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作者： Saheya, B. Zhanlav, T. Mijiddorj, R. College of Mathematics Science Inner Mongolia Normal University Hohhot China Key Laboratory of Infinite-dimensional Hamiltonian System and Its Algorithm Application Center for Applied Mathematics Hohhot China Institute of Mathematics and Digital Technology Mongolian Academy of Sciences Ulaanbaatar Mongolia Department of Informatics Mongolian National University of Education Ulaanbaatar Mongolia

In this paper, we propose the first time fifth- and sixth-order two-step schemes. Based on the proposed two-step methods, we develop three-step iterative methods with the ninth- and tenth-order of convergence. We also suggest two parametric families of these schemes. The obtained results are extended to (Formula presented.) -step iterations. The main advantages of the proposed methods are that they are higher order of convergence and utilize only one matrix inversion per iteration which makes these methods computationally more efficient. Numerical experiments are performed to confirm the theoretical results concerning the order of convergence and computational efficiency. © 2023 John Wiley & Sons Ltd.

关键词： Iterative methods

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Study on the effective elastic performance of composites containing decagonal symmetric two-dimensional quasicrystal coatings

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Applied Mathematics and Mechanics(English Edition) 2024年第9期45卷 1655-1664页

作者： Yurun WU Lu LI Lianhe LI School of Mathematics and Science Inner Mongolia Normal UniversityHohhot 010022China Inner Mongolia Applied mathematics Center Hohhot 010022China Key Laboratory of Infinite Dimensional Hamiltonian System and Its Algorithm Application Ministry of EducationHohhot 010022China

On account of the Mori-Tanaka approach,the effective elastic performance of composites containing decagonal symmetric two-dimensional(2D)quasicrystal(QC)coatings is *** expressions for the effective elastic constants of rare-earth QC reinforced magnesium-based composites are *** discussion is presented on the effects of the volume fraction of the inclusions,the aspect ratio of the inclusions,the coating thickness,and the coating material parameters on the effective elastic constants of the *** results indicate that considering the coating increases the effective elastic constants of the composites to some extent.

关键词： Mori-Tanaka approach coated inclusion decagonal symmetric twodimensional(2D)quasicrystal(QC)

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Rogue waves for the(2+1)-dimensional Myrzakulov–Lakshmanan-Ⅳ equation on a periodic background

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Communications in Theoretical Physics 2024年第4期76卷 32-42页

作者： Xiao-Hui Wang Zhaqilao College of Mathematics Science Inner Mongolia Normal UniversityHohhot 010022China Laboratory of Infinite-dimensional Hamiltonian System and Its algorithm Application Hohhot 010022China Center for Applied Mathematical Science Inner MongoliaHohhot 010022China

In this paper, the rogue wave solutions of the(2+1)-dimensional Myrzakulov–Lakshmanan(ML)-Ⅳ equation, which is described by five component nonlinear evolution equations, are studied on a periodic background. By using the Jacobian elliptic function expansion method, the Darboux transformation(DT) method and the nonlinearization of the Lax pair, two kinds of rogue wave solutions which are expressed by Jacobian elliptic functions dn and cn, are *** relationship between these five kinds of potential is summarized systematically. Firstly, the periodic rogue wave solution of one potential is obtained, and then the periodic rogue wave solutions of the other four potentials are obtained directly. The solutions we find present the dynamic phenomena of higher-order nonlinear wave equations.

关键词： rogue waves on a periodic background (2+1)-dimensional Myrzakulov-Lakshmanan-IV equation Darboux transformation Jacobian elliptic function

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Controllability of Indu-Bala product networks

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Neural Networks 2025年 190卷

作者： Qiang Zhang Junjie Huang Bo Liu Housheng Su Alatancang Chen School of Mathematical Sciences Inner Mongolia University Hohhot 010021 China School of Information Engineering Minzu University of China Beijing 100081 China National Key Laboratory of Multispectral Information Intelligent Processing Technology School of Artificial Intelligence and Automation Huazhong University of Science and Technology Wuhan 430074 China School of Mathematical Sciences the Ministry of Education Key Laboratory for Infinite-dimensional Hamiltonian System and Its Algorithm Application Inner Mongolia Normal University Hohhot 010022 China

A composite network formed by factor networks is a new type of complex network model that can describe different types of agents and multiple complicated relationships in complex systems. “Indu-Bala product” of graphs is a new graph operation with symmetry properties and good mathematical expression, which enables one to construct many pairs of respective co-spectral graphs. This work studies the controllability of a composite network formed by factor networks via Indu-Bala product based on Laplacian dynamics. The eigenvalues and eigenvectors of Indu-Bala product networks (IBPNs) can be represented by factors’ eigenvalues and eigenvectors, which can reduce the computational complexity and analytical burden. Based on the PBH test, sufficient and necessary algebraic criterions for controllability of IBPNs are established, which reveal the controllability relationship between entire network and its factors. This work will help one to construct, understand and improve the composite complex network models, and gain insight into the synergistic mechanisms of the networks.

