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26 June 2026, Volume 46 Issue 3 Previous Issue    Next Issue

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A Rigidity Result for Four-Dimensional Riemannian Manifolds with Vanishing Generalized Bach Tensor Shanlin Guan Acta mathematica scientia,Series A. 2026, 46 (3):  877-883.  Abstract ( 3 )   RICH HTML   PDF (462KB) ( 0 )   Save A Riemannian manifold $ (M^n, g) $ is called $ B^t $-flat if its generalized Bach tensor $ B^t_{ij} \equiv 0 $ for some parameter $ t $. In this paper, we show that a four-dimensional compact $ B^t $-flat Riemannian manifold with $t < 1, t \neq 0$ and satisfying a pointwise inequality must be Einstein. In particular, under the same assumption and $t \ge -\frac{1}{3}$, we conclude that it must be isometric to either a quotient of the round $\mathbb{S}^4$ or a $\mathbb{C P}^2$ with the Fubini-Study metric. This extends the result of Huang-Ma-Li [Huang G, Ma B, Li X. J Geom Phys, 2021, 170: Art 104380]. References | Related Articles | Metrics

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Composition Operators from Bloch Type Spaces into Some $\alpha$-Möbius Invariant Spaces Weiyi Liu Acta mathematica scientia,Series A. 2026, 46 (3):  884-906.  Abstract ( 2 )   RICH HTML   PDF (633KB) ( 0 )   Save This paper gives characterizations of the boundedness, compactness and weak compactness of composition operators $C_{\varphi}$ from Bloch-type spaces to weighted Dirichlet-type spaces $D_{\mu }^{p}$ ($1\le p<\infty$) and their two classes of $\alpha$-Möbius invariant subspaces ($0< \alpha< \infty$). References | Related Articles | Metrics

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Sufficient Conditions for Reducibility of Fermi Surfaces in Cartesian Product Quantum Graphs Yuting Han, Jia Zhao, Yalin Zhang Acta mathematica scientia,Series A. 2026, 46 (3):  907-918.  Abstract ( 0 )   RICH HTML   Save In order to investigate the existence of embedded eigenvalues and the properties of related characteristic functions of periodic quantum graphs under the condition of Fermi surface reducibility, this paper constructs two types of periodic Cartesian product quantum graphs. It is proved that when the foundation domain of a single-layer periodic quantum graph has only two vertices and certain conditions are met, the Fermi surfaces of both types of Cartesian product quantum graphs are reducible, and the selection conditions of the foundation domain are supplemented.} Figures and Tables | References | Related Articles | Metrics

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Fixed Point Theorems for Two Classes of $(p,\xi)$-Type Contraction Mappings in $b$-Metric Spaces Jihong Li, Zhanfei Zuo, Huaping Huang Acta mathematica scientia,Series A. 2026, 46 (3):  919-928.  Abstract ( 1 )   RICH HTML   PDF (540KB) ( 0 )   Save In this paper, the existence theorems of fixed points for two classes of $(p,\xi)$-type contractive mappings are proved in $b$-metric spaces. Through some concrete examples, it is verified that there exist cases where the classical Banach fixed point theorem cannot be applied to solve fixed point problems, but the existence of fixed points can be obtained by using the conclusions of this paper. The obtained results not only improve and generalize several existing fixed point theorems in metric spaces, but also provide new theoretical tools for solving fixed point problems, thereby broadening the application scope of fixed point research. Figures and Tables | References | Related Articles | Metrics

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The Jeribi Essential Spectrum of $2\times 2$ Upper Triangular Block Operator Matrices Huifang Shi, Deyu Wu Acta mathematica scientia,Series A. 2026, 46 (3):  929-938.  Abstract ( 2 )   RICH HTML   PDF (527KB) ( 0 )   Save Let $X$ be a complex infinite dimensional Banach space. In this paper, we mainly study the $2\times 2$ upper triangular block operator matrix $T=\left[\begin{array}{cc}A & B \\0 & D\end{array}\right]$ on $X\times X$. By using the Jeribi essential spectrum of entries $A$ and $D$ to characterize the Jeribi essential spectrum of operator matrix $T$. Some sufficient conditions for the relationship $\hat{\sigma_{J}}(T)=\sigma_{J}(A)\cup\sigma_{J}(D)$ hold are given. Also, the relationship between the Jeribi essential spectrum of operator matrix $T$ and other spectrum of $A,D$ are given. References | Related Articles | Metrics

