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ANALYSIS OF TRIPARTITE GAME IN POWER SYSTEMS BASED ON UNCERTAIN NASH EQUILIBRIUM THEORY

UPB Scientific Bulletin, Series A: Applied Mathematics and Physics 2025年第1期87卷 117-128页

作者： Wu, Liang Yan, Xiaolin Yao, Zhangsong Zhao, Teng School of Management and Ningxia Key Laboratory of intelligent information and Big Data Processing North Minzu University Ningxia Yinchuan750021 China School of Mathematical Sciences Tiangong University Tianjin300387 China School of Information Engineering Nanjing Xiaozhuang University Nanjing211171 China School of Mathematics and Information Science North Minzu University Ningxia Yinchuan750021 China

Power systems serve as the fundamental infrastructure for the socioeconomic development of modern societies. Researching power systems can stimulate the growth of the power industry and contribute to the sustainable development of society. This paper aims to address uncertainties prevalent in power systems, including extreme weather events, disruptions in renewable energy supply, and adjustments in economic policies. To achieve this objective, an uncertain Nash equilibrium model is established. Subsequently, a game theoretic analysis is conducted to maximize the interests of users, grid companies, and proxy purchasers. Under the condition of not necessarily continuous differentiability, the Riemann-Stieltjes discrete approximation method has been proposed. The difficulty of calculating the expectation of the optimal revenue function has been resolved. Weak first-order equilibrium condition based on Clarke’s generalized gradient, the convergence and convergence rate of uncertain Nash equilibrium solutions are proved. © 2025, Politechnica University of Bucharest. All rights reserved.

关键词： power system tripartite game uncertain Nash equilibrium uncertainty theory

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A numerical magnitude aware multi-channel hierarchical encoding network for math word problem solving

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Neural Computing and Applications 2025年第3期37卷 1651-1672页

作者： Xu, Junjie Chen, Yuzhong Xiao, Lingsheng Liao, Hongmiao Zhong, Jiayuan Dong, Chen College of Computer and Data Science Fuzhou University Fujian Province Fuzhou350108 China Engineering Research Center of Big Data Intelligence Ministry of Education Fuzhou China Fujian Provincial Key Laboratory of Network Computing and Intelligent Information Processing Fujian Province Fuzhou350108 China

Math word problem (MWP) represents a critical research area within reading comprehension, where accurate comprehension of math problem text is crucial for generating math expressions. However, current approaches still grapple with unresolved challenges in grasping the sensitivity of math problem text and delineating distinct roles across various clause types, and enhancing numerical representation. To address these challenges, this paper proposes a Numerical Magnitude Aware Multi-Channel Hierarchical Encoding Network (NMA-MHEA) for math expression generation. Firstly, NMA-MHEA implements a multi-channel hierarchical context encoding module to learn context representations at three different channels: intra-clause channel, inter-clause channel, and context-question interaction channel. NMA-MHEA constructs hierarchical constituent-dependency graphs for different levels of sentences and employs a Hierarchical Graph Attention Neural Network (HGAT) to learn syntactic and semantic information within these graphs at the intra-clause and inter-clause channels. NMA-MHEA then refines context clauses using question information at the context-question interaction channel. Secondly, NMA-MHEA designs a number encoding module to enhance the relative magnitude information among numerical values and type information of numerical values. Experimental results on two public benchmark datasets demonstrate that NMA-MHEA outperforms other state-of-the-art models. © The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature 2024.

关键词： Semantics

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Deep learning for parameter identification of nonlinear dynamical system driven by fractional Brownian motion

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Nonlinear Dynamics 2025年 1-20页

作者： Hou, Wentao Ma, Shaojuan School of Mathematics and Information Science North Minzu University Yinchuan China Department of Mathematics and Information Technology Yuncheng University Yuncheng China Ningxia Key Laboratory of Intelligent Information and Big Data Processing Yinchuan China

