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The Necessary and Sufficient Conditions of Exponential Stability for Heat and Wave Equations with Memory

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Journal of Systems Science & Complexity 2024年第3期37卷 1037-1051页

作者： LI Lingfei ZHANG Xiaoyi ZHOU Xiuxiang school of Science Northeast Electric Power UniversityJilin 132012China school of mathematics and Statistics Lingnan Normal UniversityZhanjiang 524048China

This paper is addressed to a study of the stability of heat and wave equations with *** necessary and sufficient conditions of the exponential stability are investigated by the theory of Laplace transform. The results show that the stability depends on the decay rate and the coefficient of the kernel functions of the memory. Besides, the feedback stabilization of the heat equation is obtained by constructing finite dimensional controller according to unstable eigenvalues. This stabilizing procedure is easy to operate and can be applicable for other parabolic equations with memory.

关键词： Memory stability stabilization

A GENERAL AVERAGING METHOD FOR AFFINE PERIODIC SOLUTIONS

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Acta Mathematica Scientia 2024年第6期44卷 2207-2224页

作者：杨雪邢佳敏李勇 College of mathematics Jilin University school of mathematics and Statistics and Center for Mathematics and Interdisciplinary SciencesNortheast Normal University

We consider the persistence of affine periodic solutions for perturbed affine periodic ***(Q,T)-affine periodic solutions have the form x(t+T)=Qx(t) for all t E R,where T> 0 is fixed and Q is a nonsingular *** are a kind of spatiotemporal symmetric solutions,*** *** give the averaging method for the existence of affine periodic solutions in two situations:one in which the initial values of the affine periodic solutions of the unperturbed system form a manifold,and another that does not rely on the structure of the initial values of the unperturbed system's affine periodic *** transversal condition is determined using the Brouwer *** also present a higher order averaging method for general degenerate systems by means of the Brouwer degree and a Lyapunov-Schmidt reduction.

关键词： 34D10 3C29 affine-periodic solution averaging method Brouwer degree perturbed system

NADARAYA-WATSON ESTIMATORS FOR REFLECTED STOCHASTIC PROCESSES

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Acta Mathematica Scientia 2024年第1期44卷 143-160页

作者：韩月才张丁文 school of mathematics Jilin UniversityChangchun130012China Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education Jilin UniversityChangchun130012China

We study the Nadaraya-Watson estimators for the drift function of two-sided reflected stochastic differential *** estimates,based on either the continuously observed process or the discretely observed process,are *** certain conditions,we prove the strong consistency and the asymptotic normality of the two *** method is also suitable for one-sided reflected stochastic differential *** results demonstrate that the performance of our estimator is superior to that of the estimator proposed by Cholaquidis et al.(Stat Sin,2021,31:29-51).Several real data sets of the currency exchange rate are used to illustrate our proposed methodology.

关键词： reflected stochastic differential equation discretely observed process continuously observed process Nadaraya-Watson estimator asymptotic behavior

A Simulation-Extrapolation Approach to the Analysis of Interval-Censored Failure Time Data with Mis-Measured Covariates

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Journal of Systems Science & Complexity 2024年

作者： FENG Fan ZHAO Shishun LI Shuwei SUN Jianguo school of Economics and Statistics Guangzhou University school of mathematics Jilin University school of mathematics Jilin University Department of Statistics University of Missouri

Interval-censored failure time data arise frequently in periodical follow-up studies including clinical trials and epidemiological surveys. In addition, some covariates may be subject to measurement errors due to the instrumental contamination, biological variation or other reasons. For the analysis of interval-censored data with mis-measured covariates, the existing methods either assume a parametric model or rely on the availability of replicated surrogate measurements for the error-prone covariate, which both have obvious limitations. To overcome these shortcomings, the authors propose a simulation-extrapolation estimation procedure under a general class of transformation models. The resulting estimators are shown to be consistent and asymptotically normal. The numerical results obtained from a simulation study indicate that the proposed method performs reasonably well in *** particular, the proposed method can reduce the estimation bias given by the naive method that does not take measurement errors into account. Finally, the proposed method is applied to a real data set on hypobaric decompression sickness.

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Linear and Nonlinear Solutions of Interfacial Waves Due to a Doublet

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Journal of Mathematical Research with Applications 2024年第2期44卷 269-284页

作者： Di LIU Zhen WANG school of mathematics Jilin University school of Mathematical Sciences Beihang University

Steady two-dimensional potential flows of two-layer fluids with a submerged doublet in the lower layer are considered. Both linear analytical solutions and fully nonlinear solutions based on boundary integral equation methods are obtained. Nonlinearity strongly influences the downstream wave height and leads to a slight phase difference. When the Froude number is small, wave height fast gets its maximum as the Froude number increases. While wave-less solutions may be obtained if the Froude number is very large. Afterward, the interfacial waves due to one point vortex or a vortex pair are compared with those due to a doublet. It is found that the nonlinear wave profiles due to a doublet are quite close to those due to a vertical vortex pair if the distance between the vortex pair is set appropriately.

关键词： interfacial waves doublet boundary integral equation method linear solutions

On non-abelian extensions of 3-Leibniz algebras

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Frontiers of mathematics in China 2024年第2期19卷 57-74页

作者： Nanyan XU Yunhe SHENG school of mathematics Jilin UniversityChangchun 130012China

In this paper,we study non-abelian extensions of 3-Leibniz algebras through Maurer-Cartan *** construct a differential graded Lie algebra and prove that there is a one-to-one correspondence between the isomorphism classes of non-abelian extensions in 3-Leibniz algebras and the equivalence classes of Maurer-Cartan elements in this differential graded Lie *** also the Leibniz algebra structure on the space of fundamental elements of 3-Leibniz algebras is *** is proved that the non-abelian extension of 3-Leibniz algebras induce the non-abelian extensions of Leibniz algebras.