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The Asymptotic Behavior of a Class of Randomly Coupled Lorenz Maps Bowen Zheng, Liang Zhang Acta mathematica scientia,Series A. 2026, 46 (3):  939-948.  Abstract ( 2 )   RICH HTML   PDF (870KB) ( 0 )   Save This paper investigates the mixing property of a class of piecewise linear Lorenz maps and the existence of absolutely continuous invariant measures for their stochastically coupled counterparts. Applying renormalization theory, it is rigorously proved that two deterministic maps within this Lorenz framework exhibit mixing. Based on this foundation, numerical experiments are designed, revealing a peculiar phenomenon of synchronized chaos: while both deterministic maps have positive Lyapunov exponents, the corresponding stochastic map possesses a negative Lyapunov exponent while still maintaining an absolutely continuous invariant measure. Further research demonstrates that this stochastic map not only possesses global ergodicity but can also induce the emergence of synchronization phenomena. Figures and Tables | References | Related Articles | Metrics

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Stochastic Attractors and Invariant Measures for Fractional Nonlocal Reaction-Diffusion Equations Yiyao Yang, Jinping Jiang, Nannan Ma Acta mathematica scientia,Series A. 2026, 46 (3):  949-962.  Abstract ( 1 )   RICH HTML   PDF (660KB) ( 0 )   Save This paper investigates the dynamical behavior of a class of fractional nonlocal reaction-diffusion equation driven by nonlinear colored noise. Firstly, the existence of solutions to the equations with nonlinear colored noise is given by the Galerkin method. Secondly, the existence of the pullback stochastic attractor for this equation is proved in an appropriate Hilbert space. Finally, the generalized Banach limit is used to prove the existence of invariant measures for this equation. References | Related Articles | Metrics

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The Limit of Vanishing Shear Viscosity for Compressible Nematic Liquid Crystal Flows with Cylindrical Symmetry Jinliang Tang, Xia Ye Acta mathematica scientia,Series A. 2026, 46 (3):  963-995.  Abstract ( 1 )   RICH HTML   PDF (694KB) ( 0 )   Save This paper is concerned with compressible nematic liquid crystal flows with cylindrical symmetry. We prove the rate of convergence as the limit of vanishing shear viscosity, and we also establish the properties of the boundary layer function. Our results do not require the smallness of the initial data. References | Related Articles | Metrics

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Global Well-Posedness of the Three-Dimensional Inhomogeneous Incompressible Nematic Liquid Crystal System with a Class of Large Velocity Dongxiang Chen, Qian He, Xiaoli Chen Acta mathematica scientia,Series A. 2026, 46 (3):  996-1014.  Abstract ( 5 )   RICH HTML   PDF (622KB) ( 0 )   Save {In this paper, we investigate the the global well-posedness problem of the three-dimensional inhomogeneous incompressible nematic liquid crystal system with a class of large velocity. More precisely, assuming that the initial data $a_0\in\dot B_{p,1}^{\frac{3}{p}}, u_0\in\dot B_{p,1}^{\frac{3}{p}-1}, d_0\in\dot B_{p,1}^{\frac{3}{p}}$ satisfies $C_{0}\left[\left\|u_{0}^{h}\right\|_{\dot{B}_{p, 1}^{\frac{3}{p}-1}}+\left(\left\|u_{0}^{3}\right\|_{\dot{B}_{p, 1}^{\frac{3}{p}-1}}+1\right)\left(\left\|a_{0}\right\|_{\dot{B}_{p, 1}^{\frac{3}{p}}}+\left\|d_{0}\right\|_{\dot{B}_{p, 1}^{\frac{3}{p}}}\right)\right] \exp \left\{C_{0}\left\|u_{0}^{3}\right\|_{\dot{B}_{p, 1}^{\frac{3}{p}-1}}^{2}\right\} \leq 1,$ then the nematic liquid crystal equation admits a unique global solution, where $C_0>0,~ 2\le p\le4.$ References | Related Articles | Metrics