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On the (Δ + 2)-Total-Colorability of Planar Graphs with 7-Cycles Containing at Most Two Chords

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Journal of Applied Mathematics and Physics 2024年第7期12卷 2702-2710页

作者： Jian Chang Jingru Liu Fan Zhang College of Mathematics Science Inner Mongolia Normal University Hohhot China Laboratory of Infinite-Dimensional Hamiltonian System and Its Algorithm Application Hohhot China

The Total Coloring Conjecture (TCC) proposes that every simple graph G is (Δ + 2)-totally-colorable, where Δ is the maximum degree of G. For planar graph, TCC is open only in case Δ = 6. In this paper, we prove tha... 详细信息

关键词： Planar Graph 7-Cycle 8-Totally-Colorable Maximum Degree

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Analysis of the Effective Elastic Performance of Multilayered Quasicrystal Composite Plates

SSRN

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SSRN 2024年

作者： Wu, Yurun Li, Lian He School of Mathematics and Science Inner Mongolia Normal University Hohhot010022 China Inner Mongolia Applied Mathematics Center Hohhot010022 China Key Laboratory of Infinite Dimensional Hamiltonian System and Its Algorithm Application Ministry of Education Hohhot010022 China

In this paper, the multilayered quasicrystal composite plates effective elastic performance are forecasted. Firstly, effective properties of the first and third layers quasicrystal composite plates containing ellipsoidal inclusions are obtained according to the Mori-Tanaka model. Secondly, the multilayered composite plates elastic performance are computed by employing the general matrix approach. The numerical examples reveal the influence of the inclusions geometry and size on the multilayered quasicrystal composite plates effective elastic constants. The findings indicate that an increase in the layers number brings about a certain degree of reduction in the effective elastic constants. © 2024, The Authors. All rights reserved.

关键词： Geometry

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Legal Judgment Prediction via Fine-Grained Element Graphs and External Knowledge

Legal Judgment Prediction via Fine-Grained Element Graphs an...

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International Joint Conference on Neural Networks (IJCNN)

作者： Yao Guo Yanling Li Fengpei Ge Haiqing Yu Sukun Wang Zhongyi Miao College of Computer Science and Technology Key Laboratory of Infinite-Dimensional Hamiltonian System and Its Algorithm Application (Ministry of Education) Inner Mongolia Normal University Hohhot China Library Beijing University of Posts and Telecommunications Beijing China College of Computer Science and Technology Inner Mongolia Normal University Hohhot China

ISBN: (数字)9798350359312

ISBN: (纸本)9798350359329

Legal Judgment Prediction (LJP), a paramount application of artificial intelligence in law, aims to infer outcomes from fact descriptions. These outcomes mainly involve determining applicable law articles, charges, and the term of penalty. Existing approaches typically treat this task as a text classification problem, utilizing end-to-end black box models for automatic prediction. However, these approaches overlook the fine-grained elements within cases and limit the model’s interpretability. In light of these limitations, we propose a novel approach for LJP. Our method employs Fine-Grained Element Graphs (FEGs) to represent fact descriptions and applies Graph Attention Network (GAT) to learn graph representation for subsequent prediction tasks. FEG is characterized by capturing the relevant adjudicative elements of each fact description and preserving important relations among them, such as causality and temporal sequences while filtering out irrelevant content. It enhances LJP task performance and provides interpretable references for legal professionals. Since increased or decreased penalties corresponding to different elements cannot be obtained from fact descriptions, we introduce Sentencing Guidance (SG) and combine it with FEGs as a supplementary feature. Experiments confirm the effectiveness of our method. Specifically, compared to the best baseline model, it improves macro-F1 by 3.09%, 0.57%, and 1.78% for the subtasks of law article prediction, charge prediction, and term of penalty prediction.

关键词： Automation Law Filtering Text categorization Semantics Neural networks Cause effect analysis

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LeGalFormer: A Graph Representation Learning and Transformer-based Approach for Legal Similar Case Retrieval

LeGalFormer: A Graph Representation Learning and Transformer...

