数学季刊

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

2025, 40(1): 1-19. doi:10.13371/j.cnki.chin.q.j.m.2025.01.001

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

关于Sauer与Schweizer结果的注记

王广胜, 李菲, 徐焱

2025, 40(1): 20-25. doi:10.13371/j.cnki.chin.q.j.m.2025.01.002

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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.

w-(b,c)-核逆

方莉, 赵良

2025, 40(1): 26-35. doi:10.13371/j.cnki.chin.q.j.m.2025.01.003

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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.

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

2025, 40(1): 36-48. doi:10.13371/j.cnki.chin.q.j.m.2025.01.004

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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……

路和圈的幂图的Wiener指标

刘赛华, 李晓蓉

2025, 40(1): 49-58. doi:10.13371/j.cnki.chin.q.j.m.2025.01.005

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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.

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

2025, 40(1): 59-73. doi:10.13371/j.cnki.chin.q.j.m.2025.01.006

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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.

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

2025, 40(1): 74-81. doi:10.13371/j.cnki.chin.q.j.m.2025.01.007

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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.

多参数Mittag-Leffler函数的一些成果

潘玉梅, 李玉芬, 蔡董欣, 严兴杰

2025, 40(1): 82-92. doi:10.13371/j.cnki.chin.q.j.m.2025.01.008

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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

关于多复变量 α-Bloch 函数

朱婷, 杨刘

2025, 40(1): 93-102. doi:10.13371/j.cnki.chin.q.j.m.2025.01.009

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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.

广义斐波那契数列在网格中的新性质

杨子贤, 白建超

2025, 40(1): 103-110. doi:10.13371/j.cnki.chin.q.j.m.2025.01.010

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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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