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Identification of Linear Systems Using Binary Sensors with Random Thresholds

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Journal of Systems Science & Complexity 2024年第3期37卷 907-923页

作者： HUANG Zhiyong SONG Qijiang school of mathematics Renmin University of ChinaBeijing 100872China school of mathematics Sino-French InstituteRenmin University of ChinaBeijing 100872China

In this paper,the problem of identifying autoregressive-moving-average systems under random threshold binary-valued output measurements is considered.With the help of stochastic approximation algorithms with expanding truncations,the authors give the recursive estimates for the parameters of both the linear system and the binary sensor.Under reasonable conditions,all constructed estimates are proved to be convergent to the true values with probability one,and the convergence rates are also established.A simulation example is provided to justify the theoretical results.

关键词： α-mixing binary sensor quantized system stochastic approximation stochastic thresh-old strongly consistent system identification

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Irrational-Behavior-Proof Conditions for Stochastic Games over Event Trees

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Journal of the Operations Research Society of China 2024年第1期12卷 243-263页

作者： Lei Wang Cui Liu Hong-Wei Gao Chong Lin school of Automation Institute of Complexity ScienceQingdao UniversityQingdao 266071ShandongChina school of mathematics and Statistics Institute of Applied Mathematics of ShandongQingdao UniversityQingdao 266071ShandongChina

In this paper,the irrational-behavior-proof conditions in a class of stochastic dynamic games over event trees are presented.Four kinds of irrational-behavior-proof conditions are proposed by the imputation distribution procedure,and their relationships are discussed.More specific properties for the general transformation of characteristic functions are developed,based on which,the irrational-behavior-proof conditions are proved to be true in a transformed cooperative game.

关键词： Dynamic cooperative game Event tree Irrational-behavior-proof condition Imputation distribution procedure Transformation of characteristic function

On equivalence of state-based potential games

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Science China(Information Sciences) 2024年第6期67卷 313-327页

作者： Han WU Jinhuan WANG Hebei University of Technology institute of mathematics school of Science

In this paper, we explore state-based potential games using the semi-tensor product of matrices.First, applying the potential equation, we derive both a necessary and sufficient condition as well as a sufficient condition to verify whether a state-based game qualifies as a potential game. Next, we present two static equivalence conditions of state-based potential games. We then delve into dynamic equivalence. We propose a criterion that allows us to identify state-based games that are dynamically equivalent to state-based potential games and share similar dynamic properties. Ultimately, we introduce the concept of state-based networked evolutionary games. We provide a necessary and sufficient condition to ensure that a state-based networked evolutionary game can be classified as a state-based potential game.

关键词： semi-tensor product of matrices state-based potential game verification equivalence state-based networked evolutionary game

A DIRECT DISCONTINUOUS GALERKIN METHOD FOR TIME FRACTIONAL DIFFUSION EQUATIONS WITH FRACTIONAL DYNAMIC BOUNDARY CONDITIONS

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Journal of Computational mathematics 2024年第1期42卷 156-177页

作者： Jingjun Zhao Wenjiao Zhao Yang Xu school of mathematics Harbin Institute of TechnologyHarbin 150001China

This paper deals with the numerical approximation for the time fractional diffusion problem with fractional dynamic boundary conditions.The well-posedness for the weak solutions is studied.A direct discontinuous Galerkin approach is used in spatial direction under the uniform meshes,together with a second-order Alikhanov scheme is utilized in temporal direction on the graded mesh,and then the fully discrete scheme is constructed.Furthermore,the stability and the error estimate for the full scheme are analyzed in detail.Numerical experiments are also given to illustrate the effectiveness of the proposed method.

关键词： Time fractional diffusion equation Numerical stability Convergence

On the convergence of tracking differentiator with multiple stochastic disturbances

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Science China(Information Sciences) 2024年第2期67卷 157-169页

作者： Zehao WU Huacheng ZHOU Baozhu GUO Feiqi DENG school of mathematics and Big Data Foshan University school of mathematics and Statistics Central South University Academy of mathematics and Systems Science Chinese Academy of Sciences Systems Engineering institute South China University of Technology

This paper investigates the convergence, noise-tolerance, and filtering performance of a tracking differentiator in the presence of multiple stochastic disturbances for the first time. We consider a general case wherein the input signal is corrupted by additive colored noise, and the tracking differentiator is disturbed by additive colored noise and white noise. The tracking differentiator is shown to track the input signal and its generalized derivatives in the mean square sense. Further, the almost sure convergence can be achieved when the stochastic noise affecting the input signal is vanishing. Herein, numerical simulations are performed to validate the theoretical results.

