中国科学院数学与系统科学研究院期刊网

15 September 2026, Volume 42 Issue 4
    

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  • Statistical Estimations for Non-Ergodic Vasicek Model Driven by Gaussian Processes
    Yong CHEN, Wu-jun GAO, Ying LI
    Acta Mathematicae Applicatae Sinica(English Series). 2026, 42(4): 1043-1067. https://doi.org/10.1007/s10255-026-0005-5
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    We study the joint asymptotic distribution of the least squares estimator of the parameter $(\theta,\,\mu)$ in non-ergodic Vasicek models driven by seven specific Gaussian processes. To facilitate the proofs, we derive the inner product formulas of the canonical Hilbert spaces associated to the seven specific Gaussian processes. The integration by parts for normalized bounded variation functions is essential to the inner product formulas. We apply the inner product formulas of the seven Gaussian processes to check the set of conditions of Es-Sebaiy, Es.Sebaiy (2021).
  • Exact Periodic Solutions of a Kind of Quintic Nonlinear Liénard Equation and Their Evolution with Hamilton Energy
    Wei-guo ZHANG, Yu-li GUO, Shao-wei LI, Xue ZHANG
    Acta Mathematicae Applicatae Sinica(English Series). 2026, 42(4): 1068-1103. https://doi.org/10.1007/s10255-026-0122-1
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    In this paper, we study the exact periodic solutions of a kind of Liénard equation with cubic and quintic nonlinearities and the evolution of periodic solutions with Hamilton energy. Firstly, the qualitative analysis of the equation is carried out by using the dynamic system theorem, then the existence conditions, the number and the approximate positions of the periodic solutions and other bounded solutions for this equation are given. By applying the analysis approach on the basis of the first integral and several appropriate transformations, we obtain all seven families of elliptic function periodic solutions of the equation under different parameters conditions. By studying the limit of these periodic solutions on the Hamilton energy evolution and directly using the analysis approach based on the first integral, all ten pairs of bell-shaped solutions and kink-shaped solutions (corresponding to homoclinic and heteroclinic orbits) for the studied equation under different parameter conditions are also given. In this paper, we establish the relationship between the Hamilton energy of the system and the periodic solution, bell-shaped solution and kink-shaped solution of the system. From the analysis in this paper, it can be seen that the reason why the Liénard equation we studied has periodic solutions, bell-shaped solutions and kink-shaped solutions is essentially determined by the energy value-taken of the Hamilton system corresponding to the equation in different ranges. As the preliminary application of the results in this paper, the periodic wave solutions and the solitary wave solutions of the typical Ablowitz equation are also given.
  • Sharp Interface Limit for the One-dimensional Compressible Navier-Stokes/Allen-Cahn System with Composite Waves
    Ya-zhou CHEN, Yi PENG, Xiao-ding SHI
    Acta Mathematicae Applicatae Sinica(English Series). 2026, 42(4): 1104-1135. https://doi.org/10.1007/s10255-024-1130-7
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    This paper is concerned with the sharp interface limit of Cauchy problem for the one-dimensional compressible Navier-Stokes/Allen-Cahn system with a composite wave consisting of the superposition of a rarefaction wave and a shock wave. Under the assumption that the viscosity coefficient and the reciprocal of mobility coefficient are directly proportional to the interface thickness, we first convert the sharp interface limit of the system into the large time behavior of the composite wave via a natural scaling. Then we prove that the composite wave is asymptotically stable under the small initial perturbations and the small strength of the rarefaction and shock wave. Finally, we show the solution of the Cauchy problem exists for all time, and converges to the composite wave solution of the corresponding Euler equations as the thickness of the interface tends to zero. The proof is mainly based on the energy method and the relative entropy.
