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The restricted EM algorithm under linear inequalities in a linear model with missing data

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Science china mathematics 2005年第6期48卷 819-828页

作者： ZHENG Shurong, SHI Ningzhong & GUO Jianhua school of mathematics and Statistics, Northeast Normal university, changchun 130024, china Institute of mathematics, jilin university, changchun 130012, china 1. school of mathematics and Statistics Northeast Normal University 130024 Changchun China 2. Institute of mathematics Jilin University 130012 Changchun China

This paper discusses the maximum likelihood estimate of β under linear inequalities A0β≥ a in a linear model with missing data, proposes the restricted EM algo rithm and proves the convergence.

关键词： EM algorithm, linear model, maximum likelihood estimate, missing data.

Arnold's theorem on properly degenerate systems with the Russmann nondegeneracy

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Science china mathematics 2005年第12期48卷 1656-1669页

作者： HAN Yuecai & LI Yong College of mathematics, jilin university, changchun 130012, china 1. College of mathematics Jilin University 130012 Changchun China

In this paper, we investigate the persistence of invariant tori for the nearly in-tegrable Hamiltonian system H(x,y) = h(y) + εp(x,y) + ε2Q(x,y), where h(y) and εp(x,y) satisfy the Russmann non-degenerate condition. Mainly we overcome the difficulties that the order of the parameter E in the perturbation ε2Q(x,y) is not enough and that the measure estimate involves in parts of frequencies with small parameter.

关键词： Arnold’s theorem the Russmann non-degenerate condition.

Towards advanced zinc anodes by interfacial modification strategies for efficient aqueous zinc metal batteries

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Journal of Energy Chemistry 2024年第6期93卷 79-110,I0003页

作者： changchun Fan Weijia Meng Jiaye Ye Key Laboratory of Bio-Inspired Smart Interfacial Science and Technology Ministry of EducationSchool of ChemistryBeihang UniversityBeijing 100191China Shaanxi Key Laboratory of New Transportation Energy and Automotive Energy Saving School of Energy and Electrical EngineeringChang’an UniversityXi’an 710061ShaanxiChina school of Chemistry and Physics Faculty of ScienceQueensland University of TechnologyBrisbaneQLD 4001Australia Centre for Materials Science Queensland University of TechnologyBrisbaneQLD 4001Australia

Developing sustainable and clean energy sources(e.g.,solar,wind,and tide energy)is essential to achieve the goal of carbon *** to the discontinuous and inco nsistent nature of common clean energy sources,high-performance energy storage technologies are a critical part of achieving this *** zinc metal batteries(AZMBs)with inherent safety,low cost,and competitive performance are regarded as one of the promising candidates for grid-scale energy ***,zinc metal anodes(ZMAs)with irreversible problems of dendrite growth,hydrogen evolution reaction,self-corrosio n,and other side reactions have seriously hindered the development and commercialization of *** increasing number of researchers are focusing on the stability of ZMAs,so assessing the effectiveness of existing research strategies is critical to the development of *** review aims to provide a comprehensive overview of the fundamentals and challenges of *** rch strategies for interfacial modification of ZMAs are systematically *** features of artificial interfacial coating and in-situ interfacial coating of ZMAs are compared and discussed in detail,as well as the effect of modified interfacial ZMA on the full-battery ***,perspectives are provided on the problems and challenges of *** review is expected to offer a constructive reference for the further development and commercialization of AZMBs.

关键词： Aqueous zinc metal batteries Zinc metal anode Interfacial modification Artificial interfacial coating In-situ interfacial coating

Quantifying quantum entanglement via machine learning models

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Communications in Theoretical Physics 2024年第7期76卷 52-56页

作者： changchun Feng Lin Chen LMIB(Beihang university) Ministry of EducationBeijing 100191China school of Mathematical Sciences Beihang UniversityBeijing 100191China International Research Institute for Multidisciplinary Science Beihang UniversityBeijing 00191China

Quantifying entanglement measures for quantum states with unknown density matrices is a challenging *** learning offers a new perspective to address this *** training machine learning models using experimentally measurable data,we can predict the target entanglement *** this study,we compare various machine learning models and find that the linear regression and stack models perform better than *** investigate the model's impact on quantum states across different dimensions and find that higher-dimensional quantum states yield better ***,we investigate which measurable data has better predictive power for target entanglement *** correlation analysis and principal component analysis,we demonstrate that quantum moments exhibit a stronger correlation with coherent information among these data features.