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Existence of Global Attractors of the Benjamin-Bona-Mahony Equation in Three-Dimensional Channel Ling Wan, Yuying Xu, Tengfei Zhang Acta mathematica scientia,Series A. 2026, 46 (3):  1015-1024.  Abstract ( 3 )   RICH HTML   PDF (578KB) ( 1 )   Save This article establishes the existence of global attractors for the (generalized) Benjamin-Bona-Mahony equation in a three-dimensional channel, when the nonlinear term satisfies the growth condition of order $m=2$, which extends the result obtained by Wang-Fussner-Bi [Wang B, Fussner D W, Bi C. J Phys A, 2007, 40(34): 10491-10504]. In particular, in order to prove the asymptotic compactness of the solution semigroup, we prove firstly the weak continuity property, and secondly the convergence in norm by taking advantage of the energy equation method. References | Related Articles | Metrics

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The Cauchy Problem for an Improved Aw-Rascle-Zhang Model Tingting Chen, Weifeng Jiang, Tong Li, Yibo Lai Acta mathematica scientia,Series A. 2026, 46 (3):  1025-1027.  Abstract ( 9 )   RICH HTML   PDF (622KB) ( 3 )   Save This paper studies the Cauchy problem for an improved Aw-Rascle-Zhang traffic flow model exhibiting non-genuine nonlinearity. The Riemann solution structure for this model contains not only shocks, rarefaction waves, and contact discontinuities, but also composite waves. A method based on a modified Glimm scheme is developed within the framework of the space of functions of bounded variation. The key aspect of this method lies in constructing a wave interaction functional using the variation of Riemann invariants, thereby controlling the total variation of the solution during its time evolution. Therefore we establish the existence of a global weak solution for the Cauchy problem with large initial data. Figures and Tables | References | Related Articles | Metrics

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Concentrated Normalized Solutions of Saturable Schrödinger Equations with the Potential Wei Long, Shuyao Lu, Dongmei Zhang Acta mathematica scientia,Series A. 2026, 46 (3):  1038-1053.  Abstract ( 23 )   RICH HTML   PDF (592KB) ( 3 )   Save By penalized methods, we investigate the existence and concentration of normalized solutions to the following saturable Schrödinger equation $-\Delta u + V(\varepsilon x)u=\lambda u -\Gamma \frac{u^2}{1 + u^2}u, \quad x\in\mathbb{R}^{2},\nonumber$ with the potential satisfying a local type assumption, where $\varepsilon$ denotes the Planck constant, $\Gamma<0$ is a coupling constant. References | Related Articles | Metrics

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Global Weak Solutions in a Three-Dimensional Coral Fertilization Model of Chemotaxis-Navier-Stokes Type with Flux Limitation Boyang Cui, Ji Liu Acta mathematica scientia,Series A. 2026, 46 (3):  1054-1082.  Abstract ( 0 )   RICH HTML   PDF (735KB) ( 0 )   Save This paper is devoted to investigating the following coral fertilization model of chemotaxis-Navier-Stokes type (*)$\left\{\begin{array}{ll}n_{t}+u \cdot \nabla n=\Delta n-\nabla \cdot\left(n f\left(|\nabla c|^{2}\right) \nabla c\right)-m n, & x \in \Omega, \\c_{t}+u \cdot \nabla c=\Delta c-c+m, & x \in \Omega, \\m_{t}+u \cdot \nabla m=\Delta m-m n, & x \in \Omega, \\u_{t}+(u \cdot \nabla) u=\Delta u-\nabla P+(n+m) \nabla \Phi, \nabla \cdot u=0, & x \in \Omega,\end{array}\right.$ where $\Omega \subset \mathbb{R}^3 $ is a bounded domain with smooth boundary, and $f\in C^{2}([0,+\infty))$ fulfills $|f(\xi)| \leq K_f \cdot (\xi + 1)^{-\frac{\theta}{2}}, \xi \geq 0,$ with constants $K_f > 0$ and $\theta \in \mathbb{R}$. It is proved that if $\theta > 0,$ then for arbitrarily appropriately regular initial data an initial-boundary value problem associated with ($*$) subject to suitably homogeneous boundary conditions admits at least one global weak solution. References | Related Articles | Metrics