  • Credibility Estimation and Empirical Bayesian Analysis of Journal Impact Factor
    Li-min WEN, Gen-fan HUANG, Yi ZHANG
    Acta Mathematicae Applicatae Sinica(English Series). 2026, 42(4): 1136-1162. https://doi.org/10.1007/s10255-024-1154-z
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    The traditional journal impact factor neglects the time difference between paper publication and citation, as well as the impact of prior information on journal quality when classifying and ranking journals. To address these issues, this paper proposes a Bayesian model for journal quality parameters. We develop a new journal impact factor and obtain Bayesian estimates of journal quality parameters. Furthermore, in cases where both the sample distribution and prior distribution of journal citation data are unknown, we employ the idea of credibility theory to confine the estimation of journal quality parameters to a linear function of the samples, and obtain the optimal linear Bayesian estimation of journal quality parameters under the criterion of minimum mean square error. The results indicate that the optimal linear Bayesian estimation of journal quality parameters can be expressed in the weighted average form of new impact factor and aggregated estimate, with the weight satisfying the property of credibility. Utilizing citation data from various journals, we obtain estimates for hyperparameters and empirical Bayesian estimates of journal quality parameters. Subsequently, we show the performance of the new estimators by comparing it with the traditional journal impact factor through numerical simulation. Finally, based on actual citation data from ten journals, we present the results, comparing traditional impact factors with the proposed new impact factors, Bayesian estimation, and credibility estimation.
  • Asymptotic Property of Parabolic Equations Involving Pseudo-relativistic Schrödinger Operators
    Chen QIAO, Su-fang TANG
    Acta Mathematicae Applicatae Sinica(English Series). 2026, 42(4): 1163-1183. https://doi.org/10.1007/s10255-024-1097-4
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    In this paper, we investigate parabolic equations involving nonlocal pseudo-relativistic Schrödinger operators $(-\Delta+m^2)^s$ with $s\in(0,1)$ and mass $m>0$ in bounded regions. We establish the asymptotic narrow region principle and asymptotic strong maximum principle for anti symmetric function. As applications, employing the method of moving planes, we show the asymptotical radial symmetry and monotonicity of positive solutions in an unit ball.
  • Insider Trading with Different Risk Preference on a Dynamic Risky Asset
    Kai XIAO, Yong-hui ZHOU
    Acta Mathematicae Applicatae Sinica(English Series). 2026, 42(4): 1184-1199. https://doi.org/10.1007/s10255-024-1039-1
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    For an insider trading model of a risky asset whose value is driven by an arithmetic Brownian motion, we establish a closed form of linear Bayesian equilibrium with a risk-neutral insider and a closed form of linear Bayesian equilibrium with a risk-averse insider respectively. It shows that (i) as time goes by, in the former equilibrium, residual information decreases but price pressure keeps constant, while in the latter, both residual information and price pressure decrease; (ii) as the insider becomes less and less risk-averse, the risk-averse equilibrium converges to the risk-neutral one; and (iii) when the volatility of the asset value goes to zero, the risk-averse equilibrium converges to the risk-averse one with a static risky asset in [Cho, K. Continuous auctions and insider trading. Finance and Stochastics, 7: 47-71 (2003)].
  • On the Existence of Ground State Solutions for Choquard Systems with Nonlinear Couplings
    Li-ping XU, Hai-bo CHEN
    Acta Mathematicae Applicatae Sinica(English Series). 2026, 42(4): 1200-1224. https://doi.org/10.1007/s10255-026-0132-z
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    In this paper, we investigate the following coupled nonlinear Choquard system: \begin{equation*} \begin{cases}-\triangle u+V_1(x)u= (J_\mu(x)\ast|u|^p ) |u|^{p-2}u+\beta |u|^{q-1}|v|^q \text{in} \mathbb {R}^N,\\ -\triangle v+V_2(x)v= (J_\mu(x)\ast|v|^p ) |v|^{p-2}v+\beta |v|^{q-1}|u|^q \text{in} \mathbb {R}^N,\\ u, v\in H^1(\mathbb {R}^N), \end{cases} \end{equation*} where $N\geq 3$, $0<\mu<N$, $\frac{2N-\mu}{N}<p<\frac{2N-\mu}{N-2}$, $1<q<p$, $\beta>0$ is a coupling parameter, and $J_\mu(x)$ is convolution kernel, and $V_i(x)$ is nonnegative continuous external potential for $i=1,2$. Using the Poho$\check{z}$aev-Nehari manifold method, we establish the existence of positive ground state solutions for the system. Furthermore, we prove a nonexistence result for nontrivial solutions under certain conditions.
