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Acta Mathematica Sinica,English Series 2025年

作者： Xian Fa HU Yong Lei FANG Bin WANG school of mathematics and Statistics Changshu Institute of Technology school of mathematics and Statistics Zaozhuang University school of mathematics and Statistics Xi'an Jiaotong University

In this paper, we formulate two new families of fourth-order explicit exponential Runge–Kutta (ERK) methods with four stages for solving first-order differential systems y′(t)+My(t)=f(y(t)). The order conditions of these ERK methods are derived by comparing the Taylor series of the exact solution, which are exactly identical to the order conditions of explicit Runge–Kutta methods, and these ERK methods reduce to classical Runge–Kutta methods once M→0. Moreover, we analyze the stability properties and the convergence of these new methods. Several numerical examples are implemented to illustrate the accuracy and efficiency of these ERK methods by comparison with standard exponential integrators.

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The deflection angle and quasi-periodic oscillations of an extended gravitational decoupled black hole solution

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Communications in Theoretical Physics 2025年第2期77卷 132-147页

作者： Farzan Mushtaq Xia Tiecheng Allah Ditta G Mustafa S K Maurya Department of mathematics Shanghai University and Newtouch Center for Mathematics of Shanghai University Department of Physics Zhejiang Normal University Research Center of Astrophysics and Cosmology Khazar University Department of Mathematical and Physical sciences College of Arts and Sciences University of Nizwa

In weak field limits, we compute the deflection angle of a gravitational decoupling extended black hole(BH) solution. We obtained the Gaussian optical curvature by examining the null geodesic equations with the help of Gauss–Bonnet theorem(GBT). We also looked into the deflection angle of light by a black hole in weak field limits with the use of the Gibbons–Werner method. We verify the graphical behavior of the black hole after determining the deflection angle of light. Additionally, in the presence of the plasma medium, we also determine the deflection angle of the light and examine its graphical behavior. Furthermore, we compute the Einstein ring via gravitational decoupling extended black hole solution. We also compute the quasi-periodic oscillations and discuss their graphical behavior.

关键词： deflection of light Gauss-Bonnet theorem gravitational decoupling

Asymptotic false discovery control of the Benjamini-Hochberg procedure for pairwise comparisons

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Science China mathematics 2025年第1期68卷 223-252页

作者： Weidong Liu Dennis Leung Qi-Man Shao school of Mathematical sciences Shanghai Jiao Tong UniversityShanghai 200240China school of mathematics and Statistics University of MelbourneVictoria 3010Australia Department of Statistics and Data Science SICMSouthern University of Science and TechnologyShenzhen 518055China

In a one-way analysis-of-variance(ANOVA) model,the number of pairwise comparisons can become large even with a moderate number of *** by this,we consider a regime with a growing number of groups and prove that,when testing pairwise comparisons,the Benjamini-Hochberg(BH) procedure can asymptotically control false discoveries,despite the fact that the involved t-statistics do not exhibit the wellknown positive dependence structure required for exact false discovery rate(FDR) *** Tukey's perspective that the difference between the means of any two groups cannot be exactly zero,our main result provides control over the directional false discovery rate and directional false discovery proportion.A key technical contribution of our work is demonstrating that the dependence among the t-statistics is sufficiently weak to establish the convergence result typically required for asymptotic FDR *** analysis does not rely on conventional assumptions such as normality,variance homogeneity,or a balanced design,thereby offering a theoretical foundation for applications in more general settings.

关键词： BH procedure directional error FDR one-way ANOVA pairwise comparison Studentized twosample t-statistic Cramer-type moderate deviation uniform law of large numbers

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Asymptotic lower and upper bounds for linear elasticity eigenvalues

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Acta Mathematica Sinica,English Series 2025年

作者： Yifan YUE Hongtao CHEN Shuo ZHANG school of Mathematical sciences Xiamen University Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computing Xiamen University LSEC Institute of Computational Mathematics and Scientific/Engineering Computation Academy of Mathematics and System Science Chinese Academy of Sciences school of Mathematical sciences University of Chinese Academy of Sciences

Lower and upper bounds for eigenvalues help estimate the location interval of eigenvalues,which is of practical meanings especially for those problems of which the eigenvalues cannot be exactly obtained. In this paper, we study the lower and upper bounds for linear elasticity eigenvalues by displacement-pressure mixed finite element schemes. By applying expansion identities for the error of eigenvalues, lower and upper numerically computable bounds for the eigenvalues are derived based on certain mathematical hypotheses. For the schemes studied here, roughly speaking, the accuracy loss of the local approximation of the discrete displacement may lead to lower bound and that of pressure to upper bound. By utilizing the min-max principle and perturbation theory for the solution operator,theoretical lower and upper bounds can be controlled by setting proper Lamé parameters.

