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Table of Content
30 September 2020, Volume 35 Issue 3
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Buildings and Groups II
CHAO Kuok Fai, LAI King Fai
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.
Global Attractor for High-dimensional Spacially Discrete FitzHugh-Nagumo System in Weighted Space
YIN Fu-qi, JIANG Hong, JIN Meng-zhao, LIU Zhi-qi
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
σ
2
×l
σ
2
. We prove the existence and uniqueness of the solution to the lattice dynamical system FitzHugh-Nagumo in l
σ
2
×l
σ
2
. 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.
Finite Di erence Method for Riesz Space Fractional Advection-dispersion Equation with Fractional Robin Boundary Condition
LIN Hai-xin, FANG Shao-mei,
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（?t
2
+ h
2
）. 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.
The Application and Property of Elastic Net Procedure for Partially Linear Models
HUANG Deng-xiang, LI Chun-hong, QIN Chao-yong, LU Chun-ting
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.
General Energy Decay of Solutions for A Wave Equation with Nonlocal Nonlinear Damping and Source Terms
ZHANG Hong-wei, LI Dong-hao, HU Qing-ying
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）.
Vanishing Theorems on Smooth Metric Measure Spaces with a Weighted p-Poincar
é
Inequality
ZHOU Jiu-ru
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
f
2
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）.
Batch Scheduling with Job Processing Time Compatibility and Rejection on a Single Machine
MENG Jin-tao, LU Xiao-xu, LI Shi-sheng, ZHOU Yong-wei
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（n
2
） 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.