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The Eigenvalue Problem for a Class of Quasilinear Schrödinger Equations with a Parameter Yinchen Fan, Liangming Shen Acta mathematica scientia,Series A. 2026, 46 (3):  1083-1091.  Abstract ( 2 )   RICH HTML   PDF (547KB) ( 0 )   Save We consider a class of quasilinear Schrödinger equations of the form $-\Delta u-\frac{\kappa u}{2}(1+u^2)^{-\frac{1}{2}}\Delta(1+u^2)^{\frac{1}{2}}=\lambda |u|^{p-2}u,\ x\in\Omega,$ where $u\in H_{0}^{1}(\Omega),$\kappa\in (-2,0)\cup (0,+\infty),\ 2\leq p<2^*,\ N\geq 3$ and $\Omega$ is a bounded domain. By using variational approaches, we establish the existence of a solution $(\lambda, u).$ Particularly, we give the accurate $L^{\infty}$ estimate. For instance, if $\kappa\in (-2,0)$ and $|u|_{p}=1,$ we construct the following $L^{\infty}$ estimate of the solution $ |u|_{\infty}\leq 2^{\frac{3}{2}+\frac{3}{2a}}(\kappa+2)^{-\frac{1}{2}-\frac{1}{2a}}(\lambda_{1}C_{N})^{\frac{1}{2a}}|\phi_{1}|_{p}^{-\frac{1}{a}}|\Omega|^{\frac{1}{p'}}, $ where $a=\frac{1}{p}-\frac{1}{2^*},p'=\frac{p}{p-1},$C_{N}$ is the best Sobolev constant and $\lambda_{1}$ and $\phi_{1}$ are the first eigenvalue and the first eigenfunction of the operator $-\Delta$ respectively. References | Related Articles | Metrics

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Existence of Solutions for Schrödinger Systems with Logarithmic Terms Jing Zhang, Mingwei Xiu Acta mathematica scientia,Series A. 2026, 46 (3):  1092-1104.  Abstract ( 1 )   RICH HTML   PDF (555KB) ( 0 )   Save In this paper, we study the existence of solutions for a class of logarithmic Schrödinger systems with critical perturbations. We obtain the existence of ground state solutions by constructing auxiliary functional and applying variational method, critical point theory and concentrated compactness principle. References | Related Articles | Metrics

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Concentrated Solutions for Critical Elliptic Equation with Sublinear Perturbation Lei Liu, Shuying Tian Acta mathematica scientia,Series A. 2026, 46 (3):  1105-1113.  Abstract ( 1 )   RICH HTML   PDF (551KB) ( 0 )   Save In this paper, we revisit the following elliptic equations with critical exponent $\begin{cases}-\Delta u=Q(x) u^{2^*-1}+\varepsilon u^s, u>0, & \text { in } \Omega, \\ u=0, & \text { on } \partial \Omega,\end{cases}$ where $N\geq 4 $, $ s\in (0,2^*-1) $ with $ 2^*=\frac{2N}{N-2} $, $ \varepsilon>0 $, $ \Omega $ is a smooth bounded domain in $ \mathbb{R}^N $. Under some conditions on $ Q(x) $, Cao and Zhong [Cao D, Zhong X. Nonlin Anal TMA, 1997, 29: 461-483] gave the existence of single-peak solutions for small $\varepsilon$ when $N\geq 4$, $ s\in (1,2^*-1) $. Recently, Duan and Tian [Duan L, Tian S. Discrete Contin Dyn Syst, 2022, 42(8): 4061-4094] proved non-existence of single-peak solutions for small $ \varepsilon $ when $ N\geq 5$, $ s=1 $ and got the existence of single-peak solutions for small $ \varepsilon $ when $ N=4$, $ s=1 $. Here we establish non-existence of single-peak solutions for the case $ N\geq 5 $ and $ s<1 $ (sublinear perturbation) by local Pohozaev identities. Our results show that the concentration of solutions to above problem is delicate and sensitive for the dimension $ N$. References | Related Articles | Metrics

