中国科学院数学与系统科学研究院期刊网

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  • ARTICLES
    Cai-feng WANG, Cong XIE, Zi-yu MA, Hui-min ZHAO
    Acta Mathematicae Applicatae Sinica(English Series). 2023, 39(4): 791-807. https://doi.org/10.1007/s10255-023-1095-y
    In order to measure the uncertainty of financial asset returns in the stock market, this paper presents a new model, called SV-dtC model, a stochastic volatility (SV) model assuming that the stock return has a doubly truncated Cauchy distribution, which takes into account the high peak and fat tail of the empirical distribution simultaneously. Under the Bayesian framework, a prior and posterior analysis for the parameters is made and Markov Chain Monte Carlo (MCMC) is used for computing the posterior estimates of the model parameters and forecasting in the empirical application of Shanghai Stock Exchange Composite Index (SSE-CI) with respect to the proposed SV-dtC model and two classic SV-N (SV model with Normal distribution) and SV-T (SV model with Student-t distribution) models. The empirical analysis shows that the proposed SV-dtC model has better performance by model checking, including independence test (Projection correlation test), Kolmogorov-Smirnov test(K-S test) and Q-Q plot. Additionally, deviance information criterion (DIC) also shows that the proposed model has a significant improvement in model fit over the others.
  • ARTICLES
    Yong LIU, Zi-yu LIU
    Acta Mathematicae Applicatae Sinica(English Series). 2024, 40(1): 1-16. https://doi.org/10.1007/s10255-023-1072-5
    We investigate some relations between two kinds of semigroup regularities, namely the e-property and the eventual continuity, both of which contribute to the ergodicity for Markov processes on Polish spaces. More precisely, we prove that for Markov-Feller semigroup in discrete time and stochastically continuous Markov-Feller semigroup in continuous time, if there exists an ergodic measure whose support has a nonempty interior, then the e-property is satisfied on the interior of the support. In particular, it implies that, restricted on the support of each ergodic measure, the e-property and the eventual continuity are equivalent for the discrete-time and the stochastically continuous continuous-time Markov-Feller semigroups.
  • ARTICLES
    Gui-qin QIU, Gao-wei CAO, Xiao-zhou YANG
    Acta Mathematicae Applicatae Sinica(English Series). 2023, 39(3): 465-490. https://doi.org/10.1007/s10255-023-1058-3
    In this paper, we investigate the global solution and the structures of interaction between two dimensional non-selfsimilar shock wave and rarefaction wave of general two-dimensional scalar conservation law in which flux functions f(u) and g(u) do not need to be convex, and the initial value contains three constant states which are respectively separated by two general initial discontinuities. When initial value contains three constant states, the cases of selfsimilar shock wave and rarefaction wave had been studied before, but no results of the cases of neither non-selfsimilar shock wave or non-selfsimilar rarefaction wave. Under the assumption that Condition H which is generalization of one dimensional convex condition, and some weak conditions of initial discontinuity, according to all the kinds of combination of elementary waves respectively staring from two initial discontinuities, we get four cases of wave interactions as S + S, S + R, R + S and R + R. By studying these interactions between non-selfsimilar elementary waves, we obtain and prove all structures of non-selfsimilar global solutions for all cases.
  • ARTICLES
    Meng CHEN, Wang-xue CHEN, Rui YANG
    Acta Mathematicae Applicatae Sinica(English Series). 2024, 40(1): 75-90. https://doi.org/10.1007/s10255-024-1104-9
    The traditional simple random sampling (SRS) design method is inefficient in many cases. Statisticians proposed some new designs to increase efficiency. In this paper, as a variation of moving extremes ranked set sampling (MERSS), double MERSS (DMERSS) is proposed and its properties for estimating the population mean are considered. It turns out that, when the underlying distribution is symmetric, DMERSS gives unbiased estimators of the population mean. Also, it is found that DMERSS is more efficient than the SRS and MERSS methods for usual symmetric distributions (normal and uniform). For asymmetric distributions considered in this study, the DMERSS has a small bias and it is more efficient than SRS for usual asymmetric distribution (exponential) for small sample sizes.
  • ARTICLES
    Qing-qing ZHENG
    Acta Mathematicae Applicatae Sinica(English Series). 2024, 40(1): 17-34. https://doi.org/10.1007/s10255-024-1100-0
    In this paper, we present a minimum residual based gradient iterative method for solving a class of matrix equations including Sylvester matrix equations and general coupled matrix equations. The iterative method uses a negative gradient as steepest direction and seeks for an optimal step size to minimize the residual norm of next iterate. It is shown that the iterative sequence converges unconditionally to the exact solution for any initial guess and that the norm of the residual matrix and error matrix decrease monotonically. Numerical tests are presented to show the efficiency of the proposed method and confirm the theoretical results.