Accurate parameters identification in nonlinear dynamical systems is crucial for understanding complex phenomena. Fractional Brownian motion is widely used in modeling nonlinear systems due to its long memory, but it also complicates parameter identification. Traditional methods typically rely on linear models or assume Gaussian white noise, which makes them less effective for handling such complex systems. Although data-driven methods have been proposed, most of them utilize simple network architectures and focus primarily on identifying the Hurst exponent or parameters of linear systems. This paper presents a deep learning-based parameter identifier capable of jointly identifying all parameters of a nonlinear dynamical system driven by fractional Brownian motion. Firstly, a new parameter identifier (Transformer-Bidirectional Long Short-Term Memory Neural Network) is constructed by combining the advantages of Transformer in dealing with long-term dependence and Bidirectional Long Short-Term Memory in extracting local features. We then incorporate fractional Brownian motion as the random effect in the nonlinear dynamical system and provide three examples to simulate the system. Finally, the proposed identifier is used to identify parameters in the three systems individually, and its performance is compared to that of the Convolutional Neural Network-Bidirectional Long Short-Term Memory-Attention Neural Network and the Parameter Estimation Neural Network to demonstrate its effectiveness. Taking Example 3 and using the mean absolute error to evaluate identification accuracy. The mean absolute error values for the Transformer-Bidirectional Long Short-Term Memory Neural Network are 0.0171, 0.0699, 0.0328 and 0.0851, which are significantly better than the Convolutional Neural Network-Bidirectional Long Short-Term Memory-Attention Neural Network, with values of 0.0277, 0.1054, 0.0494 and 0.1037, and the Parameter Estimation Neural Network, with values of 0.0419, 0.1265,

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EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR UNCERTAIN NONLINEAR SWITCHED SYSTEMS WITH V-N JUMPS

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UPB Scientific Bulletin, Series A: Applied Mathematics and Physics 2025年第1期87卷 129-140页

作者： Jia, Zhifu Li, Cunlin School of Mathematics and Physics Suqian University Suqian223800 China [Ningxia Key Laboratory of intelligent information and Big Data Processing Governance and Social Management Research Center of Northwest Ethnic Regions North Minzu University Yinchuan China

In this paper, an uncertain nonlinear switched system with V-n jumps, characterized by its sensitivity to subjective uncertainties, is modeled using uncertain differential equations with V-n jumps. To account for the discontinuous jump behavior in each subsystem, a V-n jumps process associated with an uncertain Z-n jumps variable, defined by a jump uncertainty distribution, is introduced. Under the assumptions of linear growth and Lipschitz conditions, an existence and uniqueness theorem for the solutions of uncertain nonlinear switched systems with V-n jumps is established and rigorously proven. An illustrative example is provided to demonstrate the effectiveness and applicability of the theoretical results. © 2025, Politechnica University of Bucharest. All rights reserved.

关键词： Uncertain systems

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Triple Synergistic Modulation via Sn Doping in Tetrahedrites: Electronic Structure, DOS, and Scattering Engineering for a High Thermoelectric Performance

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ACS Applied Materials and Interfaces 2025年第19期17卷 28384-28394页

作者： Huang, Lulu Wan, Shanhong Wu, Junyang Wang, Binbin Yu, Hongsong Liu, Yu Zhang, Jinhua Wu, Yucheng Zhang, Xuemei Yan, Jian Zhang, Jian School of Materials Science and Engineering Hefei University of Technology Hefei230009 China Engineering Research Center of High Performance Copper Alloy Materials and Processing Ministry of Education Hefei University of Technology Hefei230009 China Anhui Province Engineering Research Center of Flexible and Intelligent Materials School of Chemistry and Chemical Engineering Hefei University of Technology Hefei230009 China Infrared and Low Temperature Plasma Key Laboratory of Anhui Province College of Electronic Engineering National University of Defense Technology Hefei230037 China School of Physics and Electronic Information Engineering Ningxia Normal University Guyuan756000 China Key Laboratory of Materials Physics Institute of Solid State Physics Chinese Academy of Sciences Hefei230031 China

