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Functional limit theorem for moving average processes generated by dependent random variables

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Progress in Natural Science:Materials International 2006年第3期16卷 266-273页

作者： liN Zhengyan and li Degui (department of mathematics, zhejiang university, Hangzhou 310028, china) [a]department of mathematics Zhejiang University Hangzhou China

Let {Xt,t≥1} be a moving average process defined by , where {bj,j≥0} is a sequence of real num- bers and {ξt,-∞ 详细信息

Let {Xt,t≥1} be a moving average process defined by , where {bj,j≥0} is a sequence of real num- bers and {ξt,-∞linear process, we study asymptotics of (properly nor- malized). When {Xt,t≥1} is a long memory process, we establish a functional limit theorem. When {Xt,t≥1} is a linear process, we not only obtain the multi-dimensional weak convergence for {Xx,t≥1},but also weaken the moment condition on {ξt,-∞lications of our results.

关键词： functional limit theorem long memory process linear process moving average process φ-mixing.

Perturbative Painleve Analysis of General KdV System and Its Exact Soliton Solutions

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Communications in Theoretical Physics 2005年第8期44卷 197-202页

作者： liN ji YE li-Jun li Hua-Mei Institute of Nonlinear Physics, zhejiang normal university, jinhua 32.004, china Institute of Nonlinear Physics Zhejiang Normal University

Using the standard Painlevé analysis ad the perturbative method,the Painlevé test for the logarithmicbranch is investigated. Nine arbitrary functions are obtained and the B cklund transformation of the logarithmic b... 详细信息

关键词： Painlevé analysis perturbative method Jacobi elliptic solution

Optimizing near-carbon-free nuclear energy systems:advances in reactor operation digital twin through hybrid machine learning algorithms for parameter identification and state estimation

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Nuclear Science and Techniques 2024年第8期35卷 177-203页

作者： li‑Zhan Hong He‑lin Gong Hong‑Jun ji jia‑liang Lu Han li Qing li Paris Elite Institute of Technology Shanghai Jiao Tong UniversityShanghai 200240China Science and Technology on Reactor System Design Technology Laboratory Nuclear Power Institute of ChinaChengdu 610041China

Accurate and efficient online parameter identification and state estimation are crucial for leveraging digital twin simulations to optimize the operation of near-carbon-free nuclear energy *** previous studies,we developed a reactor operation digital twin(RODT).However,non-differentiabilities and discontinuities arise when employing machine learning-based surrogate forward models,challenging traditional gradient-based inverse methods and their *** study investigated deterministic and metaheuristic algorithms and developed hybrid algorithms to address these *** efficient modular RODT software framework that incorporates these methods into its post-evaluation module is presented for comprehensive *** methods were rigorously assessed based on convergence profiles,stability with respect to noise,and computational *** numerical results show that the hybrid KNNLHS algorithm excels in real-time online applications,balancing accuracy and efficiency with a prediction error rate of only 1%and processing times of less than 0.1 ***,algorithms such as FSA,DE,and ADE,although slightly slower(approximately 1 s),demonstrated higher accuracy with a 0.3%relative L_2 error,which advances RODT methodologies to harness machine learning and system modeling for improved reactor monitoring,systematic diagnosis of off-normal events,and lifetime management *** developed modular software and novel optimization methods presented offer pathways to realize the full potential of RODT for transforming energy engineering practices.

关键词： Parameter identification State estimation Reactor operation digital twin Reduced order model Inverse problem

Cobalt-Catalyzed Switchable[4+1]and[4+1+1]Spirocyclization of Aromatic Amides with 2-Diazo-1H-indene-1,3(2H)-dione:Access to Spiro Indene-2,1'-isoindolinones and Spiro Isochroman-3,1'-isoindolinones

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Chinese Journal of Chemistry 2024年第4期42卷 363-369页

作者： bin li Mengmeng Xie jingyu li Nana Shen Xinying Zhang Xuesen Fan State Key Laboratory of Antiviral Drugs Pingyuan LaboratoryKey Laboratory of Green Chemical Media and ReactionsKey Laboratory for Yellow River and Huai River Water Environmental Pollution ControlMinistry of EducationSchool of EnvironmentSchool of Chemistry and Chemical EngineeringHenan Normal UniversityXinxiangHenan453007 China

Herein,we report a condition-controlled divergent synthesis of spiro indene-2,1'-isoindolinones and spiro isochroman-3,1'-isoindolinones through cobalt-catalyzed formal[4+1]and[4+1+1]spirocyclization of aromatic amides with 2-diazo-1H-indene-1,3(2H)-*** the reaction is carried out under air in ethyl acetate,spiro indene-2,1'-isoindolinones are formed through Co(II)-catalyzed C—H/N—H[4+1]*** the reaction is run under O2 in CH3CN,on the other hand,spiro isochroman-3,1'-isoindolinones are generated through Baeyer-Villiger oxidation of the in situ formed spiro indene-2,1'-isoindolinones with O2 as a cheaper and environmental-friendly oxygen *** general,these protocols have advantages such as using non-precious and earth-abundant metal catalyst,no extra additive,high efficiency and regioselectivity.A gram-scale synthesis and the removal of the directing group further highlight its utility.

