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2023年 第38卷 第2期    刊出日期：2023-06-30

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非奇异H-张量的新判定

柳亮, 王亚强

2023, 38(2):  123-133.  doi:10.13371/j.cnki.chin.q.j.m.2023.02.002

摘要 ( 65 )   PDF (307KB) ( 34 )  

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H -tensor plays an important role in identifying positive definiteness of even
order real symmetric tensors. In this paper, some definitions and theorems related to
H -tensors are introduced firstly. Secondly, some new criteria for identifying nonsingular
H -tensors are proposed, moreover, a new theorem for identifying positive definiteness
of even order real symmetric tensors is obtained. Finally, some numerical examples are
given to illustrate our results.


带有对合的素环的微分恒等式

黄述亮

2023, 38(2):  134-144.  doi:10.13371/j.cnki.chin.q.j.m.2023.02.003

摘要 ( 53 )   PDF (319KB) ( 132 )  

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 Let R be a prime ring of characteristic different from two with the sec-
ond involution ∗ and α an automorphism of R . An additive mapping F of R is called
a generalized ( α,α )-derivation on R if there exists an ( α,α )-derivation d of R such
that F ( xy )= F ( x ) α ( y )+ α ( x ) d ( y ) holds for all x,y∈R. The paper deals with the s-
tudy of some commutativity criteria for prime rings with involution. Precisely, we
describe the structure of R admitting a generalized ( α,α )-derivation F satisfying any
one of the following properties: ( i ) F ( xx^∗) −α ( xx^∗) ∈Z ( R ). ( ii ) F ( xx^∗ )+ α ( xx^∗ ) ∈
Z ( R ). ( iii ) F ( x ) F ( xx^∗) −α ( xx^∗) ∈Z ( R ). ( iv ) F ( x ) F (x^∗)+ α ( xx^∗) ∈Z ( R ). ( v ) F ( xx^∗) −
F ( x ) F (x^∗ ) ∈Z ( R ). ( vi ) F ( xx^∗) −F (x^∗) F ( x )=0 for all x∈R . Also, some examples are
given to demonstrate that the restriction of the various results is not superfluous. In fact,
our results unify and extend several well known theorems in literature.


奇异鞍点问题中广义位移分裂迭代方法的半收敛性分析

黄卓红

2023, 38(2):  145-156.  doi:10.13371/j.cnki.chin.q.j.m.2023.02.004

摘要 ( 54 )   PDF (300KB) ( 61 )  

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 Recently, some authors (Shen and Shi, 2016) studied the generalized shift-
splitting (GSS) iteration method for singular saddle point problem with nonsymmetric
positive definite (1,1)-block and symmetric positive semidefinite (2,2)-block. In this
paper, we further apply the GSS iteration method to solve singular saddle point problem
with nonsymmetric positive semidefinite (1,1)-block and symmetric positive semidefinite
(2,2)-block, prove the semi-convergence of the GSS iteration method and analyze the
spectral properties of the corresponding preconditioned matrix. Numerical experiment is
given to indicate that the GSS iteration method with appropriate iteration parameters is
effective and competitive for practical use.


一类具有时滞的生态流行病模型的稳定性与 Hopf 分支

白宏芳

2023, 38(2):  157-183.  doi:10.13371/j.cnki.chin.q.j.m.2023.02.005

摘要 ( 96 )   PDF (1289KB) ( 150 )  

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 In this paper, an eco-epidemiological model with time delay is studied. The
local stability of the four equilibria, the existence of stability switches about the predation-
free equilibrium and the coexistence equilibrium are discussed. It is found that Hopf
bifurcations occur when the delay passes through some critical values. Formulae are
obtained to determine the direction of bifurcations and the stability of bifurcating periodic
solutions by using the normal form theory and center manifold theorem. Some numerical
simulations are carried out to illustrate the theoretical results.


变指标中心Morrey空间上带Dini核的多线性C-Z算子

马腾

2023, 38(2):  184-195.  doi:10.13371/j.cnki.chin.q.j.m.2023.02.006

摘要 ( 68 )   PDF (342KB) ( 36 )  

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 In this paper, we obtain the boundedness of multilinear Calder´ on-Zygmund
operators with kernels of Dini type and commutators with variable exponent λ -central
BMO functions in variable exponent central Morrey spaces.


带位势的基尔霍夫方程规范解的存在性

梁艳霞

2023, 38(2):  196-209.  doi:10.13371/j.cnki.chin.q.j.m.2023.02.007

摘要 ( 88 )   PDF (378KB) ( 60 )  

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 In this paper we discuss the following Kirchhoff equation

\left\{
\begin{array}{lr}
-\left(a+b \int_{\mathbb{R}^3}|\nabla u|^{2} d x\right) \Delta u+V(x)u+\lambda u=\mu|u|^{q-2}u+|u|^{p-2}u \ {\rm in}\ \mathbb{R}^3,&\\
\int_{\mathbb{R}^{3}}u^{2}dx=c^2,
\end{array}
\right.
where a, b, µ and c are positive numbers, λ is unknown and appears as a Lagrange multiplier,

14/3<q<p<6 and V is a continuous non-positive function vanishing at infinity.
Under some mild assumptions on V , we prove the existence of a mountain pass normalized solution. To the author’s knowledge, it is the first time to study the existence of
normalized solution to Kirchhoff equation with potential via the minimax principle.


矩阵方程的最小二乘{P,Q,k+1}-自反解

董昌州, 李浩雪

2023, 38(2):  210-220.  doi:10.13371/j.cnki.chin.q.j.m.2023.02.008

摘要 ( 53 )   PDF (383KB) ( 81 )  

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 Let P ∈C ^m×m and Q∈C ^n×n be Hermitian and {k +1 } -potent matrices,
i.e., P ^k+1 = P = P ^∗ , Q ^k+1 = Q = Q ^∗ , where ( · ) ∗ stands for the conjugate transpose of a
matrix. A matrix X ∈C ^m×n is called {P,Q,k +1 } -reflexive (anti-reflexive) if PXQ = X
( PXQ = −X ). In this paper, the least squares solution of the matrix equation AXB = C
subject to {P,Q,k +1 } -reflexive and anti--reflexive constraints are studied by converting
into two simpler cases: k=1 and k=2.