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Mallows Model Averaging Estimation for Linear Regression Model with Right Censored Data
Zhongqi LIANG, Xiaolin CHEN, Yanqiu ZHOU
Acta Mathematicae Applicatae Sinica(English Series). 2022, 38(1): 523.
DOI:
10.1007/s1025502210530
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This paper is concerned with an optimal model averaging estimation for linear regression model with right censored data. The weights for model averaging are picked up via minimizing the Mallows criterion. Under some mild conditions, it is shown that the identified weights possess the property of asymptotic optimality, that is, the model averaging estimator corresponding to these weights achieves the lowest squared error asymptotically. Some numerical studies are conducted to evaluate the finitesample performance of our method and make comparisons with its intuitive competitors, while an application to the PBC dataset is provided to serve as an illustration.
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The Analysis of Impact of Brexit on the PostBrexit EU Using Intervented Multivariate Time Series
Yu TIAN, Shaopei MA, Rongxiang RUI, Zhen YU, Maozai TIAN
Acta Mathematicae Applicatae Sinica(English Series). 2021, 37(3): 441458.
DOI:
10.1007/s102550211022z
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214
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The UK is the most important partner of the EU in terms of economic and other fields due to the geographical proximity. It was one of the largest economies in the EU and its per capita income is higher than the EU average, so it is a net contributor to the EU. With UKs membership of the EU ended on 31 January 2019, there are concerns that the Brexit may have a significant impact on the EU, resulting in social, economic, political, and institutional changes, etc. in EU. While the impact of Brexit on the UK has always been the subject of considerable scholarly interest in recent years, there is relatively little literature on the impact of Brexit on the EU. This paper focuses on the evaluation of the impact of Brexit on the EU economy and other relevant aspects along three dimensions: GDP, PPP, Quarterly GDP growth. Employing powerful quantitative analysis technology that includes vector autoregression model, multivariate time series model with intervention variables, and autoregression integrated moving average, this paper obtains the important and novel evidence about the potential impact of Brexit on the EU economy, pointing out that Brexit is of farreaching significance to the EU. This analysis uses several statistical models to screen out several key influencing factors, which can be used to predict the total GDP of EU in the next five years. The results show that EU economy will react negatively to "nodeal" Brexit, and its growth rate of economy will slow down significantly in next 5 years. Finally, we put forward relevant policy suggestions on how to deal with the negative impact of Brexit on EU.
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Existence and Properties of Solutions for a Class of Fractional Differential Equations
Yongqiang XU, Shuhong CHEN, Zhong TAN
Acta Mathematicae Applicatae Sinica(English Series). 2021, 37(3): 477484.
DOI:
10.1007/s1025502110259
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In this paper, we consider the initial value problem of a class of fractional differential equations. Firstly, we obtain the existence and uniqueness of the solutions by using Picard’s method of successive approximation. Then we discuss the dependence of the solutions on the initial value.
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Nullfree False Discovery Rate Control Using Decoy Permutations
Kun HE, Mengjie LI, Yan FU, Fuzhou GONG, Xiaoming SUN
Acta Mathematicae Applicatae Sinica(English Series). 2022, 38(2): 235253.
DOI:
10.1007/s1025502210775
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The traditional approaches to false discovery rate (FDR) control in multiple hypothesis testing are usually based on the null distribution of a test statistic. However, all types of null distributions, including the theoretical, permutationbased and empirical ones, have some inherent drawbacks. For example, the theoretical null might fail because of improper assumptions on the sample distribution. Here, we propose a null distributionfree approach to FDR control for multiple hypothesis testing in the casecontrol study. This approach, named
targetdecoy procedure
, simply builds on the ordering of tests by some statistic or score, the null distribution of which is not required to be known. Competitive decoy tests are constructed from permutations of original samples and are used to estimate the false target discoveries. We prove that this approach controls the FDR when the score function is symmetric and the scores are independent between different tests. Simulation demonstrates that it is more stable and powerful than two popular traditional approaches, even in the existence of dependency. Evaluation is also made on two real datasets, including an arabidopsis genomics dataset and a COVID19 proteomics dataset.
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The Proportional Mean Residual Life Regression Model with Cure Fraction and Auxiliary Covariate
Shaojia JIN, Yanyan LIU, Guangcai MAO, Mingyu SHAN
Acta Mathematicae Applicatae Sinica(English Series). 2022, 38(2): 312323.