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Stability of Radially Symmetric Transonic Shocks in Self-Similar Euler Flows Ziang Wang, Ling Gao, Xuemei Deng Acta mathematica scientia,Series A. 2026, 46 (3):  1114-1131.  Abstract ( 2 )   RICH HTML   PDF (771KB) ( 0 )   Save In this work, we investigate the stability of transonic shock phenomena with self-similar structure for the compressible, isentropic Euler system in a finite expanding nozzle or an annular domain. Assuming radial symmetry and prescribing small perturbations of the background solution at the inlet as the supersonic initial condition, we prove that a unique transonic shock solution exists for exit pseudo-velocities within a suitable range. Moreover, the shock location is a monotonically increasing function of the pseudo-velocity at the exit. Figures and Tables | References | Related Articles | Metrics

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Growth Decay Rates of Cross Diffusion Fluid Under Nonlinear Conditions Yuanfei Li Acta mathematica scientia,Series A. 2026, 46 (3):  1132-1141.  Abstract ( 1 )   RICH HTML   PDF (506KB) ( 0 )   Save Considering the cross diffusion fluid under non-homogeneous boundary conditions, the spatial properties of the solution of the cross diffusion fluid on a semi-infinite cylinder are studied, by using energy analysis method. When the cross-section of the cylinder is related to the axial variable, the growth decay rates are obtained. Finally, we extend the main results to two specific types of cylinders. References | Related Articles | Metrics

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On the Norm Growth of Strong Solutions for Nonlinear KGS System Shuang Cui, Qihong Shi Acta mathematica scientia,Series A. 2026, 46 (3):  1142-1159.  Abstract ( 1 )   RICH HTML   PDF (562KB) ( 1 )   Save This paper is concerned with the initial-boundary value problem for the nonlinear Klein-Gordon-Schrödinger (KGS) system in $\mathbb{R}^N(N\leq3)$. By introducing a regularized system and utilizing the boundedness and convergence of the solutions sequence, we prove the existence and uniqueness of global strong solutions to the nonlinear KGS system in the space $H^2 \times H^2 \times H^1$, and obtain the norm estimates for the solutions in the space $H^2 \times H^2 \times H^1$. The proof is independent of the Brezis-Gallouet technique and the compactness argument. References | Related Articles | Metrics

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Asymptotic Behavior of Solutions for Cauchy Problem of a Non-Newtonian Filtration Equation with Decaying Volumetric Moisture Content Wentao Huo, Zhongbo Fang Acta mathematica scientia,Series A. 2026, 46 (3):  1160-1182.  Abstract ( 0 )   RICH HTML   PDF (659KB) ( 0 )   Save This paper is concerned with the asymptotic behavior of solutions for the Cauchy problem of a non-Newtonian filtration equation with decaying volumetric moisture content. When the volumetric moisture content is given different decaying behaviors at infinity, we establish some new results of global existence and finite time blow-up by virtue of comparison principle and constructing appropriate Barenblatt-type super- and sub-solutions. References | Related Articles | Metrics

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Asymptotics of Sample Median Range and Sample Range from Gaussian Distribution Guang Tang, Yingyin Lu, Tingting Yu Acta mathematica scientia,Series A. 2026, 46 (3):  1183-1193.  Abstract ( 3 )   RICH HTML   Save In this paper, we investigate the limiting distributions of the normalized sample median range and sample range from Gaussian distributions. Additionally, the distributional expansions are established with the same normalizing constants. A byproduct is to deduce the convergence rates of the distributions of the normalized sample median range and sample range to their limits, which shows they have the same convergence rate. Furthermore, numerical analysis is provided to illustrate the theoretical findings. Figures and Tables | References | Related Articles | Metrics

