数学季刊

秦玉明, 韩宁

2022, 37(1): 1-9. doi:10.13371/j.cnki.chin.q.j.m.2022.01.001

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In this paper, we study the well-posedness for the thermoelastic Timoshenko system with a constant delay and mass diffusion effects. Heat and mass exchange with the environment during thermodiffusion in Timoshenko beam. The C₀ -semigroup theory will be used to prove the well-posedness of the considered problem.

一类高维组内相关结构的检验

汤平, 肖南南, 解俊山

2022, 37(1): 10-25. doi:10.13371/j.cnki.chin.q.j.m.2022.01.002

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The paper considers a high-dimensional likelihood ratio (LR) test on the intraclass correlation structure of the multivariate normal population. When the dimension p and sample size N satisfy N − 1 >p→∞ , it is proved that the logarithmic LR statistic asymptotically obeys Gaussian distribution, and the explicit expressions of the mean and the variance are also obtained. The simulations demonstrate that our high-dimensional LR test method outperforms the traditional Chi-square approximation method or F-approximation method, and performs as efficient as the accurate high-dimensional Edgeworth expansion method and the more accurate high-dimensional Edgeworth expansion method in analyzing the intraclass covariance structure of highdimensional data.

涉及分担解析函数的亚纯函数的正规族

杨祺, 袁文俊, 田宏跟

2022, 37(1): 26-36. doi:10.13371/j.cnki.chin.q.j.m.2022.01.003

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In this paper, we study the normal criterion of meromorphic functions concerning shared analytic function. We get some theorems concerning shared analytic function, which improves some earlier related results.

一类空间非局部的时滞种群模型波前解的稳定性

刘凯凯, 杨赟瑞, 李孝武

2022, 37(1): 37-51. doi:10.13371/j.cnki.chin.q.j.m.2022.01.004

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The stability of traveling wavefronts for a spatially nonlocal population model with quasi-monotonicity and delay is discussed in this article. It is shown that all monostable wavefronts are exponentially stable for large speed with the help of weighted- energy method and comparison principle. The proper selection of the weighted function is necessary to overcome the difficulty caused by the nonlocal nonlinearity for establishing the energy estimates of solutions.

冯诺依曼代数中的广义波算子

占雄峰, 阮宜飞, 黄河南北, 李启慧

2022, 37(1): 52-60. doi:10.13371/j.cnki.chin.q.j.m.2022.01.005

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Let M⊆B(H) be a countable decomposable properly infinite von Neumann algebra with a faithful normal semifinite tracial weight τ where B(H) is the set of all bounded linear operators on Hilbert space H. The main purpose of this article is to introduce generalized weak wave operators \tide{W}_± , generalized weak abelian wave operators \tide{U}_± and generalized stationary wave operators U_± in M and then to explore the relation among \tide{W}_± , \tide{U}_± , U_± and generalized wave operators W_±.

Stokes方程组的解在四种半无穷柱体上空间衰减性

李远飞, 陈雪姣, 张文彬, 李丹丹

2022, 37(1): 61-73. doi:10.13371/j.cnki.chin.q.j.m.2022.01.006

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This paper investigates the spatial behavior of the solutions of the Stokes equations in a semi-infinite cylinder. We consider four kinds of semi-infinite cylinders with boundary conditions of Dirichlet type. For each type of cylinder we obtain the spatial decay estimates for the solutions. To make the attenuation meaningful, we derive the explicit bound for the total energy in terms of the initial boundary data.

关于整数在两个不同基上表示的注记

王友军

2022, 37(1): 74-78. doi:10.13371/j.cnki.chin.q.j.m.2022.01.007

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Let a,b and n be integers larger than 1 and let α,β be integers satisfying 0 ≤α<a, 0 ≤β<b. Denote L_α,a ( n ) ,L_β,b ( n ) the numbers of digits in the canonical expansion of n in base a and b which are different from α and β, respectively. Define L_α,a,β,b (n)=L_α,a (n)+L_β,b (n). In this short note, the lower bound of L_α,a,β,b ( n ) was considered, i.e., if loga/logb is irrational, the estimate L_α,a,β,b (n)>loglogn/(logloglogn+C)−1, holds for C ?logab and n>25, which deepens the result of Stewart.

两类无穷级数的Bernoulli数表示

郭东威, 陈玉磊

2022, 37(1): 79-87. doi:10.13371/j.cnki.chin.q.j.m.2022.01.008

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In this paper, the expressions of two classes of infinite series in terms of finite series involving Bernoulli numbers are obtained. As applications, we derive some special series including Dirichlet beta function β ( s ) with argument 2 n +1 and Dirichlet lambda function λ ( s ) with argument 2 n . In addition, we solve the problem proposed recently by Zhou (2021).

鞅空间的两个嵌入定理

范利萍

2022, 37(1): 88-93. doi:10.13371/j.cnki.chin.q.j.m.2022.01.009

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It is proved in this paper that a pair of measurable functions satisfying the good −λ inequality yields quasi-norm inequalities in Lorentz spaces and weak Orlicz-Lorentz spaces. By use of this conclusion two embedding theorems are obtained in martingale spaces.

序列空间l和函数空间 L 之间具有齐次核的 Hilbert 型算子有界的参数条件

洪勇, 冯明军

2022, 37(1): 94-102. doi:10.13371/j.cnki.chin.q.j.m.2022.01.010

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By using the technique of real analysis, the parameter conditions for Hilbert-type series operator and integral operator......

具有一般非线性项的半线性抛物方程解的有限时间爆破和爆破时间上界

李娜, 房少梅

2022, 37(1): 103-110. doi:10.13371/j.cnki.chin.q.j.m.2022.01.011

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In this paper, we consider a semilinear parabolic equation with a general nonlinearity. We establish a new finite time blow-up criterion and also derive the upper bound for the blow-up time. The results partially generalize some recent ones obtained by He Ma et al.

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