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Left-Invariant Minimal Unit Vector Fields on the Solvable Lie Group

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Chinese Annals of mathematics,Series B 2023年第1期44卷 67-80页

作者： Shaoxiang ZHANG Ju TAN college of mathematics and systems science Shandong University of Science and TechnologyQingdao 266590ShandongChina School of Microelectronics and Data science Anhui University of TechnologyMaanshan 243032AnhuiChina

Bozek(1980)has introduced a class of solvable Lie groups Gn with arbitrary odd dimension to construct irreducible generalized symmetric Riemannian space such that the identity component of its full isometry group is *** this article,the authors provide the set of all left-invariant minimal unit vector fields on the solvable Lie group Gn,and give the relationships between the minimal unit vector fields and the geodesic vector fields,the strongly normal unit vectors respectively.

关键词： Solvable Lie groups Lagrangian multiplier method Minimal unit vector fields Geodesic vector fields Strongly normal unit vectors

Finite-time stabilization of nonlocal Lipschitzian stochastic time-varying nonlinear systems with Markovian switching

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science China(Information sciences) 2022年第11期65卷 196-216页

作者： Gui-Hua ZHAO Shu-Jun LIU college of science University of Shanghai for Science and Technology college of mathematics Sichuan University

In this study, we investigate the stochastic finite-time stability theory and finite-time stabilization of stochastic time-varying nonlinear systems with Markovian switching in the sense of weak solutions. First,we present the stochastic finite-time stability theory under the framework of weak solutions: the existence of weak solutions and stochastic finite-time stability theorems for stochastic time-varying nonlinear systems with Markovian switching. Second, for a class of high-order stochastic nonlinear systems with Markovian switching, a finite-time stabilization controller is constructively designed, and the trivial weak solution of a closed-loop system is proven to be globally finite-time stable in probability. The effectiveness of the proposed finite-time control method is illustrated by a numerical example.

关键词： stochastic time-varying nonlinear systems Markovian switching weak solutions stochastic finite-time stability finite-time control

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A NEW CONSTRAINTS IDENTIFICATION TECHNIQUE-BASED QP-FREE ALGORITHM FOR THE SOLUTION OF INEQUALITY CONSTRAINED MINIMIZATION PROBLEMS

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Journal of Computational mathematics 2006年第5期24卷 591-608页

作者： Chang-yin Zhou Guo-ping He Yong-li Wang Department of mathematics Shanghai Jiao Tong University Shanghai 200240 China college of Information science and Engineering Shandong University of Science and Technology Qingdao 266510 China college of Information science and Engineering Shandong University of Science and Technology Qingdao 266510 China

In this paper, we propose a feasible QP-free method for solving nonlinear inequality constrained optimization problems. A new working set is proposed to estimate the active set. Specially, to determine the working set, the new method makes use of the multiplier information from the previous iteration, eliminating the need to compute a multiplier function. At each iteration, two or three reduced symmetric systems of linear equations with a common coefficient matrix involving only constraints in the working set are solved, and when the iterate is sufficiently close to a KKT point, only two of them are involved. Moreover, the new algorithm is proved to be globally convergent to a KKT point under mild conditions. Without assuming the strict complementarity, the convergence rate is superlinear under a condition weaker than the strong second-order sufficiency condition. Numerical experiments illustrate the efficiency of the algorithm.

关键词： QP-free method Optimization Global convergence Superlinear convergence,Constraints identification technique.

A Separation Theorem for Stochastic Singular Linear Quadratic Control Problem with Partial Information

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Acta Mathematicae Applicatae Sinica 2013年第2期29卷 303-314页

作者： Hong-ji MA Ting HOU college of science Shandong University of Science and Technology Department of systems and Control Beijing University of Aeronautics and Astronautics

In this paper, we provide a separation theorem for the singular linear quadratic （LQ） control problem of ItS-type linear systems in the case of the state being partially observable. Above all, the Kalmam Bucy filtering of the dynamics is given by means of Girsanov transformation, by which the suboptimal feedback control of the LQ problem is determined. Furthermore, it is shown that the well-posedness of the LQ problem is equivalent to the solvability of a generalized differential Riccati equation （GDRE）.

关键词： singular optimal control Kalman-Bucy filtering separation theorem linear systems generalizeddifferential Riccati equation

A Few Discrete Lattice systems and Their Hamiltonian Structures,Conservation Laws

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Communications in Theoretical Physics 2017年第4期67卷 396-406页

作者：郭秀荣张玉峰张祥芝岳嵘 college of mathematics China University of Mining and Technology Basic Courses Shandong University of Science and Technology

With the help of three shift operators and r-matrix theory, a few discrete lattice systems are obtained which can be reduced to the well-known Toda lattice equation with a constraint whose Hamiltonian structures are generated by Poisson tensors of some induced Lie–Poisson bracket. The recursion operators of these lattice systems are constructed starting from Lax representations. Finally, reducing the given shift operators to get a simpler one and its expanding shift operators, we produce a lattice system with three vector fields whose recursion operator is given. Furthermore,we reduce the lattice system with three vector fields to get a lattice system whose Lax pair and conservation laws are obtained, respectively.