Achieving a high power factor and low lattice thermal conductivity is crucial for improving the thermoelectric performance. The eco-friendly Cu12Sb4S13 tetrahedrite inherently exhibits a high power factor (∼10-14 μW cm-1 K-2) and low thermal conductivity (0.5-1.00 W m-1 K-1), but these properties also impose significant limitations for further performance enhancement. To overcome these challenges, researchers have explored strategies such as codoping/synergistic element doping and nanocomposites. In this work, we demonstrate that Sn doping at the Sb site in Cu12Sb4S13 (without the use of nanocomposites) enables the synergistic modulation of both the electronic and thermal properties. The Sn doping increases the hole concentration and enhances the density of states (DOS), leading to a marked improvement in the power factor (at 750 K), 12 μW cm-1 K-2 for x = 0 to 16 μW cm-1 K-2 for x = 0.04. Simultaneously, Sn doping induces strong phonon scattering, which lowers thermal conductivity by ∼69% (at 750 K). This synergistic modulation of the electronic structure, DOS, and scattering mechanisms results in a significant enhancement in the thermoelectric performance. The optimized Cu12Sb3.96Sn0.04S13 sample exhibits an exceptional figure of merit (ZT) of 1.26 at 750 K, representing a 126% increase compared to pristine Cu12Sb4S13. These findings demonstrate the effectiveness of Sn doping in simultaneously optimizing the electrical and thermal properties of Cu12Sb4S13 through the synergistic modulation of the electronic structure, density of states, and phonon scattering mechanisms. © 2025 American Chemical Society.

关键词： Phonon scattering

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L_(1)-Smooth SVM with Distributed Adaptive Proximal Stochastic Gradient Descent with Momentum for Fast Brain Tumor Detection

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Computers, Materials & Continua 2024年第5期79卷 1975-1994页

作者： Chuandong Qin Yu Cao Liqun Meng School of Mathematics and Information Science North Minzu UniversityYinchuan750021China Ningxia Key Laboratory of Intelligent Information and Big Data Processing Yinchuan750021China

Brain tumors come in various types,each with distinct characteristics and treatment approaches,making manual detection a time-consuming and potentially ambiguous *** tumor detection is a valuable tool for gaining a deeper understanding of tumors and improving treatment *** learning models have become key players in automating brain tumor *** descent methods are the mainstream algorithms for solving machine learning *** this paper,we propose a novel distributed proximal stochastic gradient descent approach to solve the L_(1)-Smooth Support Vector Machine(SVM)classifier for brain tumor ***,the smooth hinge loss is introduced to be used as the loss function of *** avoids the issue of nondifferentiability at the zero point encountered by the traditional hinge loss function during gradient descent ***,the L_(1) regularization method is employed to sparsify features and enhance the robustness of the ***,adaptive proximal stochastic gradient descent(PGD)with momentum,and distributed adaptive PGDwithmomentum(DPGD)are proposed and applied to the L_(1)-Smooth *** computing is crucial in large-scale data analysis,with its value manifested in extending algorithms to distributed clusters,thus enabling more efficient processing ofmassive amounts of *** DPGD algorithm leverages Spark,enabling full utilization of the computer’s multi-core *** to its sparsity induced by L_(1) regularization on parameters,it exhibits significantly accelerated convergence *** the perspective of loss reduction,DPGD converges faster than *** experimental results show that adaptive PGD withmomentumand its variants have achieved cutting-edge accuracy and efficiency in brain tumor ***-trained models,both the PGD andDPGD outperform other models,boasting an accuracy of 95.21%.

关键词： Support vector machine proximal stochastic gradient descent brain tumor detection distributed computing

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A NEW GLOBAL OPTIMIZATION ALGORITHM FOR MIXED-INTEGER QUADRATICALLY CONSTRAINED QUADRATIC FRACTIONAL PROGRAMMING PROBLEM

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Journal of Computational Mathematics 2024年第3期42卷 784-813页

作者： Bo Zhang Yuelin Gao Xia Liu Xiaoli Huang School of Civil and Hydraulic Engineering School of Mathematics and StatisticsNingxia UniversityYinchuan 750021China School of Mathematics and Information Science North Minzu UniversityYinchuan 750021China Ningxia Province Key Laboratory of Intelligent Information and Data Processing Yinchuan 750021China School of Mathematics and Statistics Ningxia UniversityYinchuan 750021China

