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Study of bending angle and shadow in a new Schwarzschild-like black hole affected by plasma and non-plasma mediums

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Chinese Physics C 2024年第5期48卷 309-318页

作者： Riasat Ali Tiecheng Xia Muhammad Awais Rimsha Babar department of mathematics Newtouch Center for Mathematics of Shanghai UniversityShanghai 200444China department of mathematics University of Engineering and Technology Lahore-54890Pakistan department of mathematics GC University Faisalabad Layyah CampusLayyah-31200Pakistan

In this study,we analyze the models of the deflection angle of a new Schwarzschild-like black hole(BH)and employ the optical metric of the *** achieve this,we use the Gaussian curvature of the optical metric and the Gauss-Bonnet theorem,known as the Gibbons-Werner technique,to determine the deflection ***,we examine the deflection angle in the presence of a plasma medium and the effect of the plasma medium on the deflection *** deflection angle of the BH solution in the gauged super-gravity is computed using the Keeton-Petters *** the ray-tracing technique,we investigate the shadow of the corresponding BH and analyze the plots of the deflection angle and shadow to verify the influence of the plasma and algebraic thermodynamic parameters on the deflection angle and shadow.

关键词： new Schwarzschild-like black hole Gibbons-Werner and Keeton-Petters techniques deflection angle ray-tracing approach shadow

Ambarzumyan's Theorem for the Dirac Operator on Equilateral Tree Graphs

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Acta Mathematicae Applicatae Sinica 2024年第2期40卷 568-576页

作者： Dong-Jie WU Xin-Jian XU Chuan-Fu YANG department of mathematics School of Mathematics and StatisticsNanjing University of Science and TechnologyNanjing 210094China

The classical Ambarzumyan’s theorem states that if the Neumann eigenvalues of the Sturm-Liouville operator-d^(2)/dx^(2)+q with an integrable real-valued potential q on[0,π] are {n^(2):n≥0},then q=0 for almost all x∈[0,π].In this work,the classical Ambarzumyan’s theorem is extended to the Dirac operator on equilateral tree *** prove that if the spectrum of the Dirac operator on graphs coincides with the unperturbed case,then the potential is identically zero.

关键词： dirac operator quantum graph Ambarzumyan’s theorem inverse spectral problem

Critical observability of partially observed discrete event systems under cyber attacks

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Science China(Information Sciences) 2024年第2期67卷 333-334页

作者： Liyun TONG Jinling LIANG Yang LIU department of mathematics School of SciencesHangzhou Dianzi University School of mathematics Southeast University College of mathematics and Computer Science Zhejiang Normal University

The discrete event system(DES) is a dynamic system driven by asynchronous/sudden events and has been widely used in many critical infrastructures, such as electric transportation networks and intelligent transportatio...

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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

Gluing support τ-tilting modules via symmetric ladders of height 2

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Science China mathematics 2024年第10期67卷 2217-2236页

作者： Yingying Zhang department of mathematics Huzhou University

Gluing techniques with respect to a recollement have long been studied. Recently, ladders of recollements of abelian categories were introduced as important tools. In this paper, we present explicit constructions of gluing support τ-tilting modules via symmetric ladders of height two. Moreover, we apply the result to triangular matrix algebras to give a detailed version of the known Jasso's reduction and study maximal green sequences.

关键词： support $\tau$-tilting module torsion class semibrick ladder triangular matrix algebra maximal green sequence

Controllability of Semilinear Integrodifferential Degenerate Sobolev Equations

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Journal of Systems Science & Complexity 2024年第5期37卷 1923-1936页

作者： GE Zhaoqiang School of mathematics and Statistics Xi’an Jiaotong University

In this paper, the approximate controllability of semilinear integrodifferential degenerate Sobolev equations with nonlocal conditions is investigated in the sense of integral solution in Hilbert spaces. Some sufficient and necessary conditions are obtained. Firstly, the existence and uniqueness of integral solutions of semilinear integrodifferential degenerate Sobolev equations with nonlocal conditions are considered by GE-evolution operator theory and Sadovskii's fixed point theorem, the existence and uniqueness theorem of solutions is given. Secondly, the approximate controllability of semilinear integrodifferential degenerate Sobolev equations with nonlocal conditions is studied in the sense of integral solution. The criterion for approximate controllability is provided. The obtained results have important theoretical and practical value for the study of controllability of semilinear integrodifferential degenerate Sobolev equations with nonlocal conditions.