DOI:
10.1007/s1025502210784
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As biological studies become more expensive to conduct, it is a frequently encountered question that how to take advantage of the available auxiliary covariate information when the exposure variable is not measured. In this paper, we propose an induced cure rate mean residual life time regression model to accommodate the survival data with cure fraction and auxiliary covariate, in which the exposure variable is only assessed in a validation set, but a corresponding continuous auxiliary covariate is ascertained for all subjects in the study cohort. Simulation studies elucidate the practical performance of the proposed method under finite samples. As an illustration, we apply the proposed method to a heart disease data from the Study of Left Ventricular Dysfunction.
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Least Squares Model Averaging Based on Generalized Cross Validation
Xinmin LI, Guohua ZOU, Xinyu ZHANG, Shangwei ZHAO
Acta Mathematicae Applicatae Sinica(English Series). 2021, 37(3): 495509.
DOI:
10.1007/s102550211024x
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Frequentist model averaging has received much attention from econometricians and statisticians in recent years. A key problem with frequentist model average estimators is the choice of weights. This paper develops a new approach of choosing weights based on an approximation of generalized cross validation. The resultant least squares model average estimators are proved to be asymptotically optimal in the sense of achieving the lowest possible squared errors. Especially, the optimality is built under both discrete and continuous weigh sets. Compared with the existing approach based on Mallows criterion, the conditions required for the asymptotic optimality of the proposed method are more reasonable. Simulation studies and real data application show good performance of the proposed estimators.
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A Note on Harnack Type Inequality for the Gaussian Curvature Flow
Caipeng CHEN, Hongxin GUO, Chengzhe ZHU
Acta Mathematicae Applicatae Sinica(English Series). 2022, 38(1): 14.
DOI:
10.1007/s1025502210668
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In this short note we present a new Harnack expression for the Gaussian curvature flow, which is modeled from the shrinking self similiar solutions. As applications we give alternate proofs of Chow's Harnack inequality and entropy estimate.
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Existence and Regularity of Solution of the Liquid
^{4}
He Model Coupling with an Applied Magnetic Field
Chen PENG
Acta Mathematicae Applicatae Sinica(English Series). 2022, 38(2): 497511.
DOI:
10.1007/s1025502210917
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In this paper, we derive a timedependent GinzburgLandau model for liquid
^{4}
He coupling with an applied magnetic field basing on the Le Châtlier principle.
We also obtain the existence and uniqueness of global weak solution for this model. In addition, by utilizing the regularity estimates for linear semigroup, we prove that the model possesses a global classical solution.
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Construction of Multilevel Spacefilling Designs via Code Mappings
Huili XUE, Xingyou HUANG, Hongyi LI
Acta Mathematicae Applicatae Sinica(English Series). 2022, 38(1): 2436.
DOI:
10.1007/s102550221055y
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Spacefilling designs are widely used in various fields because of their nice spacefilling properties. Uniform designs are one of spacefilling designs, which desires the experimental points to scatter uniformly over the experimental area. For practical need, the construction and their properties of ninelevel uniform designs are discussed via two code mappings in this paper. Firstly, the algorithm of constructing ninelevel uniform designs is presented from an initial threelevel design by the TypeI code mapping and tripling technique. Secondly, the algorithm of constructing ninelevel uniform designs is presented from a threelevel base design by the TypeII code mapping and generalized orthogonal arrays. Moreover, relative properties are discussed based on the two code mappings. Finally, some numerical examples are given out for supporting our theoretical results.
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Oscillatory Behavior of Thirdorder Nonlinear Differential Equations with a Sublinear Neutral Term
Wenjuan LI, Yuanhong YU
Acta Mathematicae Applicatae Sinica(English Series). 2022, 38(2): 484496.
DOI:
10.1007/s1025502210891
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10
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The authors present some new criteria for oscillation and asymptotic behavior of solutions of thirdorder nonlinear differential equations with a sublinear neutral term of the form $$\left(r(t)(z''(t))^{\alpha}\right)'+\int^{d}_{c}q(t,\xi)f\left(x\left(\sigma(t,\xi)\right)\right)d\xi=0, \qquad t\geq t_{0}$$ where $z(t)=x(t)+\int^{b}_{a}p(t,\xi)x^{\gamma}\left(\tau(t,\xi)\right)d\xi,~0<\gamma\leq1.$ Under the conditions $\int^{\infty}_{t_{0}}r^{\frac{1}{\alpha}}(t)dt=\infty$ or $\int^{\infty}_{t_{0}}r^{\frac{1}{\alpha}}(t)dt<\infty.$ The results obtained here extend, improve and complement to some known results in the literature. Examples are provided to illustrate the theorems.