The mixed-integer quadratically constrained quadratic fractional programming(MIQCQFP)problem often appears in various fields such as engineering practice,management science and network ***,most of the solutions to such problems are often designed for their unique *** paper puts forward a new global optimization algorithm for solving the problem *** first convert the MIQCQFP into an equivalent generalized bilinear fractional programming(EIGBFP)problem with integer ***,we linearly underestimate and linearly overestimate the quadratic functions in the numerator and the denominator respectively,and then give a linear fractional relaxation technique for EIGBFP on the basis of non-negative *** that,combining rectangular adjustment-segmentation technique and midpointsampling strategy with the branch-and-bound procedure,an efficient algorithm for solving MIQCQFP globally is ***,a series of test problems are given to illustrate the effectiveness,feasibility and other performance of this algorithm.

关键词： Global optimization Branch and bound Quadratic fractional programming Mixed integer programming

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Asymptotic solution of a wide moving jam to a class of higher-order viscous traffic flow models

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Applied Mathematics and Mechanics(English Edition) 2018年第5期39卷 609-622页

作者： Chunxiu WU College of Mathematics and Computer Science Quanzhou Normal UniversityQuanzhou 362000Fujian ProvinceChina Fujian Provincial Key Laboratory of Data Intensive Computing Quanzhou 362000Fujian ProvinceChina Key Laboratory of Intelligent Computing and Information Processing Quanzhou 362000Fujian ProvinceChina

The boundary-layer method is used to study a wide moving jam to a class of higher-order viscous models. The equations for characteristic parameters are derived to determine the asymptotic solution. The sufficient and essential conditions for the wide moving jam formation are discussed in detail, respectively, and then used to prove or disprove the existence of the wide moving jam solutions to many well-known higher-order models. It is shown that the numerical results agree with the analytical results.

关键词： higher-order traffic flow model wide moving jam boundary-layer method,weighted essentially nonoscillatory (WENO) scheme

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Clustering data stream with rough set 8

Clustering data stream with rough set

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8th International Conference on Computing and Pattern Recognition, ICCPR 2019

作者： Wan, Renxia Li, Yanyan Ningxia Key Laboratory of Intelligent Information and Big Data Processing North Minzu University Yinchuan Ningxia750021 China

ISBN: (纸本)9781450376570

In this paper, the upper and lower approximations of rough set are introduced to describe the micro-cluster feature in the procedure of clustering uncertain data stream. The proposed algorithm employs presents the micro-cluster timestamp with the time decay and uses agglomerative clustering method to emerge new cluster in the buffer of outliers. Experimental results show that the proposed algorithm can generate natural clusters and outperforms the existing method in term of accuracy. © 2019 Association for Computing Machinery.

关键词： Approximation algorithms

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Overview of Chinese electronic medical records information Extraction 7

Overview of Chinese electronic medical records Information E...

引用

7th International Conference on Big data and information Analytics, BigDIA 2021

作者： Zhao, Dongchen Chang, Xia Xue, Zhenxia School of Computer Science and Engineering Ningxia Key Laboratory of Intelligent Information and Big Data Processing Yinchuan China School of Math and Information Science North Minzu University Ningxia Key Laboratory of Intelligent Information and Big Data Processing Yinchuan China

ISBN: (纸本)9781665424660

Wise medical can't be separated from the analysis and processing of medical big data, electronic medical records as the main component of medical data have important research value. Chinese electronic medical records (CEMR) as the core records patient's disease, diagnosis and treatment information, the study of CEMR information extraction can better help doctors diagnose the disease and predict the development of the disease, in order to make more effective treatment plans. This paper divides information extraction technology into two subtasks of named entity recognition and relationship extraction, analyzes and compares the mechanism, algorithm and models of its existing methods, and finally points out the development direction of information extraction in the future. © 2021 IEEE.

关键词： Diagnosis

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