  • The Multi-birth Property of Markov Branching Processes with Immigration
    Yan-yun LI, Jun-ping LI
    Acta Mathematicae Applicatae Sinica(English Series). 2026, 42(4): 1225-1244. https://doi.org/10.1007/s10255-026-0133-y
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    In this paper, we consider the multi-birth property of Markov branching processes with immigration. The joint probability generating function of multi-birth numbers for Markov branching processes with immigration until time $t$ is obtained by constructing a new $Q$-process. In particular, the probability generating function of multi-birth number is also obtained for Markov branching processes until its extinction.
  • Variational Principle for Fixed-point Free Flow
    Rui-ming LIANG, Hao-yi LEI
    Acta Mathematicae Applicatae Sinica(English Series). 2026, 42(4): 1245-1255. https://doi.org/10.1007/s10255-026-0134-x
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    Let $(X, \phi)$ be a compact flow without fixed points. We define the packing topological entropy $h_{\text{top}}^P(\phi, K)$ on subsets of $X$ through considering all the possible reparametrizations of time. For fixed-point free flows, we prove the following result: for any non-empty compact subset $K$ of $X$, \begin{align*} h_{\text{top}}^P(\phi, K) =\sup\bigl\{\overline{h}_\mu(\phi): \mu(K)=1, \ \mu \text{ is a Borel probability measure on }X\bigr\}, \end{align*} where $\overline{h}_\mu(\phi)$ denotes the upper local entropy for a Borel probability measure $\mu$ on $X$.
  • Global Stability Analysis and Optimal Control for a Dynamical Model with Asymptomatic Infectious State
    Shu-ping LI, Yu-ru YUAN, Rui-xia ZHANG
    Acta Mathematicae Applicatae Sinica(English Series). 2026, 42(4): 1256-1268. https://doi.org/10.1007/s10255-026-0129-7
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    In this paper, we present a dynamical model with asymptomatic infections and optimal control strategies based on a regular network. The basic model without control and basic mathematical results are obtained. Firstly, we obtain the basic reproduction number by using the method of the next generation matrix. Secondly, by taking advantage of the Lyapunov function, we prove that the disease-free equilibrium is globally asymptotically stable when the basic reproduction number $R_{0}<1$. By using generalized Bendixson-Dulac thereom, we prove that the unique endemic equilibrium is globally asymptotically stable when $R_{0}>1$. In addition, by using Pon-tryagin's maximum principle, several reasonable optimal control strategies are suggested to the prevention and control the disease. Finally, numerical simulations are presented to verify the above theoretical results, and we perform sensitivity analysis by partial rank correlation coefficient(PRCC) methods. It is worth noting that asymptomatic infections have a greater contribution to the epidemic of diseases.