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Priority sources identification and risks assessment of heavy metal(loid)s in agricultural soils of a typical antimony mining watershed

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Journal of Environmental sciences 2025年第1期147卷 153-164页

作者： Lianhua Liu You Li Xiang Gu Roberto Xavier Supe Tulcan Lingling Yan Chunye Lin Junting Pan Institute of Environment and Sustainable Development in Agriculture Chinese Academy of Agricultural SciencesBeijing 100081China Key Laboratory of Land Surface Pattern and Simulation Institute of Geographic Sciences and Natural Resources ResearchChinese Academy of SciencesBeijing 100101China school of Environment Beijing Normal UniversityBeijing 100875China Yiyang Academy of Agricultural sciences Yiyang 413099China Institute of Agricultural Resources and Regional Planning Chinese Academy of Agricultural SciencesBeijing 100081China

Heavy metal(loid)(HM)pollution in agricultural soils has become an environmental concern in antimony(Sb)mining ***,priority pollution sources identification and deep understanding of environmental risks of HMs face great challenges due to multiple and complex pollution sources ***,an integrated approach was conducted to distinguish pollution sources and assess human health risk(HHR)and ecological risk(ER)in a typical Sb mining watershed in Southern *** approach combines absolute principal component score-multiple linear regression(APCS-MLR)and positivematrix factorization(PMF)models with ER and HHR *** pollution sources were distinguished for both models,and APCS-MLR model was more accurate and *** HM concentration source was natural source(39.1%),followed by industrial and agricultural activities(23.0%),unknown sources(21.5%)and Sb mining and smelting activities(16.4%).Although natural source contributed the most to HM concentrations,it did not pose a significant *** and agricultural activities predominantly contributed to ER,and attention should be paid to Cd and *** mining and smelting activities were primary anthropogenic sources of HHR,particularly Sb and As *** ER and HHR assessments,Sb mining and smelting,and industrial and agricultural activities are critical sources,causing serious ecological and health *** study showed the advantages of multiple receptor model application in obtaining reliable source identification and providing better source-oriented risk *** pollution management,such as regulating mining and smelting and implementing soil remediation in polluted agricultural soils,is strongly recommended for protecting ecosystems and humans.

关键词： Antimony Heavy metal(loid) Risk assessment Pollution sources Mining and smelting

Site index determination using a time series of airborne laser scanning data

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Forest Ecosystems 2025年第01期 93-103页

作者： Maria ?snes Moan Ole Martin Bollands?s Svetlana Saarela Terje Gobakken Erik N?sset Hans Ole ?rka Lennart Noordermeer Faculty of Environmental sciences and natural Resource Management Norwegian University of Life Sciences

Site index (SI) is determined from the top height development and is a proxy for forest productivity,defined as the expected top height for a given species at a certain index *** Norway,an index age of 40 years is *** using bi-temporal airborne laser scanning (ALS) data,SI can be determined using models estimated from SI observed on field plots (the direct approach) or from predicted top heights at two points in time (the height differential approach).Time series of ALS data may enhance SI determination compared to conventional methods used in operational forest inventory by providing more detailed information about the top height *** used longitudinal data comprising spatially consistent field and ALS data collected from training plots in 1999,2010,and 2022 to determine SI using the direct and height differential approaches using all combinations of years and performed an external *** also evaluated the use of data *** of root mean square error obtained from external validation were in the ranges of 16.3%–21.4%and 12.8%–20.6%of the mean fieldregistered SI for the direct approach and the height differential approach,*** were no statistically significant effects of time series length or the number of points in time on the obtained *** assimilation did not result in any substantial improvement in the obtained *** a time series of ALS data did not yield greater accuracies compared to using only two points in time,a larger proportion of the study area could be used in ALS-based determination of SI when a time series was *** was because areas that were unsuitable for SI determination between two points in time could be subject to SI determination based on data from another part of the time series.