关键词： quantum information entanglement predict machine learning coherence

On higher analogues of Courant algebroids

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Science china mathematics 2011年第3期54卷 437-447页

作者： BI YanHui1 & SHENG YunHe2,3 1Department of mathematics and LMAM, Peking university, Beijing 100871, china 2school of mathematics, jilin university, changchun 130012, china 3school of mathematics, Dalian university of Technology, Dalian 116024, china 1. Department of mathematics and LMAM Peking University Beijing 100871 China2. School of Mathematics Jilin University Changchun 130012 China3. School of Mathematics Dalian University of Technology Dalian 116024 China

In this paper, we study the algebraic properties of the higher analogues of Courant algebroid structures on the direct sum bundle TM ⊕∧nT*M for an m-dimensional manifold. As an application, we revisit Nambu-Poisson structures and multisymplectic structures. We prove that the graph of an (n + 1)-vector field π is closed under the higher-order Dorfman bracket iff π is a Nambu-Poisson structure. Consequently, there is an induced Leibniz algebroid structure on ∧nT*M. The graph of an (n+1)-form ω is closed under the higher-order Dorfman bracket iff ω is a premultisymplectic structure of order n, i.e., dω = 0. Furthermore, there is a Lie algebroid structure on the admissible bundle A  ∧nT*M. In particular, for a 2-plectic structure, it induces the Lie 2-algebra structure given in (Baez, Hoffnung and Rogers, 2010).

关键词： higher analogues of Courant algebroids multisymplectic structures Nambu-Poisson structures Leibniz algebroids

A scheme for the RCP pattern of the nano-structure

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Communications in Nonlinear Science and Numerical Simulation 2001年第4期6卷 201-204页

作者： Guangwu YAN, Hongxue QU and Bing YAN Department of mathematics, jilin university, changchun 130012, china Institute of Atomic and Molecular Physics, jilin university. changchun 130023, china Department of mathematics Juin University Changchun 130012 China Inst. of Atom. and Molecular Physics Jilin University Changchun 130023 China

A new scheme for the Random-Continuous-Pile (RCP) pattern is proposed to simulate a two-dimensional structure The RCP pattern is plotted.

关键词： RCP pattern. Maxwell distribution balls-filling

A method of combining SE-tree to compute all minimal hitting sets

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Progress in Natural Science:Materials International 2006年第2期16卷 169-174页

作者： ZHAO Xiangfu and OUYANG Dantong (school of Computer Science and Technology, jilin university, changchun 130012, china Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education, changchun 130012, china) [a]school of Computer Science and Technology Jilin University Changchun China

In model-based diagnosis, the candidate diagnostic results are generally characterized by all minimal hitting sets for the collection of all conflict sets. In this paper, a new method is proposed to judge a hitting set by the number of conflict sets corresponding to components, and the computing procedure is formalized by combining revised SE-tree (set enumeration tree) with closed nodes to generate all minimal hitting sets. Results show that because closed nodes are added into SE-tree, the search efficiency is highly improved. Furthermore, the proposed method is easy to be understood and implemented. Compared with other effective algorithms with completeness in some experimental tests, the diagnosis efficiency of our proposed method is higher, particularly for single- and double-fault diagnosis.

关键词： model-based diagnosis conflict set minimal hitting set set enumeration tree.

Kernel model-based diagnosis

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Progress in Natural Science:Materials International 2002年第2期12卷 63-67页

作者： OUYANG Dantong(Department of Computer Science, jilin university, changchun 130012, china) jilin Univ Dept Comp Sci Changchun 130012 Peoples R China

The methods for computing the kernel consistency-based diagnoses and the kernel abductive diagnoses are only suited for the situation where part of the fault behavioral modes of the components are known. The characterization of the kernel model-based diagnosis based on the general causal theory is proposed, which can break through the limitation of the above methods when all behavioral modes of each component are known. Using this method, when observation subsets deduced logically are respectively assigned to the empty or the whole observation set, the kernel consistency-based diagnoses and the kernel abductive diagnoses can deal with all situations. The direct relationship between this diagnostic procedure and the prime implicants/implicates is proved, thus linking theoretical result with implementation.

关键词： model-based diagnosis general causal theory prime implicant/implicate diagnostic space.

NUMERICAL COMPUTATION OF BOUNDED SOLUTIONS FORA SEMILINEAR ELLIPTIC EQUATION ON AN INFINITE STRIP

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Journal of Computational mathematics 1999年第2期17卷 159-170页

作者： Fu-ming Ma(Department of mathematics, jilin ’university, changchun 130023, china) 吉林大学数学系吉林长春

In this paper, we consider the computation of bounded solutions of a semilinear elliptic equation on an infinite strip. The dynamical system approach and reduction on center manifold are used to overcome the difficult... 详细信息

关键词： numerical method nonlinear PDE center manifold