  • ARTICLES
    Yuan-an ZHAO, Gao-wei CAO, Xiao-zhou YANG
    Acta Mathematicae Applicatae Sinica(English Series). 2023, 39(4): 830-853. https://doi.org/10.1007/s10255-023-1097-9
    We investigate the global structures of the non-selfsimilar solutions for $n$-dimensional ($n$-D) non-homogeneous Burgers equation, in which the initial data has two different constant states, which are separated by a $({n-1})$-dimensional sphere. We first obtain the expressions of $n$-D shock waves and rarefaction waves emitting from the initial discontinuity. Then, by estimating the new kind of interactions of the related elementary waves, we obtain the global structures of the non-selfsimilar solutions, in which ingenious techniques are proposed to construct the $n$-D shock waves. The asymptotic behaviors with geometric structures are also proved.
  • ARTICLES
    Lu-yi LI, Ping LI, Xue-liang LI
    Acta Mathematicae Applicatae Sinica(English Series). 2024, 40(2): 269-274. https://doi.org/10.1007/s10255-024-1076-9
    Let $\mathbf{G}=\{G_i: i\in[n]\}$ be a collection of not necessarily distinct $n$-vertex graphs with the same vertex set $V$, where $\mathbf{G}$ can be seen as an edge-colored (multi)graph and each $G_i$ is the set of edges with color $i$. A graph $F$ on $V$ is called rainbow if any two edges of $F$ come from different $G_i$s'. We say that $\mathbf{G}$ is rainbow pancyclic if there is a rainbow cycle $C_{\ell}$ of length $\ell$ in $\mathbf{G}$ for each integer $\ell\in [3,n]$. In 2020, Joos and Kim proved a rainbow version of Dirac's theorem: If $\delta(G_i)\geq\frac{n}{2}$ for each $i\in[n]$, then there is a rainbow Hamiltonian cycle in $\mathbf{G}$. In this paper, under the same condition, we show that $\mathbf{G}$ is rainbow pancyclic except that $n$ is even and $\mathbf{G}$ consists of $n$ copies of $K_{\frac{n}{2},\frac{n}{2}}$. This result supports the famous meta-conjecture posed by Bondy.
  • ARTICLES
    Dong-juan NIU, Ying WANG
    Acta Mathematicae Applicatae Sinica(English Series). 2023, 39(4): 886-925. https://doi.org/10.1007/s10255-023-1090-3
    In this paper we mainly deal with the global well-posedness and large-time behavior of the 2D tropical climate model with small initial data. We first establish the global well-posedness of solution in the Besov space, then we obtain the optimal decay rates of solutions by virtue of the frequency decomposition method. Specifically, for the low frequency part, we use the Fourier splitting method of Schonbek and the spectrum analysis method, and for the high frequency part, we use the global energy estimate and the behavior of exponentially decay operator.
  • ARTICLES
    Qing GUO, Li-xiu DUAN
    Acta Mathematicae Applicatae Sinica(English Series). 2023, 39(4): 868-877. https://doi.org/10.1007/s10255-023-1086-z
    In this paper, we are concerned with the the Schrödinger-Newton system with $L^2$-constraint. Precisely, we prove that there cannot exist multi-peak normalized solutions concentrating at $k$ different critical points of $V(x)$ under certain assumptions on asymptotic behavior of $V(x)$ and its first derivatives near these points. Especially, the critical points of $V(x)$ in this paper must be degenerate.
    The main tools are a local Pohozaev type of identity and the blow-up analysis. Our results also show that the asymptotic behavior of concentrated points to Schrödinger-Newton problem is quite different from the classical Schrödinger equations, which is mainly caused by the nonlocal term.
  • ARTICLES
    Peng-fei LI, Jun-hui XIE, Dan MU
    Acta Mathematicae Applicatae Sinica(English Series). 2024, 40(1): 225-240. https://doi.org/10.1007/s10255-024-1111-x
    Let $\Omega$ be a bounded smooth domain in ${\mathbb{R}}^N \ (N\geq3)$. Assuming that 0<s<1, 1p,q)≠(N+2s/N-2s,N+2s/N-2s), and $a,b>0$ are constants, we consider the existence results for positive solutions of a class of fractional elliptic system below, \begin{align*} \left\{\begin{array}{ll} (a+b[u]^2_s)(-\Delta)^su=v^p+h_1(x,u,v,\nabla u,\nabla v), &\quad x\in\Omega,\\ (-\Delta)^sv=u^q+h_2(x,u,v,\nabla u,\nabla v), &\quad x\in\Omega,\\ u,v>0, &\quad x\in\Omega,\\ u=v=0, &\quad x\in \mathbb{R}^N\backslash\Omega. \end{array}\right. \end{align*} Under some assumptions of $h_i(x,u,v,\nabla u,\nabla v)(i=1,2)$, we get a priori bounds of the positive solutions to the problem (1.1) by the blow-up methods and rescaling argument. Based on these estimates and degree theory, we establish the existence of positive solutions to problem (1.1).