关键词： Spiro indene-2,1'-isoindolinones Spiro isochroman-3,1'-isoindolinones 3d Transition metals Cobalt-catalyzed C-H Activation Switchable[4+1]and[4+1+1]spirocyclization Aromatic amides 2-Diazo-1H-indene-1,3(2H)-dione

Uniform blow-up profiles and boundary layer for a parabolic system with localized nonlinear reaction terms

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Science china mathematics 2005年第2期48卷 185-197页

作者： li Huiling & WANG Mingxin department of mathematics, Southeast university, Nanjing 210018, china department of mathematics, Xuzhou normal university, Xuzhou 221116, china 1. department of mathematics Southeast University 210018 Nanjing China 2. department of mathematics Xuzhou Normal University 221116 Xuzhou China

This paper deals with the blow-up properties of the solution to a semilinear parabolic system with localized nonlinear reaction terms, subject to the null Dirichlet boundary condition. We first give sufficient conditions for that the classical solution blows up in the finite time, secondly give necessary conditions and a sufficient condition for that two components blow up simultaneously, and then obtain the uniform blow-up profiles in the interior. Finally we describe the asymptotic behavior of the blow-up solution in the boundary layer.

关键词： parabolic system, localized nonlinear reaction terms, blow-up profiles, boundary layer size.

ON MATRIX UNITARILY INVARIANT NORM CONDITION NUMBER

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Journal of Computational mathematics 1998年第2期16卷 121-128页

作者： Dao-sheng Zheng (department of mathematics, East china normal university, Shanghai 200062, china) E china normal Univ Dept Math Shanghai 200062 Peoples R China

In this paper, the unitarily invariant norm \\.\\ on C-mxn is used. We first discuss the problem under what case, a rectangular matrix A has minimum condition number K(A) = \\A\\ \\A(+)\\, where A(+) designates the Moore-Penrose inverse of A; and under what condition, a square matrix A has minimum condition number for its eigenproblem? Then we consider the second problem, i.e., optimum of K(A) = \\A\\ \\A(-1)\\(2) in error estimation.

关键词： matrix unitarily invariant norm condition number

Difference in microstructural characteristics of stamp-charged coke and gravity-charged coke with approximate macroscopic performance

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Journal of Iron and Steel Research International 2024年第5期31卷 1050-1062页

作者： Chong Zou Zheng-yan Huang jian-yun li bin li Shi-wei liu Yuan She School of Metallurgical Engineering Xi’an University of Architecture and TechnologyXi’an710311ShaanxiChina Technical Center of Shandong Iron and Steel Co. Ltd.(Laiwu Branch)Jinan271104ShandongChina

The microstructural characteristics including optical texture,porosity and pore structure and chemical structure of stamp-charged coke(SCC)and gravity-charged coke(GCC)with similar conventional macro-indicators were investigated,and the properties including micro-strength,reactivity of coke matrix and that after alkali enrichment were comparatively studied by various characterization *** anisotropic structure of SCC is composed of high content of fine mosaic texture,while the content of medium mosaic texture,coarse texture and fibrous texture is *** statistical average shows that the fine mosaic average of SCC(24.89%)is 3.78 times the GCC average(6.58%),and the coarse mosaic average(1.24%)is only about 1/3 of the GCC average(3.43%).The porosity of SCC is lower than that of GCC,but tamping process does not lead to the fact that the number of closed pores of SCC is significantly lower than that of *** the structure of SCC is compact,its pore number is large and the pore wall is *** of coke with diameter less than 150 nm seem unaffected by tamping *** aromatic structure of SCC was less ordered than that of GCC,which was speculated to be related to the addition of more low metamorphic coal in *** microscopic strength and structural strength of SCC are lower than those of *** reactivity of coke matrix is affected by the specific surface area,but it is not the determining factor of its *** improvement in dissolution reactivity of coke after potassium enrichment is independent of coke type.

关键词： Stamp-charged coke Optical texture Porosity Microstructure Reactivity

Point Cloud Classification Using Content-Based Transformer via Clustering in Feature Space

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IEEE/CAA Journal of Automatica Sinica 2024年第1期11卷 231-239页

作者： Yahui liu bin Tian Yisheng Lv lingxi li Fei-Yue Wang the State Key Laboratory for Management and Control of Complex Systems Institute of AutomationChinese Academy of SciencesBeijing 100190 the School of Artificial Intelligence University of Chinese Academy of SciencesBeijing 100190 IEEE the Transportation and Autonomous Systems Institute(TASI)and the department of Electrical and Computer Engineering Purdue School of Engineering and TechnologyIndiana University-Purdue University Indianapolis(IUPUI)Indianapolis 46202 USA

Recently, there have been some attempts of Transformer in 3D point cloud classification. In order to reduce computations, most existing methods focus on local spatial attention,but ignore their content and fail to establish relationships between distant but relevant points. To overcome the limitation of local spatial attention, we propose a point content-based Transformer architecture, called PointConT for short. It exploits the locality of points in the feature space(content-based), which clusters the sampled points with similar features into the same class and computes the self-attention within each class, thus enabling an effective trade-off between capturing long-range dependencies and computational complexity. We further introduce an inception feature aggregator for point cloud classification, which uses parallel structures to aggregate high-frequency and low-frequency information in each branch separately. Extensive experiments show that our PointConT model achieves a remarkable performance on point cloud shape classification. Especially, our method exhibits 90.3% Top-1 accuracy on the hardest setting of ScanObjectN N. Source code of this paper is available at https://***/yahuiliu99/PointC onT.

关键词： Content-based Transformer deep learning feature aggregator local attention point cloud classification

Extremal problems on the Hua domain of the first type

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Science china mathematics 2005年第z1期48卷 343-354页

作者： SU jianbing & YIN Weiping mathematics department, Xuzhou normal university, Xuzhou 221116, china mathematics department, Capital normal university, Beijing 100037, china 1. mathematics department Xuzhou Normal University 221116 Xuzhou China 2. mathematics department Capital Normal University 100037 Beijing China

In this paper we study some extremal problems between the Hua domain of the first type and the unit ball.

关键词： extremal problem, Hua domain of the first type, minimal circumscribed Hermitian ellipsoid.