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A New Method for Solving Nonlinear Partial Differential Equations Based on Liquid Time-Constant Networks

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Journal of systems science & Complexity 2024年第2期37卷 480-493页

作者： SUN Jiuyun DONG Huanhe FANG Yong College of mathematics and systems science Shandong University of Science and TechnologyQingdao 266590China

In this paper,physics-informed liquid networks(PILNs)are proposed based on liquid time-constant networks(LTC)for solving nonlinear partial differential equations(PDEs).In this approach,the network state is controlled via ordinary differential equations(ODEs).The significant advantage is that neurons controlled by ODEs are more expressive compared to simple activation *** addition,the PILNs use difference schemes instead of automatic differentiation to construct the residuals of PDEs,which avoid information loss in the neighborhood of sampling *** this method draws on both the traveling wave method and physics-informed neural networks(PINNs),it has a better physical ***,the KdV equation and the nonlinear Schr¨odinger equation are solved to test the generalization ability of the *** the best of the authors’knowledge,this is the first deep learning method that uses ODEs to simulate the numerical solutions of PDEs.

关键词： Nonlinear partial differential equations numerical solutions physics-informed liquid networks physics-informed neural networks

Quantum control based on three forms of Lyapunov functions

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Chinese Physics B 2024年第4期33卷 216-222页

作者：俞国慧杨洪礼 College of mathematics and systems science Shandong University of Science and TechnologyQingdao 266590China

This paper introduces the quantum control of Lyapunov functions based on the state distance, the mean of imaginary quantities and state *** this paper, the specific control laws under the three forms are *** is analyzed by the La Salle invariance principle and the numerical simulation is carried out in a 2D test *** calculation process for the Lyapunov function is based on a combination of the average of virtual mechanical quantities, the particle swarm algorithm and a simulated annealing ***, a unified form of the control laws under the three forms is given.

关键词： quantum system Lyapunov function particle swarm optimization simulated annealing algorithms quantum control

On Minor Left Prime Factorization Problem for Multivariate Polynomial Matrices

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Journal of systems science & Complexity 2024年第3期37卷 1295-1307页

作者： LU Dong WANG Dingkang XIAO Fanghui School of mathematics Southwest Jiaotong UniversityChengdu 610031China KLMM Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical sciences University of Chinese Academy of SciencesBeijing 100049China MOE-LCSM School of Mathematics and StatisticsHunan Normal UniversityChangsha 410081China

A new necessary and sufficient condition for the existence of minor left prime factorizations of multivariate polynomial matrices without full row rank is *** key idea is to establish a relationship between a matrix and any of its full row rank *** on the new result,the authors propose an algorithm for factorizing matrices and have implemented it on the computer algebra system *** examples are given to illustrate the effectiveness of the algorithm,and experimental data shows that the algorithm is efficient.

关键词： Free modules Grobner bases minor left prime(MLP) multivariate polynomial matrices polynomial matrix factorizations

Analyses of Political Crisis Impact on Tourism:A Panel Counterfactual Approach with Internet Search Index

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Journal of systems science & Complexity 2024年第4期37卷 1581-1603页

作者： HUANG Bai SUN Yuying YANG Boyu School of Statistics and mathematics Central University of Finance&EconomicsBeijing 102206China academy of mathematics and systems science Chinese Academy of SciencesBeijing 100190China Center for Forecasting science Chinese Academy of SciencesBeijing 100190China School of Economics and Management University of Chinese Academy of SciencesBeijing 100190China

Existing research has shown that political crisis events can directly impact the tourism ***,the current methods suffer from potential changes of unobserved variables,which poses challenges for a reliable evaluation of the political crisis *** paper proposes a panel counterfactual approach with Internet search index,which can quantitatively capture the change of crisis impacts across time and disentangle the effect of the event of interest from the *** also provides a tool to examine potential channels through which the crisis may affect tourist *** research empirically applies the framework to analyze the THAAD event on tourist flows from the Chinese Mainland to South *** highlight the strong and negative short-term impact of the political crisis on the tourists' intentions to visit a *** paper provides essential evidence to help decision-makers improve the management of the tourism crisis.