  • ARTICLES
    Lu CHEN, Feng YANG, Yong-li SONG
    Acta Mathematicae Applicatae Sinica(English Series). 2023, 39(3): 675-695. https://doi.org/10.1007/s10255-023-1084-1
    In this paper, we are concerned with a predator-prey model with Holling type II functional response and Allee effect in predator. We first mathematically explore how the Allee effect affects the existence and stability of the positive equilibrium for the system without diffusion. The explicit dependent condition of the existence of the positive equilibrium on the strength of Allee effect is determined. It has been shown that there exist two positive equilibria for some modulate strength of Allee effect. The influence of the strength of the Allee effect on the stability of the coexistence equilibrium corresponding to high predator biomass is completely investigated and the analytically critical values of Hopf bifurcations are theoretically determined. We have shown that there exists stability switches induced by Allee effect. Finally, the diffusion-driven Turing instability, which can not occur for the original system without Allee effect in predator, is explored, and it has been shown that there exists diffusion-driven Turing instability for the case when predator spread slower than prey because of the existence of Allee effect in predator.
  • ARTICLES
    Cong-hui ZHANG, Hai-feng ZHANG, Mei-rong ZHANG
    Acta Mathematicae Applicatae Sinica(English Series). 2024, 40(2): 275-301. https://doi.org/10.1007/s10255-024-1084-9
    The existence and stability of stationary solutions for a reaction-diffusion-ODE system are investigated in this paper. We first show that there exist both continuous and discontinuous stationary solutions. Then a good understanding of the stability of discontinuous stationary solutions is gained under an appropriate condition. In addition, we demonstrate the influences of the diffusion coefficient on stationary solutions. The results we obtained are based on the super-/sub-solution method and the generalized mountain pass theorem. Finally, some numerical simulations are given to illustrate the theoretical results.
  • ARTICLES
    Bing-guang CHEN, Xiang-chan ZHU
    Acta Mathematicae Applicatae Sinica(English Series). 2023, 39(3): 511-549. https://doi.org/10.1007/s10255-023-1071-6
    In this paper we establish the large deviation principle for the the two-dimensional stochastic Navier-Stokes equations with anisotropic viscosity both for small noise and for short time. The proof for large deviation principle is based on the weak convergence approach. For small time asymptotics we use the exponential equivalence to prove the result.
  • ARTICLES
    Ling-yue ZHANG, Heng-jian CUI
    Acta Mathematicae Applicatae Sinica(English Series). 2023, 39(3): 491-510. https://doi.org/10.1007/s10255-023-1073-4
    This paper introduces two local conditional dependence matrices based on Spearman’s ρ and Kendall’s τ given the condition that the underlying random variables belong to the intervals determined by their quantiles. The robustness is studied by means of the influence functions of conditional Spearman’s ρ and Kendall’s τ. Using the two matrices, we construct the corresponding test statistics of local conditional dependence and derive their limit behavior including consistency, null and alternative asymptotic distributions. Simulation studies illustrate a superior power performance of the proposed Kendall-based test. Real data analysis with proposed methods provides a precise description and explanation of some financial phenomena in terms of mathematical statistics.
  • ARTICLES
    Ying CHEN, Lan TAO, Li ZHANG
    Acta Mathematicae Applicatae Sinica(English Series). 2023, 39(4): 1009-1031. https://doi.org/10.1007/s10255-023-1098-8
    A coloring of graph $G$ is an injective coloring if its restriction to the neighborhood of any vertex is injective, which means that any two vertices get different colors if they have a common neighbor. The injective chromatic number $\chi_i(G)$ of $G$ is the least integer $k$ such that $G$ has an injective $k$-coloring. In this paper, we prove that (1) if $G$ is a planar graph with girth $g\geq 6$ and maximum degree $\Delta \geq 7$, then $\chi_i(G)\leq \Delta +2$; (2) if $G$ is a planar graph with $\Delta \geq24$ and without 3,4,7-cycles, then $\chi_i(G)\leq \Delta +2$.
  • ARTICLES
    Qian-yi HUANG, Liang-wei QI, Jing-ke ZHANG, Yu TANG
    Acta Mathematicae Applicatae Sinica(English Series). 2023, 39(3): 778-790. https://doi.org/10.1007/s10255-023-1065-4
    With the development of modern electronic countermeasure technology, the fight between radar jamming and anti-jamming in aviation military has become increasingly fierce. There are some special requirements for radar countermeasure experiments. For example, such experiments are often divided into several stages, and responses of the previous stages will become factors of the next stages. Moreover, the experiment design can only consider some typical level values of the factors. However, the experiment factors are mostly continuous variables. Thus when there are some jumps in the response, and the value granularity of the factor level is large, the responses fail to reflect the distortion process, which makes it difficult to explore the radar performance boundary. Therefore, it is necessary to study the sequential experiment design method with the optimization goals of response uniformization and response distortion process characterization. In this paper, a sequential experiment design strategy based on Kriging model is established. Firstly, Kriging model is used to fit the initial experimental data to obtain the response surface. In order to enhance the uniformity of response distribution, Shannon entropy is applied to the objective function as the measure of uniformity. While for the situation of response distortion, we consider replacing the existing experiment points with those whose corresponding responses have a larger gradient norm. It means that the response value near these points will change rapidly, so they are more valuable for research. Then we use the peak surface in the three-dimensional space to intuitively verify the effect of the above algorithms on response uniformization and response distortion process characterization, and use the simulated annealing algorithm to solve them. The simulation results show that our sequential experiment strategy has a good effect. Finally, we apply the strategy to the practical problem of radar countermeasure experiment, and the obtained results also perform well.
