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Table of Content
30 September 2021, Volume 36 Issue 3
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Full Friendly Index Sets of a Family of Cubic Graphs
BAI Yu-jie, WU Shu-fei
2021, 36(3): 221-234. doi:
10.13371/j.cnki.chin.q.j.m.2021.03.001
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Let G =( V,E ) be a graph. For a vertex labeling f : V →Z
2
, it induces an edge
labeling f
+
: E→Z
2
, where for each edge v
1
v
2
∈E we have f
+
( v
1
v
2
)= f ( v
1
)+ f ( v
2
). For
each i∈Z
2
, we use v
f
( i ) (respectively, e
f
( i )) to denote the number of vertices (respectively,
edges) with label i . A vertex labeling f of G is said to be friendly if vertices with different
labels differ in size by at most one. The full friendly index set of a graph G , denoted by
FFI ( G ), consists of all possible values of e
f
(1) −e
f
(0), where f ranges over all friendly
labelings of G . In this paper, motivated by a problem raised by [6], we study the full
friendly index sets of a family of cubic graphs.
Blow-Up Result for a Semi-Linear Wave Equation with a Nonlinear Memory Term of Derivative Type
OUYANG Bai-ping, XIAO Sheng-zhong
2021, 36(3): 235-243. doi:
10.13371/j.cnki.chin.q.j.m.2021.03.002
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In this paper, we study the blow-up of solutions to a semi-linear wave equation
with a nonlinear memory term of derivative type. By using methods of an iteration
argument and differential inequalities, we obtain the blow-up result for the semi-linear
wave equation when the exponent of p is under certain conditions. Meanwhile, we derive
an upper bound of the lifespan of solutions to the Cauchy problem for the semi-linear
wave equation.
Locally Conformal Pseudo-
Kähle
r Finsler Manifolds
LI Hong-jun
2021, 36(3): 244-251. doi:
10.13371/j.cnki.chin.q.j.m.2021.03.003
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In this paper, we give a necessary and sufficient condition for a strongly
pseudoconvex complex Finsler metric to be locally conformal pseudo-Kähler Finsler. As
an application, we find any complete strongly convex and locally conformal pseudo-Kähler
Finsler manifold, which is simply connected or whose fundamental group contains elements
of finite order only, can be given a Kähler metric.
The Optimal Matching Parameter of Half Discrete Hilbert Type Multiple Integral Inequalities with Non-Homogeneous Kernels and Applications
HONG Yong, HE Bing
2021, 36(3): 252-262. doi:
10.13371/j.cnki.chin.q.j.m.2021.03.004
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By using the weight function method, the matching parameters of the
half discrete Hilbert type multiple integral inequality with a non-homogeneous kernel
K ( n,||x||
ρ,m
) = G ( n
λ 1
||x||
λ 2
ρ,m
) are discussed, some equivalent conditions of the optimal
matching parameter are established, and the expression of the optimal constant factor is
obtained. Finally, their applications in operator theory are considered.
A Novel Parameter-Free Filled Function and Its Application in Least Square Method
LI Shuo, SHANG You-lin, QU De-qiang,
2021, 36(3): 263-274. doi:
10.13371/j.cnki.chin.q.j.m.2021.03.005
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The filled function algorithm is an important method to solve global opti
mization problems. In this paper, a parameter-free filled function is proposed for solving
general global optimization problem, discuss the theoretical properties of this function
and give the corresponding algorithm. The numerical experiments on some typical test
problems using the algorithm and the numerical results show that the algorithm is effec
tive. Applying the filled function method to the parameter solving problem in the logical
population growth model, and then can be effectively applied to Chinese population
prediction. The experimental results show that the algorithm has good practicability in
practical application.
Sparse Reduced-Rank Regression with Outlier Detection
LIANG Bing-jie
2021, 36(3): 275-287. doi:
10.13371/j.cnki.chin.q.j.m.2021.03.006
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Based on the multivariate mean-shift regression model, we propose a new
sparse reduced-rank regression approach to achieve low-rank sparse estimation and outlier
detection simultaneously. A sparse mean-shift matrix is introduced in the model to indicate
outliers. The rank constraint and the group-lasso type penalty for the coefficient matrix
encourage the low-rank row sparse structure of coefficient matrix and help to achieve
dimension reduction and variable selection. An algorithm is developed for solving our
problem. In our simulation and real-data application, our new method shows competitive
performance compared to other methods.
Y-Gorenstein Cotorsion Modules
HE Dong-lin, LI Yu-yan
2021, 36(3): 288-295. doi:
10.13371/j.cnki.chin.q.j.m.2021.03.007
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Let R be an associative ring with identity, and Y be a class of right R -modules,
which contains all injective right R -modules. In this paper, we introduce the definition of
Y -Gorenstein cotorsion modules, which is a generalization of cotorsion and Gorenstein
cotorsion modules. We discuss the relationship between Gorenstein cotorsion, weakly
Gorenstein cotorsion and Y -Gorenstein cotorsion modules. We investigate properties and
characterizations of Y-Gorenstein cotorsion modules.
Continuous Dependence for the 3D Primitive Equations of Large Scale Ocean Under Random Force
LI Yuan-fei
2021, 36(3): 296-307. doi:
10.13371/j.cnki.chin.q.j.m.2021.03.008
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In this paper, we consider the initial-boundary value problem for the large scale
three-dimensional (3D) viscous primitive equations under random force. Assuming that
the random force and the heat source satisfy the some assumptions, we firstly establish
rigorous a priori bounds with coefficients which depend only on boundary data, initial
data and the geometry of the problem, and then with the aid of these a priori bounds,
the continuous dependence of the solution on changes in the heat source is obtained.
Continuous Dependence for a Brinkman-Forchheimer Type Model with Temperature-Dependent Solubility
SHI Jin-cheng , XIAO Sheng-zhong
2021, 36(3): 308-319. doi:
10.13371/j.cnki.chin.q.j.m.2021.03.009
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The structural stability for the Brinkman-Forchheimer equations with
temperature-dependent solubility in a bounded region in R3 was studied. The reaction boundary conditions for the temperature T and the salt concentration were imposed.
With the aid of some useful a priori bounds, we were able to demonstrate the continuous
dependence result for the Forchheimer coefficient λ.
Batalin-Vilkovisky Structure on Hochschild Cohomology of Self-Injective Quadratic Monomial Algebras
GAO Jin, HOU Bo
2021, 36(3): 320-330. doi:
10.13371/j.cnki.chin.q.j.m.2021.03.010
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We give a complete description of the Batalin-Vilkovisky algebra structure on
Hochschild cohomology of the self-injective quadratic monomial algebras.