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Hopf-Hopf Bifurcation Analysis in a Nonlocal Leslie-Gower Model Yuying Liu, Daifeng Duan, Junjie Wei Acta mathematica scientia,Series A. 2026, 46 (3):  1194-1217.  Abstract ( 2 )   RICH HTML   PDF (2719KB) ( 0 )   Save In this paper, a nonlocal Leslie-Gower predator-prey model with delay and diffusion is investigated. Firstly, the local stability of the steady states in the model is studied with aid of the zeros in the characteristic equations. Besides, the existence of Hopf bifurcation is explored by taking $\tau$ as the varying parameter. Hopf-Hopf bifurcation singularity in the model was analyzed by choosing $tau$ and the capture rate $m$ as dual variable parameters. Furthermore, the normal form near the Hopf-Hopf singularity of the model is derived by using the central manifold theory. Finally, numerical simulations are carried out to illustrate the obtained theoretical results.The study reveals that the joint effect of two varying parameters can lead to stable spatially non-homogeneous periodic solutions in the system, which indicates that the dynamical behavior near the Hopf-Hopf singularity plays an important role in the formation and evolution of spatiotemporal patterns in the Leslie-Gower system. Figures and Tables | References | Related Articles | Metrics

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A Stabilized Finite Element $\theta$ Scheme for Non-Stationary Convection-Dominated Convection Diffusion Problems Lanxin Sun, Baowei Lai, Zhifeng Weng Acta mathematica scientia,Series A. 2026, 46 (3):  1218-1231.  Abstract ( 2 )   RICH HTML   Save This paper proposes a fully discrete $\theta$ scheme with the variational multiscale finite element method for non-stationary convection-dominated convection diffusion equations. We use an equivalent method based on the residuals of two local Gauss integrations to replace the stabilization term of the variational multiscale method. An optimal error estimate in the space-time $L^2$ norm is also derived. Moreover, numerical results demonstrate that equivalent numerical accuracy can be achieved by the Crank-Nicolson scheme with lower computational cost compared to the Backward Euler scheme. Figures and Tables | References | Related Articles | Metrics

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Solving Singularly Perturbed Delay Differential Equations Based on the Reproducing Kernel Method Yuqing Shan, Wenxin Yu, Cuiping Ran, Jing Niu Acta mathematica scientia,Series A. 2026, 46 (3):  1232-1245.  Abstract ( 1 )   RICH HTML   PDF (1228KB) ( 0 )   Save In this paper, a numerical method is proposed for solving singularly perturbed turning point problems with boundary layers. This method is based on the asymptotic expansion technique and the reproducing kernel method, and it decomposes the original problem into a boundary layer problem and a regular region problem. The regular region problem is solved by the asymptotic expansion method, while the boundary layer problem is solved by the variable stretching method and the reproducing kernel method based on the collocation method. For singularly perturbed delay differential-difference equations with a single boundary layer, we construct basis functions based on the reproducing kernel function in the $W_2^4$ space. Inside each sub - division cell, the Gaussian-Legendre nodes with 4 points are selected as collocation points. Compared with the original fitted mesh B-spline collocation method, the accuracy and convergence order obtained by our method are higher. Four numerical examples are provided to illustrate the effectiveness of this method. The results of the numerical examples show that this method can provide very accurate approximate solutions and achieve the optimal convergence order. Figures and Tables | References | Related Articles | Metrics

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A Modulus-Based Matrix Splitting Iterative Method for a Class of Vertical Linear Complementarity Problems Shuhong Wen, Yifen Ke, Lifen Xiao, Xiwen Chen Acta mathematica scientia,Series A. 2026, 46 (3):  1246-1254.  Abstract ( 7 )   RICH HTML   PDF (577KB) ( 3 )   Save By means of the modulus technique, a class of vertical linear complementarity problems is transformed into an equivalent nonlinear equation system. On this basis, a new modulus-based matrix splitting iterative method is established, and the convergence of the proposed algorithm is analyzed. Finally, one numerical example is provided for numerical experiment and the numerical result is compared with other methods. Figures and Tables | References | Related Articles | Metrics