  • ARTICLES
    Chang-feng LI, Yi-rang YUAN, Huai-ling SONG
    Acta Mathematicae Applicatae Sinica(English Series). 2023, 39(4): 808-829. https://doi.org/10.1007/s10255-023-1099-7
    In this paper the authors discuss a numerical simulation problem of three-dimensional compressible contamination treatment from nuclear waste. The mathematical model, a nonlinear convection-diffusion system of four PDEs, determines four major physical unknowns: the pressure, the concentrations of brine and radionuclide, and the temperature. The pressure is solved by a conservative mixed finite volume element method, and the computational accuracy is improved for Darcy velocity. Other unknowns are computed by a composite scheme of upwind approximation and mixed finite volume element. Numerical dispersion and nonphysical oscillation are eliminated, and the convection-dominated diffusion problems are solved well with high order computational accuracy. The mixed finite volume element is conservative locally, and get the objective functions and their adjoint vector functions simultaneously. The conservation nature is an important character in numerical simulation of underground fluid. Fractional step difference is introduced to solve the concentrations of radionuclide factors, and the computational work is shortened significantly by decomposing a three-dimensional problem into three successive one-dimensional problems. By the theory and technique of a priori estimates of differential equations, we derive an optimal order estimates in $L^2$ norm. Finally, numerical examples show the effectiveness and practicability for some actual problems.
  • ARTICLES
    Aria Ming-yue ZHU, Bao-xuan ZHU
    Acta Mathematicae Applicatae Sinica(English Series). 2023, 39(4): 854-867. https://doi.org/10.1007/s10255-023-1088-x
    An independent set in a graph $G$ is a set of pairwise non-adjacent vertices. The independence polynomial of $G$ is the polynomial $\sum\limits_{A} x^{|A|}$, where the sum is over all independent sets $A$ of $G$. In 1987, Alavi, Malde, Schwenk and Erdős conjectured that the independence polynomial of any tree or forest is unimodal. Although this unimodality conjecture has attracted many researchers' attention, it is still open. Recently, Basit and Galvin even asked a much stronger question whether the independence polynomial of every tree is ordered log-concave. Note that if a polynomial has only negative real zeros then it is ordered log-concave and unimodal. In this paper, we observe real-rootedness of independence polynomials of rooted products of graphs. We find some trees whose rooted product preserves real-rootedness of independence polynomials. In consequence, starting from any graph whose independence polynomial has only real zeros, we can obtain an infinite family of graphs whose independence polynomials have only real zeros. In particular, applying it to trees or forests, we obtain that their independence polynomials are unimodal and ordered log-concave.
  • ARTICLES
    Nai-dan DENG, Chun-wei WANG, Jia-en XU
    Acta Mathematicae Applicatae Sinica(English Series). 2024, 40(1): 109-128. https://doi.org/10.1007/s10255-024-1102-y
    In this paper, the insurance company considers venture capital and risk-free investment in a constant proportion. The surplus process is perturbed by diffusion. At first, the integro-differential equations satisfied by the expected discounted dividend payments and the Gerber-Shiu function are derived. Then, the approximate solutions of the integro-differential equations are obtained through the sinc method. Finally, the numerical examples are given when the claim sizes follow different distributions. Furthermore, the errors between the explicit solution and the numerical solution are discussed in a special case.
  • ARTICLES
    Wen-qing XU, Sha-sha WANG, Da-chuan XU
    Acta Mathematicae Applicatae Sinica(English Series). 2024, 40(1): 91-108. https://doi.org/10.1007/s10255-024-1115-6
    The classical Archimedean approximation of $\pi$ uses the semiperimeter or area of regular polygons inscribed in or circumscribed about a unit circle in $\mathbb{R}^2 $ and it is well-known that by using linear combinations of these basic estimates, modern extrapolation techniques can greatly speed up the approximation process. % reduce the associated approximation errors. Similarly, when $n$ vertices are randomly selected on the circle, the semiperimeter and area of the corresponding random inscribed and circumscribing polygons are known to converge to $\pi$ almost surely as $ n \to \infty $, and by further applying extrapolation processes, faster convergence rates can also be achieved through similar linear combinations of the semiperimeter and area of these random polygons. In this paper, we further develop nonlinear extrapolation methods for approximating $\pi$ through certain nonlinear functions of the semiperimeter and area of such polygons. We focus on two types of extrapolation estimates of the forms $ \mathcal{X}_n = \mathcal{S}_n^{\alpha} \mathcal{A}_n^{\beta} $ and $ \mathcal{Y}_n (p) = \left( \alpha \mathcal{S}_n^p + \beta \mathcal{A}_n^p \right)^{1/p} $ where $ \alpha + \beta = 1 $, $ p \neq 0 $, and $ \mathcal{S}_n $ and $ \mathcal{A}_n $ respectively represents the semiperimeter and area of a random $n$-gon inscribed in the unit circle in $ \mathbb{R}^2 $, and $ \mathcal{X}_n $ may be viewed as the limit of $ \mathcal{Y}_n (p) $ when $ p \to 0 $. By deriving probabilistic asymptotic expansions with carefully controlled error estimates for $ \mathcal{X}_n $ and $ \mathcal{Y}_n (p) $, we show that the choice $ \alpha = 4/3 $, $ \beta = -1/3 $ minimizes the approximation error in both cases, and their distributions are also asymptotically normal.