关键词： 3-Leibniz algebras Leibniz algebra non-abelian extension Maurer-Cartan element

Micro segment analysis of supercritical methane thermal-hydraulic performance and pseudo-boiling in a PCHE straight channel

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Petroleum Science 2024年第2期21卷 1275-1289页

作者： Qian Li Zi-Jie Lin Liu Yang Yue Wang Yue Li Wei-Hua Cai Laboratory of Thermo-Fluid Science and Nuclear Engineering Northeast Electric Power UniversityJilin132000JilinChina school of Energy and Power Engineering Northeast Electric Power UniversityJilin132000JilinChina

The printed circuit heat exchanger(PCHE) is receiving wide attention as a new kind of compact heat exchanger and is considered as a promising vaporizer in the LNG process. In this paper, a PCHE straight channel in the length of 500 mm is established, with a semicircular cross section in a diameter of 1.2 *** simulation is employed to investigate the flow and heat transfer performance of supercritical methane in the channel. The pseudo-boiling theory is adopted and the liquid-like, two-phase-like, and vapor-like regimes are divided for supercritical methane to analyze the heat transfer and flow *** results are presented in micro segment to show the local convective heat transfer coefficient and pressure drop. It shows that the convective heat transfer coefficient in segments along the channel has a significant peak feature near the pseudo-critical point and a heat transfer deterioration when the average fluid temperature in the segment is higher than the pseudo-critical point. The reason is explained with the generation of vapor-like film near the channel wall that the peak feature related to a nucleateboiling-like state and heat transfer deterioration related to a film-boiling-like state. The effects of parameters, including mass flow rate, pressure, and wall heat flux on flow and heat transfer were *** calculating of the averaged heat transfer coefficient of the whole channel, the traditional method shows significant deviation and the micro segment weighted average method is adopted. The pressure drop can mainly be affected by the mass flux and pressure and little affected by the wall heat flux. The peak of the convective heat transfer coefficient can only form at high mass flux, low wall heat flux, and near critical pressure, in which condition the nucleate-boiling-like state is easier to appear. Moreover,heat transfer deterioration will always appear, since the supercritical flow will finally develop into a filmboiling-like state. So hea

关键词： Printed circuit heat exchanger Vaporization Supercritical methane Pseudo-boiling Micro segment analysis

A Mean-Field Game for a Forward-Backward Stochastic System With Partial Observation and Common Noise

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IEEE/CAA Journal of Automatica Sinica 2024年第3期11卷 746-759页

作者： Pengyan Huang Guangchen Wang Shujun Wang Hua Xiao the school of Control Science and Engineering Shandong University the school of Statistics and mathematics Shandong University of Finance and Economics IEEE the school of Management Shandong University the school of mathematics and Statistics Shandong University

This paper considers a linear-quadratic(LQ) meanfield game governed by a forward-backward stochastic system with partial observation and common noise,where a coupling structure enters state equations,cost functionals and observation ***,to reduce the complexity of solving the meanfield game,a limiting control problem is *** virtue of the decomposition approach,an admissible control set is *** a filter technique and dimensional-expansion technique,a decentralized control strategy and a consistency condition system are derived,and the related solvability is also ***,we discuss an approximate Nash equilibrium property of the decentralized control ***,we work out a financial problem with some numerical simulations.

关键词： Decentralized control strategy ϵ-Nash equilibrium forward-backward stochastic system mean-field game partial observation

A method to determine the bonded-particle model parameters for simulation of ores

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Particuology 2024年第3期86卷 24-38页

作者： Shuwei Wu Guoqiang Wang Longfei Fan Wei Guan Jianbo Guo Zhengbin Liu Yukuan Wang school of Mechanical and Aerospace Engineering Jilin UniversityChangchun130025China

The bonded-particle model(BPM)is commonly used in the numerical analysis of ore *** improve the accuracy of simulating the mechanical process of ore process of ore crushing in a crusher,the parameters of the BPM for the ore must be *** this study,a calibration method was proposed for the scientific determination of the parameters of the BPM for ore undergoing uniaxial ***,physical tests and simulations were conducted to determine the mechanical response(uniaxial compressive strength and macroscopic stiffness)of ore during uniaxial ***,the sensitivity of the mechanical response to the values of microscopic parameters was tested using a Plackett-Burman ***,the microscopic parameters with the greatest impact on the response were identified,and the range of parameters that met the target response was determined using a steepest ascent design;Second,a second-order model of the mechanical response was established using the sensitive parameters by combining a Box-Behnken design with response surface methodology to obtain the optimal BPM *** tests showed that the normal stiffness per unit area,critical shear stress,and bonded disk radius had significant effects on the uniaxial compressive strength(UCS)and macroscopic stiffness(MS).To verify the validity of the proposed calibration method,laboratory tests were *** consistency of the simulation results with experimental results indicated that response surface methodology with the Plackett-Burman design,steepest ascent design,and Box-Behnken design can be an effective method for calibrating the BPM of ores.

关键词： Bonded-particle model Discrete element method Calibration method Design of experiment Uniaxial compression test