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1planar Graphs without 4cycles or 5cycles are 5colorable
Lili SONG, Lei SUN
Acta Mathematicae Applicatae Sinica(English Series). 2022, 38(1): 169176.
DOI:
10.1007/s1025502210739
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A graph is 1planar if it can be drawn on the Euclidean plane so that each edge is crossed by at most one other edge. A proper vertex
k
coloring of a graph
G
is defined as a vertex coloring from a set of
k
colors such that no two adjacent vertices have the same color. A graph that can be assigned a proper
k
coloring is
k
colorable. A cycle is a path of edges and vertices wherein a vertex is reachable from itself. A cycle contains
k
vertices and
k
edges is a
k

cycle
. In this paper, it is proved that 1planar graphs without 4cycles or 5cycles are 5colorable.
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Analytical Expressions to Counterparty Credit Risk Exposures for Interest Rate Derivatives
Shuang LI, Cheng PENG, Ying BAO, Yanlong ZHAO, Zhen CAO
Acta Mathematicae Applicatae Sinica(English Series). 2022, 38(2): 254270.
DOI:
10.1007/s1025502210748
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This paper proposes an approximate analytical solution method to calculate counterparty credit risk exposures. Compared with the Standard Approach for measuring Counterparty Credit Risk and the Internal Modeling Method provided by Basel Committee, the proposed method significantly improves the calculation efficiency based on sacrificing a little accuracy. Taking Forward Rate Agreement as an example, this article derives the exact expression for Expected Exposure. By approximating the distribution of Forward Rate Agreement’s future value to a normal distribution, the approximate analytical expression for Potential Future Exposure is derived. Numerical results show that this method is reliable and is robust under different parameters.
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On Disjoint Cycles of the Same Length in Tournaments
On Disjoint Cycles of the Same Length in Tournaments
Acta Mathematicae Applicatae Sinica(English Series). 2022, 38(2): 271281.
DOI:
10.1007/s102550221072x
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A tournament is an orientation of the complete graph. Tournaments form perhaps the most interesting class of digraphs and it has a great potential for application. Tournaments provide a model of the statistical technique called the method of paired comparisons and they have also been studied in connection with sociometric relations in small groups. In this paper, we investigate disjoint cycles of the same length in tournaments. In 2010, Lichiardopol conjectured that for given integers
l
≥ 3 and
k
≥ 1, any tournament with minimum outdegree at least (
l
 1)
k
 1 contains
k
disjoint
l
cycles, where an
l
cycle is a cycle of order
l
. BangJensen et al. verified the conjecture for
l
= 3 and Ma et al. proved that it also holds for
l
≥ 10. This paper provides a proof of the conjecture for the case of 9 ≥
l
≥ 4
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Precise Large Deviations for Sums of Claimsize Vectors in a Twodimensional Sizedependent Renewal Risk Model
Keang FU, Xinmei SHEN, Huijie LI
Acta Mathematicae Applicatae Sinica(English Series). 2021, 37(3): 539547.
DOI:
10.1007/s102550211030z
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Consider a twodimensional renewal risk model, in which the claim sizes {
X
_{k}
;
k
≥ 1} form a sequence of i.i.d. copies of a nonnegative random vector whose two components are dependent. Suppose that the claim sizes and interarrival times form a sequence of i.i.d. random pairs, with each pair obeying a dependence structure via the conditional distribution of the interarrival time given the subsequent claim size being large. Then a precise largedeviation formula of the aggregate amount of claims is obtained.
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The Minimum Stretch Spanning Tree Problem for Typical Graphs
Lan LIN, Yixun LIN
Acta Mathematicae Applicatae Sinica(English Series). 2021, 37(3): 510522.
DOI:
10.1007/s1025502110286
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With applications in communication networks, the minimum stretch spanning tree problem is to find a spanning tree
T
of a graph
G
such that the maximum distance in
T
between two adjacent vertices is minimized. The problem has been proved NPhard and fixedparameter polynomial algorithms have been obtained for some special families of graphs. In this paper, we concentrate on the optimality characterizations for typical classes of graphs. We determine the exact formulae for the complete
k
partite graphs, split graphs, generalized convex graphs, and several planar grids, including rectangular grids, triangular grids, and triangulatedrectangular grids.