关键词： Composite search index counterfactual analysis political crisis search query data tourism demand

Fiducial Approach for the Storage Reliability Assessment of Complex Repairable systems

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Journal of systems science & Complexity 2024年第4期37卷 1653-1671页

作者： YANG Yang ZHAO Letian CHEN Siyi YU Dan University of Chinese academy of sciences Beijing 100190China Computer Application Institute of Nuclear Industry Beijing 100142China academy of mathematics and systems science Chinese Academy of SciencesBeijing 100190China

In recent years,there has been a growing focus on high-reliability products in industrial and military *** plays a crucial role in these products,and as a result,research on storage reliability has gained more *** paper specifically targets a class of products with complex structures that require long-term storage,regular testing,and ***,an expression method for system availability is provided based on the reliability structure of the system and the maintenance situation of the constituent equipment in *** the expression of system availability is typically complex and difficult to compute,and the storage life of the system cannot be represented as an explicit function of the reliability indicators of the constituent equipment,it is challenging to evaluate the availability and storage life of repairable *** address this,the paper proposes a comprehensive evaluation methodology for assessing the storage reliability of complex repairable systems based on fiducial *** approach is employed to derive point estimates and determine the lower fiducial limits for both system availability and storage ***,simulation results demonstrate that this comprehensive evaluation method for storage reliability of complex repairable systems is not only convenient but also highly effective.

关键词： Availability fiducial method repairable system storage life

Stability in Inverse Problem of Determining Two Parameters for the Moore-Gibson-Thompson Equation with Memory Terms

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Journal of systems science & Complexity 2024年

作者： FU Songren CHEN Liangbiao ZHANG Ji-Feng Key Laboratory of systems and Control Academy of Mathematics and Systems Science Chinese Academy ofSciences School of Automation and Electrical Engineering Zhongyuan University of Technology Key Laboratory of systems and Control Academy of Mathematics and Systems Science ChineseAcademy of Sciences

In this paper, the authors consider the inverse problem for the Moore-Gibson-Thompson equation with a memory term and variable diffusivity, which introduce a sort of delay in the dynamics,producing nonlocal effects in time. The H¨older stability of simultaneously determining the spatially varying viscosity coefficient and the source term is obtained by means of the key pointwise Carleman estimate for the Moore-Gibson-Thompson equation. For the sake of generality in mathematical tools,the analysis of this paper is discussed within the framework of Riemannian geometry.

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Uniqueness of the Reissner-Nordstrom metric near the null infinity

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science China mathematics 2024年第8期67卷 1933-1956页

作者： Xiaokai He Xiaoning Wu Naqing Xie School of mathematics and Statistics Hunan First Normal UniversityChangsha 410205China Institute of mathematics Academy of Mathematics and Systems Science and Hua Loo-Keng Key Laboratory of MathematicsChinese Academy of SciencesBeijing 100190China School of Mathematical sciences Fudan UniversityShanghai 200433China

In the Newman-Penrose formalism,we prove that the Reissner-Nordstrom metric is the only asymptotically fat,static,axially symmetric,Petrov type-D analytic solution of the electro-vacuum Einstein-Maxwell equations near... 详细信息

关键词： uniqueness theorem Reissner-Nordstrom metric Newman-Penrose formalism

Holder continuous weak solutions of the 2D Boussinesq equation with thermal diffusion

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science China mathematics 2024年第8期67卷 1777-1806页

作者： Tianwen Luo Tao Tao Liqun Zhang Yau Mathematical sciences Center Tsinghua UniversityBeijing 100084China School of mathematics Shandong UniversityJinan 250100China Institute of mathematics Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical sciences University of Chinese Academy of SciencesBeijing 100049China

We show the existence of Holder continuous periodic weak solutions of the 2D Boussinesq equation with thermal diffusion which satisfy the prescribed kinetic *** precisely,for any smooth e(t):[0,1]→R+andε∈(0,110),there exist v∈C 110−ε([0,1]×T2)andθ∈C 1,120−εt 2 C 2,1 x 10−ε([0,1]×T2),which satisfy(1.1)in the sense of distribution and e(t)=ˆT2|v(t,x)|2 dx,∀t∈[0,1].

关键词： 2D Boussinesq equation with thermal diffusion Holder continuous periodic weak solutions prescribed kinetic energy

An infinite-dimensional representation of the Ray-Knight theorems

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science China mathematics 2024年第1期67卷 149-162页

作者： Elie Aidékon Yueyun Hu Zhan Shi School of Mathematical sciences Fudan UniversityShanghai 200433China LAGA UniversitéSorbonne Paris NordVilletaneuse 93430France Institute of Applied mathematics Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China

The classical Ray-Knight theorems for the Brownian motion determine the law of its local time process either at the first hitting time of a given value a by the local time at the origin,or at the first hitting time of a given position b by the Brownian *** extend these results by describing the local time process jointly for all a and b,by means of the stochastic integral with respect to an appropriate white *** result applies toμ-processes,and has an immediate application:aμ-process is the height process of a Feller continuous-state branching process(CSBP)with immigration(Lambert(2002)),whereas a Feller CSBP with immigration satisfies a stochastic differential equation(SDE)driven by a white noise(Dawson and Li(2012));our result gives an explicit relation between these two descriptions and shows that the SDE in question is a reformulation of Tanaka’s formula.

关键词： Ray-Knight theorem μ-process white noise Tanaka's formula