  • ARTICLES
    Xue WANG, Hong-en JIA, Ming LI, Kai-tai LI
    Acta Mathematicae Applicatae Sinica(English Series). 2023, 39(3): 605-622. https://doi.org/10.1007/s10255-023-1066-3
    In this paper, a linearized energy stable numerical scheme is used to solve the modified CahnHilliard-Navier-Stokes model, which is a phase-field model for two-phase incompressible flows. The time discretization is based on the convex splitting of the energy functional, which leads to a linearized system. In order to maintain the energy stability, the definition domain of energy function is extended to infinity. The stability of the scheme is proved and the error estimate is given. Numerical experiments are done to demonstrate the effectiveness for the proposed scheme.
  • ARTICLES
    Ya-zhou CHEN, Hakho HONG, Xiao-ding SHI
    Acta Mathematicae Applicatae Sinica(English Series). 2024, 40(1): 45-74. https://doi.org/10.1007/s10255-023-1070-7
    This paper is concerned with the large time behavior of the Cauchy problem for Navier-Stokes/Allen-Cahn system describing the interface motion of immiscible two-phase flow in 3-D. The existence and uniqueness of global solutions and the stability of the phase separation state are proved under the small initial perturbations. Moreover, the optimal time decay rates are obtained for higher-order spatial derivatives of density, velocity and phase. Our results imply that if the immiscible two-phase flow is initially located near the phase separation state, then under small perturbation conditions, the solution exists globally and decays algebraically to the complete separation state of the two-phase flow, that is, there will be no interface fracture, vacuum, shock wave, mass concentration at any time, and the interface thickness tends to zero as the time $t\rightarrow+\infty$.
  • ARTICLES
    Bing SU, Fu-kang ZHU, Ju HUANG
    Acta Mathematicae Applicatae Sinica(English Series). 2023, 39(4): 972-989. https://doi.org/10.1007/s10255-023-1096-x
    The spatial and spatiotemporal autoregressive conditional heteroscedasticity (STARCH) models receive increasing attention. In this paper, we introduce a spatiotemporal autoregressive (STAR) model with STARCH errors, which can capture the spatiotemporal dependence in mean and variance simultaneously. The Bayesian estimation and model selection are considered for our model. By Monte Carlo simulations, it is shown that the Bayesian estimator performs better than the corresponding maximum-likelihood estimator, and the Bayesian model selection can select out the true model in most times. Finally, two empirical examples are given to illustrate the superiority of our models in fitting those data.
  • ARTICLES
    Ya-jie LI, Hao-kun QI, Zheng-bo CHANG, Xin-zhu MENG
    Acta Mathematicae Applicatae Sinica(English Series). 2023, 39(3): 550-570. https://doi.org/10.1007/s10255-023-1055-6
    This paper investigates the stochastic dynamics of trophic cascade chemostat model perturbed by regime switching, Gaussian white noise and impulsive toxicant input. For the system with only white noise interference, sufficient conditions for stochastically ultimate boundedness and stochastically permanence are obtained, and we demonstrate that the stochastic system has at least one nontrivial positive periodic solution. For the system with Markov regime switching, sufficient conditions for extinction of the microorganisms are established. Then we prove the system is ergodic and has a stationary distribution. The results show that both impulsive toxins input and stochastic noise have great effects on the survival and extinction of the microorganisms. Finally, a series of numerical simulations are presented to illustrate the theoretical analysis.
  • ARTICLES
    WANG Wei-fan, WANG Yi-qiao, YANG Wan-shun
    Acta Mathematicae Applicatae Sinica(English Series). 2024, 40(1): 35-44. https://doi.org/10.1007/s10255-024-1101-z
    An acyclic edge coloring of a graph $G$ is a proper edge coloring such that there are no bichromatic cycles in $G$. The acyclic chromatic index $\chi'_a(G)$ of $G$ is the smallest $k$ such that $G$ has an acyclic edge coloring using $k$ colors. It was conjectured that every simple graph $G$ with maximum degree $\Delta$ has $\chi'_a(G)\le \Delta+2$. A 1-planar graph is a graph that can be drawn in the plane so that each edge is crossed by at most one other edge. In this paper, we show that every 1-planar graph $G$ without $4$-cycles has $\chi'_a(G)\le \Delta+22$.
  • ARTICLES
    En-wen ZHU, Zi-wei DENG, Han-jun ZHANG, Jun CAO, Xiao-hui LIU
    Acta Mathematicae Applicatae Sinica(English Series). 2024, 40(2): 320-346. https://doi.org/10.1007/s10255-024-1072-0
    This paper considers the random coefficient autoregressive model with time-functional variance noises, hereafter the RCA-TFV model. We first establish the consistency and asymptotic normality of the conditional least squares estimator for the constant coefficient. The semiparametric least squares estimator for the variance of the random coefficient and the nonparametric estimator for the variance function are constructed, and their asymptotic results are reported. A simulation study is presented along with an analysis of real data to assess the performance of our method in finite samples.
