数学季刊

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1. 具有指数临界增长的薛定谔方程的高能正规化解

张小藏, 许丽萍

数学季刊 2025, 40 (1): 1-19. DOI: 10.13371/j.cnki.chin.q.j.m.2025.01.001

摘要（150）

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In this paper, we study high energy normalized solutions for the following Schrödinger equation ……

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2. 秩为1的偶格顶点算子代数上的半共形向量簇

楚彦军, 高艺博

数学季刊 2025, 40 (1): 36-48. DOI: 10.13371/j.cnki.chin.q.j.m.2025.01.004

摘要（116）

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In this paper, we shall study structures of even lattice vertex operator algebras by using the geometry of the varieties of their semi-conformal vectors. We first give the varieties of semi-conformal vectors of a family of vertex operator algebras……

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3. 具有Riemann-Liouville分数阶积分的强阻尼波动方程的爆破现象

向常永, 段霁松, 龙群飞

数学季刊 2025, 40 (3): 304-312. DOI: 10.13371/j.cnki.chin.q.j.m.2025.03.006

摘要（115）

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We investigate the blow-up effect of solutions for a non-homogeneous wave equation
u_tt−∆u−∆u_t=I₀^α+ (|u|^p)+ω(x),
where p >1, 0≤α<1 and ω(x) with \int_{\mathbb{R}^{N}} ω(x)dx >0. By a way of combining the argument by contradiction with the test function techniques, we prove that not only any non-trivial solution blows up in finite time under 0< α <1, N ≥1 and p >1, but also any non-trivial solution blows up in finite time under α= 0, 2≤ N ≤4 and p being the Strauss exponent.

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4. w-(b,c)-核逆

方莉, 赵良

数学季刊 2025, 40 (1): 26-35. DOI: 10.13371/j.cnki.chin.q.j.m.2025.01.003

摘要（111）

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We introduce and study a new kind of generalized inverses named w-(b,c)-core inverses, which is a generalization of the (b,c)-core inverse. An example is given to show that w-(b,c)-core inverses need not be (b,c)-core inverses. In addition, the dual version of the w-(b,c)-core inverse is studied. Some results on (b,c)-core inverses and e-(b,c)-core
inverses are unified and generalized.

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5. 四维扭化BCV空间的次黎曼极限，带挠率的联络以及Gauss-Bonnet定理

李洪峰, 刘克峰, 王勇

数学季刊 2025, 40 (2): 111-134. DOI: 10.13371/j.cnki.chin.q.j.m.2025.02.001

摘要（104）

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In this paper, we compute sub-Riemannian limits of some important curvature variants associated with the connection with torsion for four dimensional twisted BCV spaces and derive a Gauss-Bonnet theorem for four dimensional twisted BCV spaces.

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6. 非线性抛物型积分-微分方程的高阶标量辅助变量方法

闫丽娜, 张根根, 黄琼敖

数学季刊 2025, 40 (3): 262-270. DOI: 10.13371/j.cnki.chin.q.j.m.2025.03.003

摘要（102）

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An efficient and accurate scalar auxiliary variable (SAV) scheme for numerically solving nonlinear parabolic integro-differential equation (PIDE) is developed in this paper. The original equation is first transformed into an equivalent system, and the k-order backward differentiation formula (BDFk) and central difference formula are used to discretize the temporal and spatial derivatives, respectively. Different from the traditional discrete method that adopts full implicit or full explicit for the nonlinear integral terms, the proposed scheme is based on the SAV idea and can be treated semi-implicitly, taking into account both accuracy and effectiveness. Numerical results are presented to
demonstrate the high-order convergence (up to fourth-order) of the developed schemes and it is computationally efficient in long-time computations.

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7. 具有Markov转换的双因素随机波动率跳扩散模型下幂期权定价

韩书书, 韦煜明

数学季刊 2025, 40 (1): 59-73. DOI: 10.13371/j.cnki.chin.q.j.m.2025.01.006

摘要（76）

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In this paper, we incorporate Markov regime-switching into a two-factor stochastic volatility jump-diffusion model to enhance the pricing of power options. Furthermore, we assume that the interest rates and the jump intensities of the assets are stochastic. Under the proposed framework, first, we derive the analytical pricing formula for power options by using Fourier transform technique, Esscher transform and characteristic function. Then we provide the efficient approximation to calculate the analytical pricing formula of power options by using the FFT approach and examine the accuracy of the approximation by Monte Carlo simulation. Finally, we provide some sensitivity analysis of the model parameters to power options. Numerical examples show this model is suitable for empirical work in practice.