  • Multiple Solutions for a Nonlinear Biharmonic Equation on Locally Finite Graph
    Juan ZHAO
    Acta Mathematicae Applicatae Sinica(English Series). 2026, 42(4): 1269-1279. https://doi.org/10.1007/s10255-025-0033-6
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    Let $G=(V, E)$ be a locally finite graph. Given any $O \in V$. Denote the function $\rho(x)$ as follows: \begin{equation*} \rho(x)=\left\{ \begin{array}{l} \mathrm{dist}(x, O), \quad \thinspace \thinspace \thinspace \thinspace x \neq O\\[3mm] 1, \quad \quad \qquad \quad\ x=O, \end{array} \right. \end{equation*} where $\mathrm{dist}(x, O)$ represents the distance between $x$ and $O$. In this paper, we investigate a perturbed nonlinear biharmonic equation $$\Delta ^{2} u-\mathrm{div}(a(x) \nabla u)+b(x)u=\frac{f(x, u)}{\rho(x)^{\beta}}+\epsilon h(x)$$ on $G=(V, E)$, where $a(x)$ and $b(x)$ are two functions with a positive lower bound defined on $G$, $\beta \geq 0, \epsilon>0$. If $h$ and $f$ satisfy certain assumptions, we prove that there exists some positive constant $\epsilon_{1}>0$ such that for all $\epsilon \in (0, \epsilon_{1})$, the above equation has two distinct nontrivial positive solutions.
  • Bipartite Turán Problem on Complete Bipartite Graphs
    Lan-xin WANG, Xia ZHANG
    Acta Mathematicae Applicatae Sinica(English Series). 2026, 42(4): 1280-1290. https://doi.org/10.1007/s10255-026-0114-1
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    The bipartite Turán number of a bipartite graph $H$, denoted by $\mathrm{ex}(m,n;H)$, is the maximum number of edges in subgraphs of $K_{m,n}$ containing no copies of $H$. In this paper, we determine the bipartite Turán number of the complete bipartite graphs $\mathrm{ex}(m, n ; K_{s,t}) = mn-(\lfloor(n-t) / s\rfloor(m-s)+m+n-s-t+1)$ when $n \geq s + t$ and $t \geq s$, if one of the following is satisfied: $n=s+t;$ $m \leq s+ (t-1)/ (\lfloor (n-t) /s\rfloor+1);$ $s|(n-t)$ and $m\leq sn/(n-t),$ being $m \geq 2s$ if $m=sn/(n-t).$
  • List Conflict-free Coloring of Planar Graphs
    Ya-li WU, Xin ZHANG
    Acta Mathematicae Applicatae Sinica(English Series). 2026, 42(4): 1291-1300. https://doi.org/10.1007/s10255-025-0083-9
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    conflict-free coloring of a graph $G$ ensures that each vertex has at least one color appearing uniquely in its open neighborhood. In contrast, a list coloring provides each vertex with a list of possible colors and mandates that the vertex be colored with a color from this list. By merging these two concepts, a list conflict-free coloring is achieved when each vertex is colored with a color from its list and also has at least one color appearing uniquely in its open neighborhood. In this paper, we prove that every planar graph admits a list conflict-free 12-coloring. This finding enhances a previous result by Cheilaris, Smorodinsky, and Sulovský, which established that every planar graph on $n$ vertices admits a list conflict-free $(4\ln n + 1)$-coloring.
  • The Central Limit Theorem for Stochastic Volterra Equations with Singular Kernels
    Huijie QIAO
    Acta Mathematicae Applicatae Sinica(English Series). 2026, 42(4): 1301-1311. https://doi.org/10.1007/s10255-026-0006-4
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    This work concerns stochastic Volterra equations with singular kernels. Under the suitable conditions, we prove the central limit theorem for them. Moreover, we apply our result to stochastic Volterra equations with the kernels of fractional Brownian motions with the Hurst parameter $H\in(0, 1)$.