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Multiplicative forms on Poisson groupoids

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Science China mathematics 2025年第1期68卷 169-206页

作者： Zhuo Chen Honglei Lang Zhangju Liu Department of Mathematical sciences Tsinghua UniversityBeijing 100084China College of Science China Agricultural UniversityBeijing 100083China school of mathematics and Statistics Henan UniversityKaifeng 475004China

First,we prove a decomposition formula for any multiplicative differential form on a Lie groupoid ***,we prove that if G is a Poisson Lie groupoid,then the spaceΩ_(mult)·(G)of multiplicative forms on G has a differential graded Lie algebra(DGLA)***,when combined withΩ·(M),which is the space of forms on the base manifold M of G,Ω_(mult)·(G)forms a canonical DGLA crossed *** supplements a previously known fact that multiplicative multi-vector fields on G form a DGLA crossed module with the Schouten algebraΓ(∧·A)stemming from the Lie algebroid A of G.

关键词： multiplicative form Poisson groupoid Lie algebra crossed module characteristic pair

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On the Riemann–Hilbert problem for the reverse space-time nonlocal Hirota equation with step-like initial data

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Communications in Theoretical Physics 2025年第2期77卷 32-40页

作者： Bei-Bei Hu Ling Zhang Zu-Yi Shen Ji Lin school of mathematics and Finance Chuzhou University Applied mathematics Research Center Chuzhou University Department of Physics Zhejiang Normal University

In this paper, we use the Riemann–Hilbert(RH) method to investigate the Cauchy problem of the reverse space-time nonlocal Hirota equation with step-like initial data: q(z, 0) = o(1) as z →-∞ and q(z, 0) = δ + o(1) as z → ∞, where δ is an arbitrary positive constant. We show that the solution of the Cauchy problem can be determined by the solution of the corresponding matrix RH problem established on the plane of complex spectral parameter λ. As an example, we construct an exact solution of the reverse space-time nonlocal Hirota equation in a special case via this RH problem.

关键词： nonlocal Hirota equation Cauchy problem Riemann-Hilbert problem step-like initial data

Privacy-preserving explainable AI: a survey

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Science China(Information sciences) 2025年第1期68卷 23-56页

作者： Thanh Tam NGUYEN Thanh Trung HUYNH Zhao REN Thanh Toan NGUYEN Phi Le NGUYEN Hongzhi YIN Quoc Viet Hung NGUYEN school of Information and Communication Technology Griffith University school of Computer and Communication sciences Ecole Polytechnique Federale de Lausanne Faculty of mathematics and Computer Science University of Bremen Faculty of Information Technology HUTECH University Department of Computer Science Hanoi University of Science and Technology school of Electrical Engineering and Computer Science The University of Queensland

As the adoption of explainable AI(XAI) continues to expand, the urgency to address its privacy implications intensifies. Despite a growing corpus of research in AI privacy and explainability, there is little attention on privacy-preserving model explanations. This article presents the first thorough survey about privacy attacks on model explanations and their countermeasures. Our contribution to this field comprises a thorough analysis of research papers with a connected taxonomy that facilitates the categorization of privacy attacks and countermeasures based on the targeted explanations. This work also includes an initial investigation into the causes of privacy leaks. Finally, we discuss unresolved issues and prospective research directions uncovered in our analysis. This survey aims to be a valuable resource for the research community and offers clear insights for those new to this domain. To support ongoing research, we have established an online resource repository, which will be continuously updated with new and relevant findings.

关键词： privacy-preserving explainable AI privacy attacks privacy defences PrivEx PPXAI

On Halmos'third problem on Banach spaces

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Science China mathematics 2025年第2期68卷 399-420页

作者： Lixin Cheng Junsheng Fang Chunlan Jiang school of Mathematical sciences Xiamen UniversityXiamen 361005China school of Mathematical sciences Hebei Normal UniversityShijiazhuang 050016China

In 1970,Halmos posed ten open problems in Hilbert *** third problem asks:If an intransitive operator T has an inverse,is its inverse also intransitive?This question is closely related to the invariant subspace *** Enflo's celebrated counterexample on l_(1)provided a negative answer to the invariant subspace problem,the Banach space version of Halmos'third problem has attracted increasing *** this paper,we provide an affirmative answer to this problem under certain spectral *** an application,we show that for an invertible operator T with Dunford's property(C),if T-1is intransitive and there exists a connected componentΩof intσ(T-1)^(^)off the origin and satisfiesΩ∩ρF(T-1)≠φ,then T is also ***,we show that a necessary and sufficient condition for the existence of a bounded linear operator without nontrivial invariant subspaces on the infinite-dimensional space L1(Ω,Σ,μ)(resp.C(K),the space of bounded continuous functions on a complete metric space K)is that(Ω,Σ,μ)isσ-finite(resp.K is compact).

关键词： invariant subspace bounded linear operator Banach space

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