  • ARTICLES
    Ming-hua YANG, Si-ming HUANG, Jin-yi SUN
    Acta Mathematicae Applicatae Sinica(English Series). 2024, 40(1): 241-268. https://doi.org/10.1007/s10255-024-1119-2
    In this paper, we study a global zero-relaxation limit problem of the electro-diffusion model arising in electro-hydrodynamics which is the coupled Planck-Nernst-Poisson and Navier-Stokes equations. That is, the paper deals with a singular limit problem of \begin{eqnarray*}\label{1.2} \left\{ \begin{array}{ll} u_t^{\epsilon}+u^{\epsilon}\cdot\nabla u^{\epsilon}-\Delta u^{\epsilon}+\nabla\mathbf{P}^{\epsilon}=\Delta \phi^{\epsilon}\nabla\phi^{\epsilon}, \ \ \ &{\rm in}\ \mathbb{R}^{3}\times(0, \infty), \\[5pt] \nabla\cdot u^{\epsilon}=0, \ \ \ &{\rm in}\ \mathbb{R}^{3}\times(0, \infty), \\[5pt] n_t^{\epsilon}+u^{\epsilon}\cdot\nabla n^{\epsilon}-\Delta n^{\epsilon}=-\nabla\cdot(n^{\epsilon}\nabla \phi^{\epsilon}), &{\rm in}\ \mathbb{R}^{3}\times(0, \infty),\\[5pt] c_t^{\epsilon}+u^{\epsilon}\cdot\nabla c^{\epsilon}-\Delta c^{\epsilon}=\nabla\cdot(c^{\epsilon}\nabla\phi^{\epsilon}), &{\rm in}\ \mathbb{R}^{3}\times(0, \infty),\\[5pt] \epsilon^{-1} \phi^{\epsilon}_t= \Delta \phi^{\epsilon}- n^{\epsilon}+ c^{\epsilon}, &{\rm in}\ \mathbb{R}^{3}\times(0, \infty),\\[5pt] (u^{\epsilon}, n^{\epsilon}, c^{\epsilon},\phi^{\epsilon})|_{t=0}= (u_{0}, n_{0}, c_{0},\phi_{0}), &{\rm in}\ \mathbb{R}^{3} \end{array} \right. \end{eqnarray*} involving with a positive, large parameter $\epsilon$. The present work show a case that $(u^{\epsilon}, n^{\epsilon}, c^{\epsilon})$ stabilizes to $(u^{\infty}, n^{\infty}, c^{\infty}):=(u, n, c)$ uniformly with respect to the time variable as $\epsilon\rightarrow+\infty$ with respect to the strong topology in a certain Fourier-Herz space.
  • ARTICLES
    Ding-huai WANG, Jiang ZHOU
    Acta Mathematicae Applicatae Sinica(English Series). 2023, 39(3): 583-590. https://doi.org/10.1007/s10255-023-1077-0
    We prove that the weak Morrey space $WM^{p}_{q}$ is contained in the Morrey space $M^{p}_{q_{1}}$ for $1\leq q_{1}< q\leq p<\infty$. As applications, we show that if the commutator $[b,T]$ is bounded from $L^p$ to $L^{p,\infty}$ for some $p\in (1,\infty)$, then $b\in \mathrm{BMO}$, where $T$ is a Calder\'on-Zygmund operator. Also, for $1
  • ARTICLES
    Yuan-yuan KE, Jia-Shan ZHENG
    Acta Mathematicae Applicatae Sinica(English Series). 2023, 39(4): 1032-1064. https://doi.org/10.1007/s10255-023-1092-1
    In this paper we deal with the initial-boundary value problem for the coupled Keller-Segel-Stokes system with rotational flux, which is corresponding to the case that the chemical is produced instead of consumed, $$ \left\{ \begin{array}{l} n_t+u\cdot\nabla n=\Delta n-\nabla\cdot(nS(x,n,c)\nabla c),\quad x\in \Omega, t>0, \\ c_t+u\cdot\nabla c=\Delta c-c+n,\quad x\in \Omega, \ \ t>0, \\ u_t+\nabla P=\Delta u+n\nabla \phi,\quad x\in \Omega, \ \ t>0, \\ \nabla\cdot u=0,\quad x\in \Omega, t>0 \end{array} \right. (KSS) $$ subject to the boundary conditions $(\nabla n-nS(x,n,c)\nabla c)\cdot\nu=\nabla c\cdot\nu=0$ and $u=0$, and suitably regular initial data $(n_0 (x),c_0 (x),u_0 (x))$, where $\Omega\subset \mathbb{R}^3$ is a bounded domain with smooth boundary $\partial\Omega$. Here $S$ is a chemotactic sensitivity satisfying $|S(x,n,c)|\leq C_S(1+n)^{-\alpha}$ with some $C_S> 0$ and $\alpha> 0$. The greatest contribution of this paper is to consider the large time behavior of solutions for the system (KSS), which is still open even in the 2D case. We can prove that the corresponding solution of the system (KSS) decays to $(\frac{1}{|\Omega|}\int_{\Omega}n_0,\frac{1}{|\Omega|}\int_{\Omega}n_0,0)$ exponentially, if the coefficient of chemotactic sensitivity is appropriately small. As a precondition to consider the asymptotic behavior, we also show the global existence and boundedness of the corresponding initial-boundary problem KSS with a simplified method. We find a new phenomenon that the suitably small coefficient $C_S$ of chemotactic sensitivity could benefit the global existence and boundedness of solutions to the model KSS.