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Hosoya and MerrifieldSimmons Indices in Random Polyphenyl Chains
Weiling YANG
Acta Mathematicae Applicatae Sinica(English Series). 2021, 37(3): 485494.
DOI:
10.1007/s1025502110268
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The Hosoya index of a graph is the total number of matchings in it. And the MerrifieldSimmons index is the total number of independent sets in it. They are typical examples of graph invariants used in mathematical chemistry for quantifying relevant details of molecular structure. In this paper, we obtain explicit analytical expressions for the expectations of the Hosoya index and the MerrifieldSimmons index of a random polyphenyl chain.
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Asymmetric Information, Heterogeneous Prior Beliefs and Market Regulation
Hong LIU, Ying JIANG, Huainian ZHANG
Acta Mathematicae Applicatae Sinica(English Series). 2021, 37(3): 459476.
DOI:
10.1007/s102550211023y
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This paper studies the trading behavior of an irrational insider and its influence on the market equilibrium in the presence of market regulation. We find that the market with only one insider with private information is almost close to a strong efficient market, under the condition of market regulation. In the equilibrium, the probability of the insider being caught trading with private information is zero, which shows that the reasonable behavior of the regulator is to essentially give up regulation. But the market efficiency and the irrational trader’s trading intensity all greatly improve because of the existence of the market regulation.
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On the Second Smallest and the Largest Normalized Laplacian Eigenvalues of a Graph
Xiaoguo TIAN, Ligong WANG, You LU
Acta Mathematicae Applicatae Sinica(English Series). 2021, 37(3): 628644.
DOI:
10.1007/s102550211032x
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Let
G
be a simple connected graph with order n. Let
L
(
G
) and
Q
(
G
) be the normalized Laplacian and normalized signless Laplacian matrices of
G
, respectively. Let
λ
_{k}
(
G
) be the kth smallest normalized Laplacian eigenvalue of
G
. Denote by
ρ
(
A
) the spectral radius of the matrix
A
. In this paper, we study the behaviors of
λ
_{2}
(
G
) and
ρ
(
L
(
G
)) when the graph is perturbed by three operations. We also study the properties of
ρ
(
L
(
G
)) and
X
for the connected bipartite graphs, where
X
is a unit eigenvector of
L
(
G
) corresponding to
ρ
(
L
(
G
)). Meanwhile we characterize all the simple connected graphs with
ρ
(
L
(
G
)) =
ρ
(
Q
(
G
)).
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Exponential Stability for Timechanged Stochastic Differential Equations
Min ZHU, Junping LI, Dezhi LIU
Acta Mathematicae Applicatae Sinica(English Series). 2021, 37(3): 617627.
DOI:
10.1007/s102550211031y
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So far there have been few results presented on the exponential stability for timechanged stochastic differential equations. The main aim of this work is to fill this gap. By making use of general Lyapunov methods and timechanged Itô formula, we establish the exponential stability and almost sure exponential stability of solution to timechanged SDEs. Finally, we construct some examples to illustrate the effectiveness of our established theory.
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Discussion on Fractional (
a
,
b
,
k
)critical Covered Graphs
Wei ZHANG, Sufang WANG
Acta Mathematicae Applicatae Sinica(English Series). 2022, 38(2): 304311.
DOI:
10.1007/s1025502210766
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15
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A graph G is called a fractional [
a
,
b
]covered graph if for each
e
∈ E(G), G contains a fractional [
a
,
b
]factor covering e. A graph G is called a fractional (
a
,
b
,
k
)critical covered graph if for any
W
⊆
V
(
G
) with 
W
 =
k
,
G

W
is fractional [
a
,
b
]covered, which was first defined and investigated by Zhou, Xu and Sun [S. Zhou, Y. Xu, Z. Sun, Degree conditions for fractional (
a
,
b
,
k
)critical covered graphs, Information Processing Letters 152(2019)105838]. In this work, we proceed to study fractional (
a
,
b
,
k
)critical covered graphs and derive a result on fractional (
a
,
b
,
k
)critical covered graphs depending on minimum degree and neighborhoods of independent sets.