关键词： Approximate controllability GE-evolution operator integral solution Sadovskii’s fixed point theorem semilinear integrodifferential degenerate Sobolev equations

Maximizing conditional independence for unsupervised domain adaptation

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Science China(Information Sciences) 2024年第5期67卷 136-149页

作者： Yiming ZHAI Chuanxian REN Youwei LUO Daoqing DAI School of mathematics Sun Yat-Sen University

Unsupervised domain adaptation(UDA) studies how to transfer a learner from a labeled source domain to an unlabeled target domain with different distributions. Existing methods mainly focus on matching marginal distributions of the source and target domains, which probably leads to a misalignment of samples from the same class but different domains. In this paper, we tackle this misalignment issue by achieving the class-conditioned transferring from a new perspective. Specifically, we propose a method named maximizing conditional independence(MCI) for UDA, which maximizes the conditional independence of feature and domain given class in the reproducing kernel Hilbert spaces. The optimization of conditional independence can be viewed as a surrogate for minimizing class-wise mutual information between feature and domain. An interpretable empirical estimation of the conditional dependence measure is deduced and connected with the unconditional case. Besides, we provide an upper bound on the target error by taking the class-conditional distribution into account, which provides a new theoretical insight for class-conditioned transferring. Extensive experiments on six benchmark datasets and various ablation studies validate the effectiveness of the proposed model in dealing with UDA.

关键词： conditional independence kernel method domain adaptation class-conditioned transferring

Prescribed-time stabilization and inverse optimal control of stochastic high-order nonlinear systems

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Science China(Information Sciences) 2024年第2期67卷 144-156页

作者： Ran LIU Hui WANG Wuquan LI School of mathematics and Statistics Science Ludong University

This paper investigates the prescribed-time state-feedback stabilization and prescribed-time inverse optimality problems for stochastic high-order nonlinear systems. First, a time-varying controller is designed by developing scaled quartic Lyapunov functions, which can guarantee that the system has a unique strong solution almost surely on the prescribed interval for any system initial conditions and that the states and the control converge to the origin in a mean-square form within the prescribed time. Then, the controller is redesigned to address the problem of prescribed-time inverse optimal mean-square stabilization. Finally,a concrete example is provided to confirm the efficiency of the proposed design schemes.

关键词： stochastic high-order nonlinear systems prescribed-time stabilization the scaled design inverse optimality

Topologically Correct Intersection Curves of Two Trimmed Quadrics with Tolerance Control

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Journal of Systems Science & Complexity 2024年第5期37卷 2207-2239页

作者： SHAO Wenbing CHEN Falai department of mathematics University of Science and Technology of China

Surface/surface intersection is a fundamental problem in Compute Aided Design and Geometric Modeling since it is essential to solid modeling, numerically controlled machining, feature recognition, computer animation, etc. In practical applications, quadric surfaces, which are the most basic type of surfaces, are typically bounded surfaces trimmed by a sequence of planes. In this paper,a robust algorithm is proposed for computing the intersection curve segments of two trimmed quadrics based on the parametric representation of the intersection curves of two quadrics. The proposed algorithm guarantees correct topology and ensures that the approximation errors of the end points of the intersection curve segments are less than a given tolerance. The error control is based on an effective solution to a set of polynomial inequality system using the root isolation technique. Some examples are presented to validate the robustness and effectiveness of the proposed algorithm.

关键词： Polynomial inequality system root isolation surface/surface intersection tolerance control trimmed quadrics