Chinese Quarterly Journal of Mathematics

Well-Posedness for Timoshenko System with Thermodiffusion Effects and Delay

QIN Yu-ming, HAN Ning

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.

A Test on High-Dimensional Intraclass Correlation Structure

TANG Ping, XIAO Nan-nan, XIE Jun-shan

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.

The Normal Family of Meromorphic Functions Concerning Shared Analytic Function

YANG Qi, YUAN Wen-jun, TIAN Hong-gen

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.

Stability of Traveling Wavefronts for a Spatially Nonlocal Population Model with Delay

LIU Kai-kai, YANG Yun-rui, LI Xiao-wu

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.

Generalized Wave Operators in Von Neumann Algebras

ZHAN Xiong-feng, RUAN Yi-fei, HUANG He-nan-bei, LI Qi-hui

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_±.

Spatial Decay Estimates for the Solutions to Stokes Equations in Four Kinds of Semi-Infinite Cylinders

LI Yuan-fei, CHEN Xue-jiao, ZHNAG Wen-bin, LI Dan-dan

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.

A Note on the Representation of an Integer in Two Different Bases

WANG You-jun

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.

Expressions of Two Classes of Infinite Series in Terms of Bernoulli Numbers

GUO Dong-wei, CHEN Yu-lei

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).

Two Embedding Theorems in Martingale Spaces

FAN Li-ping

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.

Parameter Conditions for Hilbert-Type Operator Bounded with Homogeneous Kernels between Sequence Space l and Function Space L

HONG Yong, FENG Ming-jun

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......

Finite Time Blowup with Upper Bound of Blowup Time of Solutions to Semilinear Parabolic Equations with General Nonlinearity

LI Na, FANG Shao-mei

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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