关键词： discrete lattice system r-matrix Hamiltonian structure

ON THE OBSERVABILITY AND DETECTABILITY OF LINEAR STOCHASTIC systems WITH MARKOV JUMPS AND MULTIPLICATIVE NOISE

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Journal of systems science & Complexity 2010年第1期23卷 102-115页

作者： Yuanhua NI Weihai ZHANG Haitao FANG Key Laboratory of systems and Control Institute of Systems Science Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China. college of Information and Electrical Engineering Shandong University of Science and Technology Qingdao China.

This paper presents the notions of exact observability and exact detectability for Markov jump linear stochastic systems of Ito type with multiplieative noise （for short, MJLSS）. Stochastic Popov-Belevith-Hautus （PBH） Criterions for exact observability and exact detectability are respectively obtained. As an application, stochastic H2/H∞ control for such MJLSS is discussed under exact detectability.

关键词： Exact detectability exact observability Markov jump systems multiplicative noise PBH Criterion stochastic H2/H∞ control.

Vector Loop Algebra and Its Applications to Tu Hierarchy

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Communications in Theoretical Physics 2007年第5期47卷 773-776页

作者： WANG Yan college of Information science and Engineering Shandong University of Science and Technology Qingdao 266510 China Department of mathematics and systems science Taishan University Taian 271021 China

A vector loop algebra and its extended loop algebra are proposed, which are devoted to obtaining the Tu hierarchy. By making use of the extended trace identity, the Harniltonian structure of the Tu hierarchy is constr... 详细信息

关键词： vector loop algebra Hamiltonian structure quadratic identity

Dual Lie bialgebra structures of Poisson types

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science China mathematics 2015年第6期58卷 1151-1162页

作者： SONG Guang'Ai SU YuCai college of mathematics and Information science Shandong Institute of Business and Technology Department of mathematics Tongji University

Let A = F [x, y] be the polynomial algebra on two variables x, y over an algebraically closed field F of characteristic zero. Under the Poisson bracket, A is equipped with a natural Lie algebra structure. It is proven that the maximal good subspace of A* induced from the multiplication of the associative commutative algebra A coincides with the maximal good subspace of A* induced from the Poisson bracket of the Poisson Lie algebra A. Based on this, structures of dual Lie bialgebras of the Poisson type are investigated. As by-products,five classes of new infinite-dimensional Lie algebras are obtained.

关键词： algebra Poisson commutative maximal associative infinite triangular polynomial multiplication subspace

Electrochemical conversion of methane to bridge the gap in the artificial carbon cycle

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Journal of Energy Chemistry 2025年第1期100卷 286-308页

作者： Yuhao Peng Yuefeng Song Ihar Razanau Juanxiu Xiao Wei Xiao Di Hu Guoxiong Wang college of Chemistry and Molecular sciences Hubei Key Laboratory of Electrochemical Power Sources Wuhan University State Key Laboratory of Catalysis Dalian National Laboratory for Clean Energy iChEM (Collaborative Innovation Center of Chemistry for Energy Materials) Dalian Institute of Chemical Physics Chinese Academy of Sciences Laboratory of Physical-Chemical Technologies SSPA Scientific and Practical Materials Research Centre of NAS of Belarus State Key Laboratory of Marine Resources Utilization in South China Sea Collaborative Innovation Center of Marine Science and Technology School of Marine Science and Engineering Hainan University Department of Chemical and Environmental Engineering University of Nottingham Ningbo China

Methane, an abundant one-carbon（C1） resource, is extensively used in the industrial production of vital fuels and value-added chemicals. However, current industrial methane conversion technologies are energy-and carbon-intensive, mainly due to the high activation energy required to break the inert C–H bond, low selectivity, and problematic side reactions, including CO2emissions and coke deposition. Electrochemical conversion of methane（ECM） using intermittent renewable energy offers an attractive solution, due to its modular reactor design and operational flexibility across a broad spectrum of temperatures and pressures. This review emphasizes conversion pathways of methane in various reaction systems, highlighting the significance and advantages of ECM in facilitating a sustainable artificial carbon cycle. This work provides a comprehensive overview of conventional methane activation mechanisms and delineates the complete pathways of methane conversion in electrolysis contexts. Based on surface/interface chemistry, this work systematically analyzes proposed reaction pathways and corresponding strategies to enhance ECM efficiency towards various target products, including syngas, hydrocarbons, oxygenates, and advanced carbon materials. The discussion also encompasses opportunities and challenges for the ECM process, including insights into ECM pathways, rational electrocatalyst design, establishment of benchmarking protocols, electrolyte engineering, enhancement of CH4conversion rates, and minimization of CO2emission.

关键词： Methane Electrochemical conversion Reaction mechanism Catalyst design Electrode Electrocatalysis