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2021年 第36卷 第2期    刊出日期：2021-06-30

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随机变量的共轭梯度方法

许铭修, 黎景辉

2021, 36(2):  111-121.  doi:10.13371/j.cnki.chin.q.j.m.2021.02.001

摘要 ( 171 )   PDF (322KB) ( 206 )  

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We study the conjugate gradient method for solving a system of linear
equations with coefficients which are measurable functions and establish the rate of
convergence of this method.


邻域集值双量化粗糙集

李文涛, 李璋, 朱春龙, 徐伟华

2021, 36(2):  122-140.  doi:10.13371/j.cnki.chin.q.j.m.2021.02.002

摘要 ( 104 )   PDF (448KB) ( 169 )  

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 Double-quantitative rough approximation, containing two types of quan-
titative information, indicated stronger generalization ability and more accurate data
processing capacity than the single-quantitative rough approximation. In this paper,
the neighborhood-based double-quantitative rough set models are firstly presented in a
set-valued information system. Secondly, the attribute reduction method based on the
lower approximation invariant is addressed, and the relevant algorithm for the approx-
imation attribute reduction is provided in the set-valued information system. Finally,
to illustrate the superiority and the effectiveness of the proposed reduction approach,
experimental evaluation is performed using three datasets coming from the University of
California-Irvine (UCI) repository.


耦合Lyapunov 矩阵方程的AOR迭代法

张士君, 王世恒, 王珂

2021, 36(2):  141-148.  doi:10.13371/j.cnki.chin.q.j.m.2021.02.003

摘要 ( 149 )   PDF (285KB) ( 256 )  

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 An AOR (Accelerated Over-Relaxation) iterative method is suggested by
introducing one more parameter than SOR (Successive Over-Relaxation) method for
solving coupled Lyapunov matrix equations (CLMEs) that come from continuous-time
Markovian jump linear systems. The proposed algorithm improves the convergence rate,
which can be seen from the given illustrative examples. The comprehensive theoretical
analysis of convergence and optimal parameter needs further investigation.


具有导数型非线性项的半线性双波动方程解的全局非存在性

欧阳柏平, 林奕武

2021, 36(2):  149-159.  doi:10.13371/j.cnki.chin.q.j.m.2021.02.004

摘要 ( 95 )   PDF (315KB) ( 219 )  

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In this paper, we study the blow-up of solutions to a semilinear double-wave
equation with nonlinearity of derivative type. By using the iteration method and the
differential inequality techniques, we can get the estimates of the lifespan and the blow-up
of solutions in the subcritical case under some assumptions.


T2SVNSs 的熵和相似性度量及其应用

耿娟娟, 叶万红, 张菊, 徐东胜

2021, 36(2):  160-175.  doi:10.13371/j.cnki.chin.q.j.m.2021.02.005

摘要 ( 122 )   PDF (336KB) ( 256 )  

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The objective of this paper is to present a new approach for solving the multicriteria group decision-making (MCGDM) problems in type-2 single valued neutrosophic
set (T2SVNS) environment. Firstly, we give the concepts SVNS, T2SVNS and tangent
similarity measure with T2SVN information. Secondly, we define a new entropy function
for determining unknown attribute weights. In addition, a MCGDM method is developed
based on entropy and tangent similarity measure of T2SVNSs. Finally, an illustrative
example and comparative analysis are given to confirm the rationality and feasibility of
the proposed method.


由Frobenius对产生的Hovey三元组

刘硕

2021, 36(2):  176-187.  doi:10.13371/j.cnki.chin.q.j.m.2021.02.006

摘要 ( 93 )   PDF (420KB) ( 142 )  

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We revisit Auslander-Buchweitz approximation theory and fifind some relations

with cotorsion pairs and model category structures. From the notion of weak-cogenerators,

we introduce the concept of Frobenius pair (X ,ω) in a triangulated category T . We show

how to construct from a Frobenius pair (X ,ω) a triangulated model structure on X ^∧.

求解全局优化问题的一种新的非参数填充函数

刘金赞, 屈德强

2021, 36(2):  188-195.  doi:10.13371/j.cnki.chin.q.j.m.2021.02.007

摘要 ( 108 )   PDF (282KB) ( 257 )  

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 In the paper, to solve the global optimization problems, we propose a novel
parameter-free filled function. Based on the non-parameter filled function, a new filled
function algorithm is designed. In the algorithm, the selection and adjustment of parameters can be ignored by the characteristic that the filled function is parameter-free. In
addition, in the region lower than the current local minimizer of the objective function, the
filled function is continuously differentiable which enables any gradient descent method
to be used as a local search method in the algorithm. Through numerical experiments by
solving two test problems, the effectiveness of the algorithm is verified.


高阶变系数非线性发展方程的Painlev\'{e} 分析

王媛

2021, 36(2):  196-203.  doi:10.13371/j.cnki.chin.q.j.m.2021.02.008

摘要 ( 182 )   PDF (266KB) ( 218 )  

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There is a close relationship between the Painlev´e integrability and other
integrability of nonlinear evolution equation. By using the Weiss-Tabor-Carnevale (WTC)
method and the symbolic computation of Maple, the Painlev´e test is used for the higher
order generalized non-autonomous equation and the third order Korteweg-de Vries equation
with variable coefficients. Finally the Painlev´e integrability condition of this equation is
gotten.


Auslander范畴和自由正规化扩张

谷勤勤, 卓远帆

2021, 36(2):  204-209.  doi:10.13371/j.cnki.chin.q.j.m.2021.02.009

摘要 ( 132 )   PDF (299KB) ( 158 )  

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具退化非局部阻尼和源项的非线性耦合粘弹性波方程组解的指数增长性

刘烁, 张宏伟, 呼青英

2021, 36(2):  210-220.  doi:10.13371/j.cnki.chin.q.j.m.2021.02.010

摘要 ( 152 )   PDF (298KB) ( 212 )  

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This paper is concerned with a system of nonlinear viscoelastic
wave equations with degenerate nonlocal damping and memory terms. We will
prove that the energy associated to the system is unbounded. In fact, it will
be proved that the energy will grow up as an exponential function as time goes
to infinity, provided that the initial data are positive initial energy.