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Generalized Lagrangian Duality in Setvalued Vector Optimization via Abstract Subdifferential
Yanfei CHAI, Sanyang LIU, Siqi WANG
Acta Mathematicae Applicatae Sinica(English Series). 2022, 38(2): 337351.
DOI:
10.1007/s1025502210793
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6
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In this paper, we investigate dual problems for nonconvex setvalued vector optimization via abstract subdifferential. We first introduce a generalized augmented Lagrangian function induced by a coupling vectorvalued function for setvalued vector optimization problem and construct related setvalued dual map and dual optimization problem on the basic of weak efficiency, which used by the concepts of supremum and infimum of a set. We then establish the weak and strong duality results under this augmented Lagrangian and present sufficient conditions for exact penalization via an abstract subdifferential of the object map. Finally, we define the suboptimal path related to the dual problem and show that every cluster point of this suboptimal path is a primal optimal solution of the object optimization problem. In addition, we consider a generalized vector variational inequality as an application of abstract subdifferential.
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On a Damped Vibration Problem Involving
p
Laplacian Operator: Fast Homoclinic Orbits
Peng CHEN, Xianhua TANG, Yuanyuan ZHANG
Acta Mathematicae Applicatae Sinica(English Series). 2022, 38(2): 368387.
DOI:
10.1007/s1025502210837
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n this paper, we deal with the nonlinear secondorder differential equation with damped vibration term involving
p
Laplacian operator. Of particular interest is the resolution of an open problem. An interesting outcome from our result is that we can obtain the fast homoclinic solution with general superlinear growth assumption in suitable Sobolev space. To our knowledge, our theorems appear to be the first such result about damped vibration problem with
p
Laplacian operator.
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A New Sufficient Degree Condition for a Graphic Sequence to Be Forcibly
k
EdgeConnected
Jianhua YIN, Jiyun GUO
Acta Mathematicae Applicatae Sinica(English Series). 2022, 38(1): 223228.
DOI:
10.1007/s1025502210579
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A graphic sequence
π
=(
d
_{1}
,
d
_{2}
, ...,
d
_{n}
) is said to be
forcibly
k
edgeconnected if every realization of
π
is
k
edgeconnected. In this paper, we obtain a new sufficient degree condition for
π
to be forcibly
k
edgeconnected. We also show that this new sufficient degree condition implies a strongest monotone degree condition for
π
to be forcibly 2edgeconnected and a conjecture about a strongest monotone degree condition for
π
to be forcibly 3edgeconnected due to Bauer et al. (Networks, 54(2) (2009) 9598), and also implies a strongest monotone degree condition for
π
to be forcibly 4edgeconnected.
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Multiple Positive Solutions for One Dimensional Third Order
p
Laplacian Equations with Integral Boundary Conditions
Youyuan YANG, Qiru WANG
Acta Mathematicae Applicatae Sinica(English Series). 2022, 38(1): 116127.
DOI:
10.1007/s1025502210659
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15
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In this paper, we consider the one dimensional third order
p
Laplacian equation (Φ
_{p}
(
u
"))'+
h
(
t
)
f
(
t
,
u
(
t
))=0 with integral boundary conditions
u
(0)
α
u
'(0)= ∫
t
_{0}
^{1}
g
_{1}
(
s
)
u
(
s
)
ds
,
u
(1)+
β
u
'(1)= ∫
t
_{0}
^{1}
g
_{2}
(
s
)
u
(
s
)
ds
,
u
"(0)=0. By using kernel functions and the AveryPeterson fixed point theorem, we establish the existence of at least three positive solutions.
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Diffusioninduced Spatiotemporal Oscillations in an Epidemic Model with Two Delays
Yanfei DU, Ben NIU, Junjie WEI
Acta Mathematicae Applicatae Sinica(English Series). 2022, 38(1): 128153.
DOI:
10.1007/s102550221062z
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We investigate a diffusive, stagestructured epidemic model with the maturation delay and freelymoving delay. Choosing delays and diffusive rates as bifurcation parameters, the only possible way to destabilize the endemic equilibrium is through Hopf bifurcation. The normal forms of Hopf bifurcations on the center manifold are calculated, and explicit formulae determining the criticality of bifurcations are derived. There are two different kinds of stable oscillations near the first bifurcation: on one hand, we theoretically prove that when the diffusion rate of infected immature individuals is sufficiently small or sufficiently large, the first branch of Hopf bifurcating solutions is always spatially homogeneous; on the other, fixing this diffusion rate at an appropriate size, stable oscillations with different spatial profiles are observed, and the conditions to guarantee the existence of such solutions are given by calculating the corresponding eigenfunction of the Laplacian at the first Hopf bifurcation point. These bifurcation behaviors indicate that spatial diffusion in the epidemic model may lead to spatially inhomogeneous distribution of individuals.