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Optimal Investment and Risk Management Strategies Considering Catastrophe Bond Issuance Under Ambiguity Aversion Bing Liu, Tong Qian, Peng Li Acta mathematica scientia,Series A. 2026, 46 (3):  1255-1269.  Abstract ( 1 )   RICH HTML   PDF (1364KB) ( 1 )   Save The frequency of natural disasters, exacerbated by climate and environmental changes, poses severe challenges to insurance companies' risk management. Therefore, it is crucial to explore optimal investment and reinsurance strategies for insurance companies when facing catastrophic risks such as natural disasters. This paper innovatively integrates two factors, catastrophe bond issuance and model uncertainty, into traditional research on optimal investment-reinsurance strategies. By employing stochastic control theory and dynamic programming methods, the paper derives analytical solutions for optimal investment-reinsurance-catastrophe bond issuance strategies. Through numerical simulation analysis, it reveals the dynamic characteristics of optimal investment-reinsurance strategies after insurance companies issue catastrophe bonds. Simultaneously, it discusses the sensitivity and economic impact of key parameters such as market correlation and ambiguity aversion coefficients on strategy selection. The research results indicate that catastrophe bond issuance/purchase can effectively substitute for reinsurance, with a decrease in reinsurance purchases as the issuance/purchase volume increases. Enhanced correlation between catastrophe bonds and the insurance market prompts insurance companies to reduce venture investments and increase catastrophe bond holdings. In uncertain environments, insurance companies rely more on catastrophe bonds for risk management and tend to invest in markets with high certainty. Additionally, as capital increases, investment strategies become more conservative. Figures and Tables | References | Related Articles | Metrics

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On Accumulated Length of Insolvency Periods Under Reorganization Bankruptcy Ruixing Ming, Yuqi Liu, Chenqing Lin, Wenyuan Wang Acta mathematica scientia,Series A. 2026, 46 (3):  1270-1291.  Abstract ( 1 )   RICH HTML   PDF (808KB) ( 1 )   Save abstract:Reorganization bankruptcy refers to a corporate rehabilitation mechanism permitting debtors to restructure operations while maintaining business continuity. This study develops a triple-threshold regulatory framework to simulate financial distress pathways in institutions mirroring real-world reorganization bankruptcy proceedings. Departing from traditional solvency assessments using a single zero-boundary criterion (where bankruptcy occurs upon falling below a single zero-value threshold), we propose a tripartite classification of financial health: solvency adequacy, insolvent or capital deficiency, and compulsory liquidation. The model's theoretical novelty lies in capturing strategic operational adjustments during capital deficiency phases to achieve regulatory compliance within "corrective grace period", with failure triggering orderly liquidation protocols. Through advanced analytical methodology involving joint Laplace transforms of liquidation timing and accumulated length of the capital deficiency durations, this research elucidates critical interdependencies between organizational capital architecture and the operational viability of reorganization-bankruptcy-style restructuring mechanisms observed in practice. finance; reorganization bankruptcy; accumulated length of insolvency periods. Figures and Tables | References | Related Articles | Metrics

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Ground State Normalized Solutions to the Kirchhoff Equation with Potential Term: Mass Sub-Critical Case Qun Wang, Aixia Qian Acta mathematica scientia,Series A. 2026, 46 (3):  1292-1303.  Abstract ( 7 )   RICH HTML   PDF (613KB) ( 3 )   Save We study the existence of normalized solution to the following nonlinear mass sub-critical Kirchhoff equation $-\left(a+b\int_{\mathbb{R}^{N}}|\nabla u|^{2}\right)\triangle u+V(x)u+\lambda u=|u|^{p-2}u \ \ {in} \ {\mathbb{R}^{N}},1\leq N\leq3$ having the normalization constrain $\int_{\mathbb{R}^{N}}|u|^{2}{\rm d}x=c$, for any $a,b,c>0$ prescribed, $2<p<2+\frac{8}{N}$. By a proof of the strict sub-additivity inequality utilizing the iterative framework developed by Zhong $\&$ Zou [Zhong X, Zou W. Diff Inte Equa, 2023, 36(1/2): 133-160], we get the existence of global constraint minimizers when the potential $V(x)$ satisfies some appropriate assumptions and prove the existence of ground state normalized solution. References | Related Articles | Metrics