  • ARTICLES
    Chuan-quan LI, Pei-wen XIAO, Chao YING, Xiao-hui LIU
    Acta Mathematicae Applicatae Sinica(English Series). 2024, 40(3): 630-655. https://doi.org/10.1007/s10255-024-1024-8
    Tensor data have been widely used in many fields, e.g., modern biomedical imaging, chemometrics, and economics, but often suffer from some common issues as in high dimensional statistics. How to find their low-dimensional latent structure has been of great interest for statisticians. To this end, we develop two efficient tensor sufficient dimension reduction methods based on the sliced average variance estimation (SAVE) to estimate the corresponding dimension reduction subspaces. The first one, entitled tensor sliced average variance estimation (TSAVE), works well when the response is discrete or takes finite values, but is not $\sqrt{n}$ consistent for continuous response; the second one, named bias-correction tensor sliced average variance estimation (CTSAVE), is a de-biased version of the TSAVE method. The asymptotic properties of both methods are derived under mild conditions. Simulations and real data examples are also provided to show the superiority of the efficiency of the developed methods.
  • ARTICLES
    Yan-fang XUE, Jian-xin HAN, Xin-cai ZHU
    Acta Mathematicae Applicatae Sinica(English Series). 2023, 39(3): 696-706. https://doi.org/10.1007/s10255-023-1083-2
    We study the following quasilinear Schrödinger equation \begin{equation*}\label{for1f} -\Delta u+V(x)u-\Delta (u^2)u=K(x)g(u), \qquad x\in \mathbb{R}^3, \end{equation*} where the nonlinearity $g(u)$ is asymptotically cubic at infinity, the potential $V(x)$ may vanish at infinity. Under appropriate assumptions on $K(x)$, we establish the existence of a nontrivial solution by using the mountain pass theorem.
  • ARTICLES
    Jia-qi YANG
    Acta Mathematicae Applicatae Sinica(English Series). 2024, 40(1): 205-210. https://doi.org/10.1007/s10255-024-1114-7
    We consider the relation between the direction of the vorticity and the global regularity of 3D shear thickening fluids. It is showed that a weak solution to the non-Newtonian incompressible fluid in the whole space is strong if the direction of the vorticity is 11-5p/2-Hölder continuous with respect to the space variables when 2
  • ARTICLES
    Li-na GUO, Ai-yong CHEN, Shuai-feng ZHAO
    Acta Mathematicae Applicatae Sinica(English Series). 2024, 40(3): 577-599. https://doi.org/10.1007/s10255-024-1081-z
    This paper studies the global phase portraits of uniform isochronous centers system of degree six with polynomial commutator. Such systems have the form $\dot{x}=-y+xf(x,y),\ \dot{y}=x+yf(x,y)$, where $f(x,y)=a_{1}x+a_{2}xy+a_{3}xy^{2}+a_{4}xy^{3}+a_{5}xy^4=x\sigma(y)$, and any zero of $1+a_{1}y+a_{2}y^2+a_{3}y^{3}+a_{4}y^{4}+a_{5}y^{5}$, $y=\overline{y}$ is an invariant straight line. At last, all global phase portraits are drawn on the Poincarédisk.
  • ARTICLES
    Rong-Xian YUE, Xin LIU, Kashinath CHATTERJEE
    Acta Mathematicae Applicatae Sinica(English Series). 2023, 39(4): 878-885. https://doi.org/10.1007/s10255-023-1089-9
    This paper considers a linear regression model involving both quantitative and qualitative factors and an $m$-dimensional response variable y. The main purpose of this paper is to investigate $D$-optimal designs when the levels of the qualitative factors interact with the levels of the quantitative factors. Under a general covariance structure of the response vector y, here we establish that the determinant of the information matrix of a product design can be separated into two parts corresponding to the two marginal designs. Moreover, it is also proved that $D$-optimal designs do not depend on the covariance structure if we assume hierarchically ordered system of regression models.