  • Energy Detection for Cognitive Radio with Distributional Uncertainty and Signal Variety under Nonlinear Expectation Theory
    Jia-liang FU, Wen-xuan LANG
    Acta Mathematicae Applicatae Sinica(English Series). 2026, 42(4): 1312-1325. https://doi.org/10.1007/s10255-026-0104-3
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    Classical energy detection (ED) methods for cognitive radio (CR) have addressed noise uncertainty as deviations in noise power and signal uncertainty as variability in signal characteristics, which use probabilistic methods and assume fixed probability distributions for both. In practical scenarios, due to the uncertainty in probability models and the significant variation of primary signals encountered by receivers across different radio technologies, wireless environments exhibit not only distributional uncertainty but also substantial signal variety. In this paper, we develop a generalized formulation of energy detection based on nonlinear expectation theory, where both the signal and noise distributions are uncertain. We utilize the $G$-normal distribution to characterize channel noise. Moreover, to capture practical signal variety, the absolute values of transmitted signal random variables are assumed to lie within a bounded range $[\underline{\sigma}_X,\overline{\sigma}_X]$. The worst-case detection performance is then characterized by a double supremum over all admissible distributions and all possible signal realizations. We derive estimates for the minimum and maximum detection error probabilities, and demonstrate the validity of the results through numerical simulations. The proposed model generalizes the classical theoretical analysis of energy detection and offers a potential theoretical foundation for robust detection and information-theoretic analysis under distributional uncertainty.
  • Minimum Aberration for Mixed-level Baseline Fractional Factorial Designs
    Zhao-hui YAN, Sheng-li ZHAO
    Acta Mathematicae Applicatae Sinica(English Series). 2026, 42(4): 1326-1342. https://doi.org/10.1007/s10255-025-0035-4
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    The minimum aberration (MA) criterion plays a crucial role in the study of comparing and selecting fractional factorial designs. In this paper, the concept of MA is naturally generalized to mixed-level baseline designs. Based on the relationship between the model matrix and design matrix of mixed-level baseline designs, the formulation of the MA criterion for baseline mixed-level designs and the efficient complete search algorithm are explored, which covers the existing results for $s$-level cases. A catalogue of MA baseline designs with run sizes of 8 to 27 is provided.
  • Large Time Behaviour of Weak Solutions to the Surface Growth Model
    Jia-qi YANG, Wen-xuan ZHU
    Acta Mathematicae Applicatae Sinica(English Series). 2026, 42(4): 1343-1352. https://doi.org/10.1007/s10255-026-0001-9
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    The one-dimensional scalar surface growth model, arising from the physical process of molecular epitaxy, shares many striking similarities with the three-dimensional incompressible Navier–Stokes equations. While significant results exist regarding the existence and regularity of solutions for this model, the large-time behavior of solutions remains unexplored, to the best of our knowledge. This paper aims to establish the first decay result for weak solutions. We prove that there exists a weak solution $u$ satisfying $$\|u\|_2 \lesssim(1+t)^{-\frac{1}{8}}$$. Furthermore, we demonstrate that this decay rate is sharp by constructing initial data for which the corresponding weak solution $u$ satisfies $$\|u\|_2 \gtrsim(1+t)^{-\frac{1}{8}}$$.
  • Structure and Coloring of (P3 ∪ P2)-free Graphs: Sparse Triangles
    Bao-gang XU, Xiao-wen ZHANG
    Acta Mathematicae Applicatae Sinica(English Series). 2026, 42(4): 1353-1364. https://doi.org/10.1007/s10255-025-0010-0
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    Let $G$ be a graph. The distance between two vertices $u, v\in V(G)$ is the length of the shortest path between them, denoted by $d_G(u,v)$. For two subgraphs $H$ and $F$ of $G$, we define $d_G(H,F)=min\{d_G(u,v): u\in V(H)\ \text{and}\ v\in V(F)\}$ as the distance between them. In this paper, we prove that if $G$ is ($P_3\cup P_2$)-free and the distance of any two triangles of $G$ is at least $1$, then $\chi(G)\le 4$ (this generalizes some results of Wang and Zhang (The $\chi$-Boundedness of $(P_3\cup P_2)$-Free Graphs. J. of Math., 8 pp (2022)), and we draw all such $G's$ when $\omega(G)=3$ and $\chi(G)=4$.
