define a(B,N) pair and construct a building out of it. Then we give a description of Chevalley groups, their(B,N) pair and the associated buildings. We illustrates this theory with many examples from classical groups.

加权空间中高维空间离散化的FitzHugh-Nagumo系统的全局吸引子

尹福其 , 姜红 , 金蒙召 , 刘志奇

2020, 35(3): 255-277. doi:10.13371/j.cnki.chin.q.j.m.2020.03.002

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In this paper, We study the global attractor and its properties on infinite lattice dynamical system FitzHugh-Nagumo in a weighted space l_σ²×l_σ². We prove the existence and uniqueness of the solution to the lattice dynamical system FitzHugh-Nagumo in l_σ²×l_σ². Then we get a bounded absorbing set, which suggests the existence of global attractors. Finally, we study the uniform boundedness and the upper semicontinuity of the global attractor.

带有分数阶Robin边界条件的Riesz空间分数阶对流-扩散方程的有限差分方法

林海欣 , 房少梅,

2020, 35(3): 278-289. doi:10.13371/j.cnki.chin.q.j.m.2020.03.003

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In this paper, a Riesz space fractional advection-dispersion equation with fractional Robin boundary condition is considered. By applying the fractional central difference formula and the weighted and shifted Gru¨nwald-Letnikov formula, we derive a weighted implicit finite difference scheme with accuracy O（?t²+ h²）. The solvability,stability, and convergence of the proposed numerical scheme are proved. A numerical example is presented to confirm the accuracy and efficiency of the scheme.

Elastic Net方法在部分线性模型的应用

黄登香, 李春红 , 覃朝勇 , 卢春婷

2020, 35(3): 290-301. doi:10.13371/j.cnki.chin.q.j.m.2020.03.004

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Variable selection plays an important role in high-dimensional data analysis.But the high-dimensional data often induces the strongly correlated variables problem,which should be properly handled. In this paper, we propose Elastic Net procedure for partially linear models and prove the group effect of its estimate. A simulation study shows that the Elastic Net procedure deals with the strongly correlated variables problem better than the Lasso, ALasso and the Ridge do. Based on the real world data study,we can get that the Elastic Net procedure is particularly useful when the number of predictors p is much bigger than the sample size n.

具非局部非线性阻尼和源项的波方程解的能量衰减估计

张宏伟, 李栋浩, 呼青英

2020, 35(3): 302-310. doi:10.13371/j.cnki.chin.q.j.m.2020.03.005

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We consider a wave equation with nonlocal nonlinear damping and source terms. We prove a general energy decay property for solutions by constructing a stable set and using the multiplier technique. The main difficult is how to handle with the nonlocal nonlinear damping term. Our result extends and improves the result in the literature such as the work by Jorge Silva and Narciso（Evolution Equation and Control Theory, 2017（6）:437-470） and Narciso（Evolution Equations and Control Theory, 2020, 9（2）: 487-508）.

具有加权p-Poincaré不等式的光滑测度空间上的消灭定理

周久儒

2020, 35(3): 311-319. doi:10.13371/j.cnki.chin.q.j.m.2020.03.006

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This paper deals with vanishing results for L_f² harmonic p-forms on complete metric measure spaces with a weighted p-Poincaré inequality. Some results are without curvature assumptions for 1 ≤ p ≤ n-1 and the others are with assumptions on lower bound of the m-Bakry-émery Ricci curvature for p = 1. These are weighted version for the corresponding results of the present author（J. Math. Anal. Appl., 2020, 490）.

具有工件加工时间相容性和可拒绝的单机分批排序

孟金涛, 鲁晓旭, 李士生, 周永卫

2020, 35(3): 320-330. doi:10.13371/j.cnki.chin.q.j.m.2020.03.007

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We address a scheduling problem with job processing time compatibility and rejection on a parallel-batching machine. The processing time of each job is defined by an interval and any number of jobs can be assigned into a batch provided that the processing time intervals of the jobs in the common batch are not disjoint. Three problems are considered:（1） minimize the sum of the makespan of accepted jobs and the total rejection penalty of rejected jobs;（2） minimize the makespan of accepted jobs subject to an upper bound on the total rejection penalty of rejected jobs;（3） minimize the total rejection penalty of rejected jobs subject to an upper bound on the makespan of accepted jobs.We provide an O（n²） time algorithm for the first problem. Moreover, for the other two problems, we first show that they are N P-hard, and then present pseudo-polynomial time dynamic programming algorithms and fully polynomial time approximation schemes for them, respectively.

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