  • ARTICLES
    Sheng-jie HE, Rong-Xia HAO, Ai-mei YU
    Acta Mathematicae Applicatae Sinica(English Series). 2023, 39(3): 591-604. https://doi.org/10.1007/s10255-023-1061-8
    A mixed graph $\widetilde{G}$ is obtained by orienting some edges of $G$, where $G$ is the underlying graph of $\widetilde{G}$. The positive inertia index, denoted by $p^{+}(\widetilde{G})$, and the negative inertia index, denoted by $n^{-}(\widetilde{G})$, of a mixed graph $\widetilde{G}$ are the integers specifying the numbers of positive and negative eigenvalues of the Hermitian adjacent matrix of $\widetilde{G}$, respectively. In this paper, the positive and negative inertia indices of the mixed unicyclic graphs are studied. Moreover, the upper and lower bounds of the positive and negative inertia indices of the mixed graphs are investigated, and the mixed graphs which attain the upper and lower bounds are characterized respectively.
  • ARTICLES
    Zhi-min REN, Yong-yi LAN
    Acta Mathematicae Applicatae Sinica(English Series). 2024, 40(2): 414-429. https://doi.org/10.1007/s10255-024-1120-9
    In this paper, we investigate the following $p$-Kirchhoff equation \begin{eqnarray*} \left\{\begin{array}{ll} \big(a+b\int_{\mathbb{R}^{N}}(|\nabla u|^{p}+|u|^{p})dx\big)\big(-\Delta_{p}u+|u|^{p-2}u\big)=|u|^{s-2}u+\mu u,~x\in \mathbb{R}^{N},\\ \int_{\mathbb{R}^{N}}|u|^{2}dx=\rho, \end{array} \right. \end{eqnarray*} where $a> 0, \,b \geq 0 , \,\rho>0$ are constants, $p^{\ast}=\frac{Np}{N-p}$ is the critical Sobolev exponent, $\mu$ is a Lagrange multiplier, $-\Delta_{p}u=-{\rm div}(|\nabla u|^{p-2}\nabla u), \ 2<p<N<2p, \ \mu\in\mathbb{R}$, and $ s\in(2\frac{N+2}{N}p-2,~p^{\ast})$. We demonstrate that the $p$-Kirchhoff equation has a normalized solution using the mountain pass lemma and some analysis techniques.
  • ARTICLES
    Jin LIANG, Yang LIN
    Acta Mathematicae Applicatae Sinica(English Series). 2023, 39(3): 765-777. https://doi.org/10.1007/s10255-023-1082-3
    In this paper, a new corporate bond pricing model with credit migration risk is proposed. This model sets different thresholds for the rising or falling of credit ratings, which forms a buffer zone that could reduce the frequency of credit rating changes. Mathematically, this model is a system of partial differential equations with overlapping area. The existence, uniqueness, regularity and asymptotic behavior of the solution are obtained. Furthermore, a numerical scheme and its stability, convergence and accuracy are discussed in detail. Calibration and analysis of the parameters are also suggested.
  • ARTICLES
    Xin ZHONG
    Acta Mathematicae Applicatae Sinica(English Series). 2023, 39(4): 990-1008. https://doi.org/10.1007/s10255-023-1094-z
    We are concerned with singularity formation of strong solutions to the two-dimensional (2D) full compressible magnetohydrodynamic equations with zero resistivity in a bounded domain. By energy method and critical Sobolev inequalities of logarithmic type, we show that the strong solution exists globally if the temporal integral of the maximum norm of the deformation tensor is bounded. Our result is the same as Ponce's criterion for 3D incompressible Euler equations. In particular, it is independent of the magnetic field and temperature. Additionally, the initial vacuum states are allowed.
  • ARTICLES
    Qiang WEN, Guo-qiang REN, Bin LIU
    Acta Mathematicae Applicatae Sinica(English Series). 2024, 40(1): 164-191. https://doi.org/10.1007/s10255-024-1107-6
    In this paper, we consider a susceptible-infective-susceptible (SIS) reaction-diffusion epidemic model with spontaneous infection and logistic source in a periodically evolving domain.~Using the iterative technique, the uniform boundedness of solution is established.~In addition, the spatial-temporal risk index $\mathcal{R}_0(\rho)$ depending on the domain evolution rate $\rho(t)$ as well as its analytical properties are discussed.~The monotonicity of $\mathcal{R}_0(\rho)$ with respect to the diffusion coefficients of the infected $d_I$, the spontaneous infection rate $\eta(\rho(t)y)$ and interval length $L$ is investigated under appropriate conditions.~Further, the existence and asymptotic behavior of periodic endemic equilibria are explored by upper and lower solution method.~Finally, some numerical simulations are presented to illustrate our analytical results.~Our results provide valuable information for disease control and prevention.
  • ARTICLES
    Ke-Jie LI, Xin ZHANG
    Acta Mathematicae Applicatae Sinica(English Series). 2024, 40(2): 467-477. https://doi.org/10.1007/s10255-024-1026-6
    The strong chromatic index of a graph is the minimum number of colors needed in a proper edge coloring so that no edge is adjacent to two edges of the same color. An outerplane graph with independent crossings is a graph embedded in the plane in such a way that all vertices are on the outer face and two pairs of crossing edges share no common end vertex. It is proved that every outerplane graph with independent crossings and maximum degree $\Delta$ has strong chromatic index at most $4\Delta-6$ if $\Delta\geq 4$, and at most 8 if $\Delta\leq 3$. Both bounds are sharp.