  • Strichartz Type Estimates of the Airy Equation
    Jie CHEN, Fan GU, Bo-ling GUO
    Acta Mathematicae Applicatae Sinica(English Series). 2026, 42(4): 1365-1371. https://doi.org/10.1007/s10255-026-0094-1
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    In this article, we show the necessary and sufficient conditions for the inequality $\|u\|_{L_t^qL_x^r}\lesssim \|u\|_{X^{s,b}}$, where $$\|u\|_{X^{s,b}}:=\|\hat{u}(\tau,\xi)\langle \xi\rangle^s\langle \tau-\xi^3\rangle^b \|_{L_{\tau,\xi}^2}. $$Here, we provide a complete classification of the indices relationships for which this inequality holds true. Such estimates will be very useful in solving the well-posedness for low regularity well-posedness of the Korteweg-de Vries equations and stochastic Korteweg-de Vries equations.
  • Trees with Independence Polynomials Having Only Real Zeros
    Lily Li LIU, Hong-yue TANG, Jing-rui ZHAO
    Acta Mathematicae Applicatae Sinica(English Series). 2026, 42(4): 1372-1400. https://doi.org/10.1007/s10255-025-0082-x
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    In 1987, Alavi, Malde, Schwenk and Erdös conjectured that the independence polynomial of any tree or forest is unimodal. This conjecture is still open. Recently, Zhu et al. confirmed this conjecture for certain classes of trees. Motivated by them, in this paper, we first construct infinite families of trees and their composite graphs, and then obtain that their independence polynomials have only real zeros. In consequence, we also confirm the conjecture of Alavi et al. for more special cases. In fact, several results in this paper generalize those of Zhu et al.
  • List Injective (△ + 4)-coloring of Planar Graphs
    Yue-hua BU, Hong-rui ZHENG, Hong-guo ZHU
    Acta Mathematicae Applicatae Sinica(English Series). 2026, 42(4): 1401-1408. https://doi.org/10.1007/s10255-025-0072-z
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    For a planar graph $G$ and two distinct vertices $u,v\in V(G)$ which share a common neighbor, a coloring is called injective if $u$ and $v$ receive different colors. The injective choosability number of $G$ is the smallest integer $k$ such that $G$ is injective $k$-choosable, denoted by $\chi _i^l(G)$. In this paper, we prove that $\chi _i^l(G) \le \Delta + 4$ if $\Delta \ge 15$ for $G$ without 3-cycles and disjoint 4-cycles, which improves the results of Li et al.(2022) who gave that $\chi _i^l(G) \le \Delta + 4$ if $\Delta \ge 22$ and $\chi _i^l(G) \le \Delta + 5$ if $\Delta \ge 15$ for $G$ without 3-cycles and disjoint 4-cycles.
  • Unbounded Solutions of Third-order Infinite Interval Problems Relevant to the Laminar Mixing Layer
    Ming-he PEI, Li-bo WANG, Xue-zhe LV
    Acta Mathematicae Applicatae Sinica(English Series). 2026, 42(4): 1409-1430. https://doi.org/10.1007/s10255-026-0135-9
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    In this paper, we consider the existence, uniqueness, and qualitative properties of solutions of nonlinear third-order two-point boundary value problems on the half-line by using the shooting method together with the Bolzano's theorem and the maximum principle. Meanwhile, the nonlinear third-order three-point boundary value problems on the whole real line are studied by employing the matching method. As applications, we present the existence, uniqueness, and qualitative properties of solutions of the Blasius equations $u'''+uu''=0$ with one of the following boundary conditions \begin{align*} &u'(-\infty)=C, u(0)=0, u'(+\infty)=1, \qquad \ \ \hbox{with} \ \ 0\leq C<1,\\ &u'(-\infty)=C, u'''(0)=0, u'(+\infty)=1, \qquad \hbox{with} \ \ 0\leq C<1, \end{align*} which arise from the laminar mixing layer between two parallel flows with different velocities.
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