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The Distance Matching Extension in
K
_{1, k}
free Graphs with High Local Connectedness
Weichan LIU, Guiying YAN
Acta Mathematicae Applicatae Sinica(English Series). 2022, 38(1): 3743.
DOI:
10.1007/s1022502210696
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32
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A matching is extendable in a graph
G
if
G
has a perfect matching containing it. A distance q matching is a matching such that the distance between any two distinct matching edges is at least
q
. In this paper, we prove that any distance 2
k
3 matching is extendable in a connected and locally (
k
1)connected
K
_{1, k}
free graph of even order. Furthermore, we also prove that any distance
q
matching
M
in an rconnected and locally (
k
1)connected
K
_{1, k}
free graph of even order is extendable provided that
M
is bounded by a function on
r
,
k
and
q
. Our results improve some results in [J. Graph Theory 93 (2020), 5C20].
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Highdimensional Tests for Mean Vector: Approaches without Estimating the Mean Vector Directly
Bo CHEN, Haimeng WANG
Acta Mathematicae Applicatae Sinica(English Series). 2022, 38(1): 7886.
DOI:
10.1007/s102550221070z
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12
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Several tests for multivariate mean vector have been proposed in the recent literature. Generally, these tests are directly concerned with the mean vector of a highdimensional distribution. The paper presents two new test procedures for testing mean vector in large dimension and small samples. We do not focus on the mean vector directly, which is a different framework from the existing choices. The first test procedure is based on the asymptotic distribution of the test statistic, where the dimension increases with the sample size. The second test procedure is based on the permutation distribution of the test statistic, where the sample size is fixed and the dimension grows to infinity. Simulations are carried out to examine the finitesample performance of the tests and to compare them with some popular nonparametric tests available in the literature.
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Existence of
p
mean Almost Periodic Mild Solution for Fractional Stochastic Neutral Functional Differential Equation
Xiaoke SUN, Ping HE
Acta Mathematicae Applicatae Sinica(English Series). 2021, 37(3): 645656.
DOI:
10.1007/s1025502110339
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157
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A class of fractional stochastic neutral functional differential equation is analyzed in this paper. With the utilization of the fractional calculations, semigroup theory, fixed point technique and stochastic analysis theory, a sufficient condition of the existence for
p
mean almost periodic solution is obtained, which are supported by two examples.
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Approximate Controllability of Secondorder Semilinear Evolution Systems with Finite Delay
Xiaofeng SU, Xianlong FU
Acta Mathematicae Applicatae Sinica(English Series). 2021, 37(3): 573589.
DOI:
10.1007/s1025502110277
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114
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In this work, we study the approximate controllability for a class of semilinear secondorder control systems with finite delay. Sufficient conditions for approximate controllability are established by constructing fundamental solutions and using the resolvent condition and techniques on cosine family of linear operators. To illustrate the applications of the obtained results, an example is provided in the end.
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Gini Correlation for Feature Screening
Junying ZHANG, Xiaofeng LIU, Riquan ZHANG, HangWANG
Acta Mathematicae Applicatae Sinica(English Series). 2021, 37(3): 590601.
DOI:
10.1007/s1025502110121
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82
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In this paper we propose the Gini correlation screening (GCS) method to select the important variables with ultrahigh dimensional data. The new procedure is based on the Gini correlation coefficient via the covariance between the response and the rank of the predictor variables rather than the Pearson correlation and the Kendall
τ
correlation coefficient. The new method does not require imposing a specific model structure on regression functions and only needs the condition which the predictors and response have continuous distribution function. We demonstrate that, with the number of predictors growing at an exponential rate of the sample size, the proposed procedure possesses consistency in ranking, which is both useful in its own right and can lead to consistency in selection. The procedure is computationally efficient and simple, and exhibits a competent empirical performance in our intensive simulations and real data analysis.
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A Difference Scheme with Intrinsic Parallelism for Fractional Diffusionwave Equation with Damping
LiFei WU, XiaoZhong YANG, Min LI
Acta Mathematicae Applicatae Sinica(English Series). 2021, 37(3): 602616.