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8. 多参数Mittag-Leffler函数的一些成果

潘玉梅, 李玉芬, 蔡董欣, 严兴杰

数学季刊 2025, 40 (1): 82-92. DOI: 10.13371/j.cnki.chin.q.j.m.2025.01.008

摘要（75）

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In this article, the multi-parameters Mittag-Leffler function is studied in detail. As a consequence, a series of novel results such as the integral representation, series representation and Mellin transform to the above function, are obtained. Especially, we associate the multi-parameters Mittag-Leffler function with two special functions which are the generalized Wright hypergeometric and the Fox’s-H functions. Meanwhile, some interesting integral operators and derivative operators of this function, are also discussed

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9. 关于多复变量 α-Bloch 函数

朱婷, 杨刘

数学季刊 2025, 40 (1): 93-102. DOI: 10.13371/j.cnki.chin.q.j.m.2025.01.009

摘要（75）

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In this paper, we establish characterizations of α-Bloch functions and little α-Bloch functions on the unit ball as well as the unit polydisk of C^m, which generalize and improve results of Aulaskari-Lappan, Minda, Aulaskari-Wulan, and Wu. Some examples are also given to complement our theory.

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10. 矩阵方程在线性时不变系统的应用

周艳平, 陈艳萍, 张娟

数学季刊 2025, 40 (3): 221-237. DOI: 10.13371/j.cnki.chin.q.j.m.2025.03.001

摘要（73）

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With the development of science and technology, the design and optimization of control systems are widely applied. This paper focuses on the application of matrix equations in linear time-invariant systems. Taking the inverted pendulum model as an example, the algebraic Riccati equation is used to solve the optimal control problem, and the system performance and stability are achieved by selecting the closed-loop pole and designing the gain matrix. Then, the numerical methods for solving the stochastic algebraic Riccati equations are applied to practical problems, with Newton’s iteration method as the outer iteration and the solution of the mixed-type Lyapunov equations as the inner iteration. Two methods for solving the Lyapunov equations are introduced, providing references for related research.

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11. 简单几何区域上庞加莱不等式中的最佳常数

陈红如, 马高超, 张蓓

数学季刊 2025, 40 (2): 148-157. DOI: 10.13371/j.cnki.chin.q.j.m.2025.02.003

摘要（71）

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In this paper, we explicitly establish Poincar´e inequality for 1≤p <∞ over simple geometric domains, such as segment, rectangle, triangle or tetrahedron. We obtain sharper bounds of the constant in Poincar´e inequality and, in particular, the explicit relation between the constant and the geometric characters of the domain.

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12. 具有变系数和记忆边界流的抛物型方程的爆破解

张安蕾, 刘丙辰

数学季刊 2025, 40 (1): 74-81. DOI: 10.13371/j.cnki.chin.q.j.m.2025.01.007

摘要（70）

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This paper deals with a semilinear parabolic problem involving variable coefficients and nonlinear memory boundary conditions. We give the blow-up criteria for all nonnegative nontrivial solutions, which rely on the behavior of the coefficients when time variable tends to positive infinity. Moreover, the global existence of solutions are discussed for non-positive exponents.

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13. 关于Sauer与Schweizer结果的注记

王广胜, 李菲, 徐焱

数学季刊 2025, 40 (1): 20-25. DOI: 10.13371/j.cnki.chin.q.j.m.2025.01.002

摘要（70）

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n this paper, we obtain some normality criteria for families of meromorphic functions concering shared values, which extends the related results of Schwick, and SauerSchweizer, and can be viewed as a complement of the related results due to Pang-Zalcman, Xu-Fang.