关键词： tracking differentiator convergence noise-tolerance filtering performance multiple stochastic disturbances

Spacelike Framed Curves with Lightlike Components and Singularities of Their Evolutes and Focal Surfaces in Minkowski 3-space

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Acta Mathematica Sinica,English Series 2024年第6期40卷 1521-1532页

作者： Peng Cheng LI Dong He PEI Xin ZHAO 1.school of mathematics and Statistics, Northeast Normal University 2.Department of mathematics, Harbin institute of Technology 3.school of mathematics and Statistics, Qingdao University school of mathematics and Statistics Northeast Normal University Department of mathematics Harbin Institute of Technology school of mathematics and Statistics Qingdao University

In this paper, we define the evolute and focal surface of a spacelike framed curve with lightlike components in Minkowski 3-space. It is a generalization of the previous results of regular spacelike curves, since singularities are allowed in the original spacelike curves studied by spacelike framed curves with lightlike components. Meanwhile, we show a new geometric invariant to characterise singularities of the focal surface. Then, the classification theorem and recognition theorem for the singularities of the focal surface in generic are also given.

关键词： Evolutes focal surfaces spacelike framed curves singularities 57R45 53B30 58C25 58K05

The KAM theorem on the modulus of continuity about parameters

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Science China mathematics 2024年第3期67卷 577-592页

作者： Zhicheng Tong Jiayin Du Yong Li school of mathematics Jilin UniversityChangchun 130012China institute of mathematics Jilin UniversityChangchun 130012China school of mathematics and Statistics Center for Mathematics and Interdisciplinary SciencesNortheast Normal UniversityChangchun 130024China

In this paper,we study the Hamiltonian systems H(y,x,ξ,ε)=〈ω(ξ),y〉+εP(y,x,ξ,ε),where ω and P are continuous about ξ.We prove that persistent invariant tori possess the same frequency as the unperturbed tori,under a certain transversality condition and a weak convexity condition for the frequency mapping ω.As a direct application,we prove a Kolmogorov-Arnold-Moser(KAM) theorem when the perturbation P holds arbitrary Holder continuity with respect to the parameter ξ.The infinite-dimensional case is also considered.To our knowledge,this is the first approach to the systems with the only continuity in the parameter beyond H?lder's type.

关键词： Hamiltonian systems invariant tori frequency-preserving weak regularity

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Spectral flow, Llarull's rigidity theorem in odd dimensions and its generalization

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Science China mathematics 2024年第5期67卷 1103-1114页

作者： Yihan Li Guangxiang Su Xiangsheng Wang Chern institute of mathematics&LPMC Nankai UniversityTianjin 300071China school of mathematics Shandong UniversityJinan 250100China

For a compact spin Riemannian manifold(M,g^(TM))of dimension n such that the associated scalar curvature kT M verifies that k^(TM)≥n(n-1),Llarull’s rigidity theorem says that any area-decreasing smooth map f from M to the unit sphere Sn of nonzero degree is an isometry.In this paper,we present a new proof of Llarull’s rigidity theorem in odd dimensions via a spectral flow argument.This approach also works for a generalization of Llarull’s theorem when the sphere Sn is replaced by an arbitrary smooth strictly convex closed hypersurface in Rn+1.The results answer two questions by Gromov(2023).

关键词： Dirac operator scalar curvature spectral flow

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Unsteady MHD Casson Nanofluid Flow Past an Exponentially Accelerated Vertical Plate:An Analytical Strategy

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Computer Modeling in Engineering & Sciences 2024年第7期140卷 431-460页

作者： T.Aghalya R.Tamizharasi Department of mathematics School of Advanced SciencesVellore Institute of TechnologyVelloreTamilnadu632014India

In this study,the characteristics of heat transfer on an unsteady magnetohydrodynamic(MHD)Casson nanofluid over an exponentially accelerated vertical porous plate with rotating effects were investigated.The flow was driven by the combined effects of the magnetic field,heat radiation,heat source/sink and chemical reaction.Copper oxide(CuO)and titanium oxide(TiO2)are acknowledged as nanoparticle materials.The nondimensional governing equations were subjected to the Laplace transformation technique to derive closed-form solutions.Graphical representations are provided to analyze how changes in physical parameters,such as the magnetic field,heat radiation,heat source/sink and chemical reaction,affect the velocity,temperature and concentration profiles.The computed values of skin friction,heat and mass transfer rates at the surface were tabulated for various sets of input parameters.It is perceived that there is a drop in temperature due to the rise in the heat source/sink and the Prandtl number.It should be noted that a boost in the thermal radiation parameter prompts an increase in temperature.An increase in the Prandtl number,heat source/sink parameter,time and a decrease in the thermal radiation parameter result in an increase in theNusselt number.The computed values of the skin friction,heat andmass transfer rates at the surface were tabulated for various values of the flow parameters.The present results were compared with those of previously published studies andwere found to be in excellent agreement.This research has practical applications in areas such as drug delivery,thermal medicine and cancer treatment.

关键词： Thermal radiation radiative flux nanofluid copper oxide titanium oxide accelerated plate