DOI:
10.1007/s102550211015y
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Anomalous diffusion is a widespread physical phenomenon, and numerical methods of fractional diffusion models are of important scientific significance and engineering application value. For time fractional diffusionwave equation with damping, a difference (ASCN, alternating segment CrankNicolson) scheme with intrinsic parallelism is proposed. Based on alternating technology, the ASCN scheme is constructed with four kinds of Saul’yev asymmetric schemes and CrankNicolson (CN) scheme. The unconditional stability and convergence are rigorously analyzed. The theoretical analysis and numerical experiments show that the ASCN scheme is effective for solving time fractional diffusionwave equation.
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Influence of Discretization Step on Asymptotic Stability of a Certain Class of Twodimensional Continuousdiscrete Fractional Linear Systems
Souad BOUGUESSA, Djillali BOUAGADA, Mohammed Amine GHEZZAR
Acta Mathematicae Applicatae Sinica(English Series). 2022, 38(1): 6877.
DOI:
10.1007/s1025502210601
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The effectiveness of this paper lies in the influence of the discretization step on the asymptotic stability of the positive twodimensional fractional linear systems. It aims at investigating whether, how and when this step affects the asymptotically stable twodimensional positive fractional linear continuousdiscrete systems. To accomplish this study, a new test was outlined and used so that the asymptotic stability of the system was measured both before and after being exposed to the sampling step. Furthermore, the conditions of that stability were assessed. As a result, the outcome of the approximation shows that the stability is preserved under a particular set of conditions. On this basis, the newly proposed approach is recommended for testing the intended stability of such systems. A numerical example is tested to show the accuracy and the applicability of the proposed tests.
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Positive Solutions for a Class of Fractional
p
Laplacian Equation with Critical Sobolev Exponent and Decaying Potentials
Na LI, Xiaoming HE
Acta Mathematicae Applicatae Sinica(English Series). 2022, 38(2): 463483.
DOI:
10.1007/s1025502210908
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7
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In this paper, we study the existence of positive solution for the $p$Laplacian equations with fractional critical nonlinearity \[ \begin{cases} (\Delta)^{s}_{p}u+V(x)u^{p2}u=K(x)f(u)+P(x)u^{p^{*}_{s}2}u, \qquad x\in \mathbb{R}^{N}, \\ u\in \mathcal {D}^{s,p}(\mathbb{R}^{N}), \end{cases} \] where $s\in(0,1), \ p^{*}_{s}=\frac{Np}{Nsp}, \ N>sp, \ p>1$ and $ V(x),K(x)$ are positive continuous functions which vanish at infinity, $f$ is a function with a subcritical growth, and $P(x)$ is bounded, nonnegative continuous function. By using variational method in the weighted spaces, we prove the above problem has at least one positive solution.
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General Decay for a Thermoelastic Problem of a Microbeam with GurtinPipkin Thermal Law
Dongqin CHEN, Wenjun LIU, Zhijing CHEN
Acta Mathematicae Applicatae Sinica(English Series). 2022, 38(2): 426440.
DOI:
10.1007/s1025502210873
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In this paper, we study the wellposedness and the asymptotic stability of a onedimensional thermoelastic microbeam system, where the heat conduction is given by GurtinPipkin thermal law. We first establish the wellposedness of the system by using the semigroup arguments and LumerPhillips theorem. We then obtain an explicit and general formula for the energy decay rates through perturbed energy method and some properties of the convex functions.
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A Delayed HIV Infection Model with the Homeostatic Proliferation of CD4
^{+}
T Cells
Qianghui XU, Jicai HUANG, Yueping DONG, Yasuhiro TAKEUCHI
Acta Mathematicae Applicatae Sinica(English Series). 2022, 38(2): 441462.
DOI:
10.1007/s1025502210882
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In this paper, we investigate a delayed HIV infection model that considers the homeostatic proliferation of CD4
^{+}
T cells. The existence and stability of uninfected equilibrium and infected equilibria (smaller and larger ones) are studied by analyzing the characteristic equation of the system. The intracellular delay does not affect the stability of uninfected equilibrium, but it can change the stability of larger positive equilibrium and Hopf bifurcation appears inducing stable limit cycles. Furthermore, direction and stability of Hopf bifurcation are well investigated by using the central manifold theorem and the normal form theory. The numerical simulation results show that the stability region of larger positive equilibrium becomes smaller as the increase of time delay. Moreover, when the maximum homeostatic growth rate is very small, the larger positive equilibrium is always stable. On the contrary, when the rate of supply of T cells is very small, the larger positive equilibrium is always unstable.