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14. 呈指数型增长的函数类中的Volterra奇异积分方程的解的存在性

张雯雯, 李平润

数学季刊 2025, 40 (2): 135-147. DOI: 10.13371/j.cnki.chin.q.j.m.2025.02.002

摘要（69）

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The goal of this paper is to investigate the theory of Noether solvability for Volterra singular integral equations (VSIEs) with convolution and Cauchy kernels in a more general function class. To obtain the analytic solutions, we transform such equations into boundary value problems with discontinuous coefficients by the properties of Fourier analysis. In view of the analytical Riemann-Hilbert method, the generalized Liouville theorem and Sokhotski-Plemelj formula, we get the uniqueness and existence of solutions for such problems, and study the asymptotic property of solutions at nodes. Therefore, this paper improves the theory of singular integral equations and boundary value problems.

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15. 变系数常微分方程边值问题的数值方法

赵婷婷, 蔡伟云

数学季刊 2025, 40 (3): 295-303. DOI: 10.13371/j.cnki.chin.q.j.m.2025.03.005

摘要（68）

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In order to solve the problem of the variable coefficient ordinary differential equation on the bounded domain, the Lagrange interpolation method is used to approximate the exact solution of the equation, and the error between the numerical solution and the exact solution is obtained, and then compared with the error formed by the difference method, it is concluded that the Lagrange interpolation method is more effective in solving the variable coefficient ordinary differential equation.

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16. 带有尖形式Fourier系数的Gauss圆内格点问题

陈锋

数学季刊 2025, 40 (3): 313-323. DOI: 10.13371/j.cnki.chin.q.j.m.2025.03.007

摘要（67）

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Let f be a Hecke eigenform of even integral weight k for the full modular group SL₂(Z). Denote by λ_f (n) the nth normalized coefficient of f. The sum of Fourier coefficients of cusp form over the quadratic polynomial m² +n² is considered, i.e.,...

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17. Dirichlet L-函数的均值

黄炳荣, 黄俊皓

数学季刊 2025, 40 (4): 360-371. DOI: 10.13371/j.cnki.chin.q.j.m.2025.04.003

摘要（66）

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In this paper, we establish asymptotic formulas for a cubic moment of Dirichlet L-functions restricted to a coset, as well as for a mixed moment of Dirichlet L-functions and twists of GL(2) L-functions along a coset. Our main tool is a power-saving estimate of bilinear forms of hyper-Kloosterman sums due to Kowalski–Michel–Sawin.

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18. 路和圈的幂图的Wiener指标

刘赛华, 李晓蓉

数学季刊 2025, 40 (1): 49-58. DOI: 10.13371/j.cnki.chin.q.j.m.2025.01.005

摘要（65）

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The Wiener index of a graph is defined to be the sum of the distances of all pairs of vertices in the graph. The kth power G^kof a graph G is the graph on V (G) and two vertices are adjacent if and only if their distance in G is less or equal to k. In this paper, we computed the Wiener index of the kth power of paths and cycles for any k ≥2.

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19. 多孔弹性问题多物理场间断有限元方法后验误差估计

葛志昊, 贺文龙, 马梦霞

数学季刊 2025, 40 (3): 238-261. DOI: 10.13371/j.cnki.chin.q.j.m.2025.03.002

摘要（63）

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In this paper, we design a new error estimator and give a posteriori error analysis for a poroelasticity model. To better overcome “locking phenomenon” on pressure and displacement, we proposed a new error estimators based on multiphysics discontinuous Galerkin method for the poroelasticity model. And we prove the upper and lower bound of
the proposed error estimators, which are numerically demonstrated to be computationally very efficient. Finally, we present numerical examples to verify and validate the efficiency of the proposed error estimators, which show that the adaptive scheme can overcome “locking phenomenon” and greatly reduce the computation cost.

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20. 广义斐波那契数列在网格中的新性质

杨子贤, 白建超

数学季刊 2025, 40 (1): 103-110. DOI: 10.13371/j.cnki.chin.q.j.m.2025.01.010

摘要（61）

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Fibonacci sequence, generated by summing the preceding two terms, is a classical sequence renowned for its elegant properties. In this paper, leveraging properties of generalized Fibonacci sequences and formulas for consecutive sums of equidistant sub-sequences, we investigate the ratio of the sum of numbers along main-diagonal and sub-diagonal of odd-order grids containing generalized Fibonacci sequences. We show that this ratio is solely dependent on the order of the grid, providing a concise and splendid identity.

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