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Uniform Regularity for the Isentropic Compressible Magnetohydrodynamic System
Jishan FAN, Fucai LI, GEN NAKAMURA
Acta Mathematicae Applicatae Sinica(English Series). 2022, 38(2): 410416.
DOI:
10.1007/s1025502210846
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In this paper we first establish the uniform regularity of smooth solutions with respect to the viscosity coefficients to the isentropic compressible magnetohydrodynamic system in a periodic domain $\mathbb{T}^n$. We then apply our result to obtain the isentropic compressible magnetohydrodynamic system with zero viscosity.
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Discussions on Orthogonal Factorizations in Digraphs
Sizhong ZHOU, Hongxia LIU
Acta Mathematicae Applicatae Sinica(English Series). 2022, 38(2): 417425.
DOI:
10.1007/s1025502210864
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9
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Let $m$, $t$, $r$ and $k_i$ $(1\leq i\leq m)$ be positive integers with $k_i\geq\frac{(t+3)r}{2}$, and $G$ be a digraph with vertex set $V(G)$ and arc set $E(G)$. Let $H_1,H_2,\cdots,H_t$ be $t$ vertexdisjoint subdigraphs of $G$ with $mr$ arcs. In this article, it is verified that every $[0,k_1+k_2+\cdots+k_m(m1)r]$digraph $G$ has a $[0,k_i]_1^{m}$factorization $r$orthogonal to every $H_i$ for $1\leq i\leq t$.
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Stabilization and Synchronization of Discretetime Fractional Chaotic Systems with Nonidentical Dimensions
Samir BENDOUKHA
Acta Mathematicae Applicatae Sinica(English Series). 2021, 37(3): 523538.
DOI:
10.1007/s1025502110295
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157
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This paper investigates the stabilization and synchronization of two fractional chaotic maps proposed recently, namely the 2D fractional Hénon map and the 3D fractional generalized Hénon map. We show that although these maps have non–identical dimensions, their synchronization is still possible. The proposed controllers are evaluated experimentally in the case of non–identical orders or time–varying orders. Numerical methods are used to illustrate the results.
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NavierStokes/AllenCahn System with Generalized Navier Boundary Condition
Yazhou CHEN, Qiaolin HE, Bin HUANG, Xiaoding SHI
Acta Mathematicae Applicatae Sinica(English Series). 2022, 38(1): 98115.
DOI:
10.1007/s1022502210687
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In this paper, we focus on the immiscible compressible twophase flow described by the coupled compressible NavierStokes system and the modified AllenCahn equations. The generalized Navier boundary condition and the relaxation boundary condition are established in order to solve the problem of moving contact lines on the solid boundary by using the principle of minimum energy dissipation. The existence and uniqueness for local strong solution in three dimensional bounded domain for this type of boundary value problem is obtained by the elementary energy method and the maximum principle.
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Hypergraph Turán Numbers of Vertex Disjoint Cycles
Ran GU, Xueliang LI, Yongtang SHI
Acta Mathematicae Applicatae Sinica(English Series). 2022, 38(1): 229234.
DOI:
10.1007/s102550221056x
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The Turán number of a
k
uniform hypergraph
H
, denoted by
e
x
_{k}
(
n
;
H
), is the maximum number of edges in any
k
uniform hypergraph
F
on
n
vertices which does not contain
H
as a subgraph. Let
C
_{e}
^{(k)}
denote the family of all
k
uniform minimal cycles of length
e
,
S
(
e
_{1}
, ...,
e
_{r}
) denote the family of hypergraphs consisting of unions of
r
vertex disjoint minimal cycles of length
e
_{1}
, ...,
e
_{r}
, respectively, and
C
_{e}
^{(k)}
denote a
k
uniform linear cycle of length
e
. We determine precisely
e
x
_{k}
(
n
;
S
(
e
_{1}
, ...,
e
_{r}
)) and
e
x
_{k}
(
n
;
C
_{e1}
^{(k)}
, ...,
C
_{er}
^{(k)}
) for sufficiently large
n
. Our results extend recent results of Füredi and Jiang who determined the Turán numbers for single
k
uniform minimal cycles and linear cycles.
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