引用

International Joint Conference on Neural Networks (IJCNN)

作者： Shang Gao Yanling Li Fengpei Ge Min Lin Haiqing Yu Sukun Wang Zhongyi Miao College of Computer Science and Technology Key Laboratory of Infinite-Dimensional Hamiltonian System and Its Algorithm Application Ministry of Education Inner Mongolia Normal University Hohhot China Library Beijing University of Posts and Telecommunications Beijing China College of Computer Science and Technology Inner Mongolia Normal University Hohhot China

ISBN: (数字)9798350359312

ISBN: (纸本)9798350359329

Legal Similar Case Retrieval (LSCR) is a critical application in legal Artificial Intelligence (AI). It involves retrieving the most relevant cases from legal case databases through query cases. Legal cases are semi-structured documents characterized by long text sequences and high specialization. Existing approaches rely on pre-trained language models for retrieval. However, these methods are constrained by the length of text input, preventing them from fully comprehending cases, which results in poor retrieval performance. Knowledge Graph (KG) are a type of graph structure data with dense knowledge and clear logic, which can represent the criminal processes and relationships among characters within legal cases. Currently, the mainstream approach for handling KG remains Graph Neural Networks (GNNs). However, these methods are limited by message passing and are prone to over-smoothing problems in the process of aggregating node features. To address these issues, we propose a Legal similar case retrieval model that combines Graph representation learning with the Transformer, called LeGalFormer. Three encoding methods are introduced to incorporate the structural information of the graph into the Transformer architecture. We evaluate the model on a real legal dataset, and the experimental results show that LeGalFormer significantly enhances the model's understanding capacity and achieves state-of-the-art performance.

关键词： Representation learning Training Law Message passing Transformers Encoding Graph neural networks

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Match and Retrieval: Legal Similar Case Retrieval via Graph Matching Network

Match and Retrieval: Legal Similar Case Retrieval via Graph ...

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IEEE International Conference on Data Mining Workshops (ICDM Workshops)

作者： Shang Gao Yanling Li Fengpei Ge Min Lin Haiqing Yu Sukun Wang Zhongyi Miao College of Computer Science and Technology Key Laboratory of Infinite-Dimensional Hamiltonian System and Its Algorithm Application (Ministry of Education) Inner Mongolia Normal University Hohhot China Library Beijing University of Posts and Telecommunications Beijing China College of Computer Science and Technology Inner Mongolia Normal University Hohhot China

Legal document retrieval is a crucial application in the field of legal Artificial Intelligence (AI). It involves retrieving the most relevant legal cases from a legal document database when inputting a query. Mainstream solutions typically employ pre-trained language models or large language models for retrieval. However, both of these methods rely on black-box models trained on unlabeled data, resulting in a lack of interpretability in the model's retrieval outcomes. Graph Neural Networks (GNNs) possess strong representational and interpretable capabilities. Therefore, representing legal cases using graph-structured data and performing the Legal Similar Case Retrieval (LSCR) task through GNNs is a promising approach. Nevertheless, typical GNNs primarily focus on node information within graph-structured data and overlook edge and inter-graph interaction information, leading to lower retrieval accuracy. To address these issues, in this paper, we propose a Legal case retrieval model utilizing a Graph Matching Network, called Legal-GMN. We evaluate the model on a dataset composed of real legal judgment cases. Experimental results demonstrate that Legal-GMN effectively enhances the retrieval accuracy for the LSCR task. Compared with baseline methods, Legal-GMN improves retrieval precision by approximately 15% and enhances retrieval efficiency by approximately 90%. Remarkably, while maintaining State-Of-The-Art (SOTA) performance, Legal-GMN can also generate visualized graphs of the retrieval process, significantly enhancing its interpretability.

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Analytic aspects of generalized central trinomial coefficients

arXiv

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arXiv 2023年

作者： Liang, Huyile Wang, Yaling Wang, Yi College of Mathematics Science Inner Mongolia Normal University Hohhot010022 China Center for Applied Mathematics Inner Mongolia Hohhot010022 China Key Laboratory of Infinite-dimensional Hamiltonian System and Its Algorithm Application Ministry of Education Hohhot010022 China School of Mathematical Sciences Dalian University of Technology Dalian116024 China

The divisibility and congruence of usual and generalized central trinomial coefficients have been extensively investigated. The present paper is devoted to analytic properties of these numbers. We show that usual central trinomial polynomials Tn(x) have only real roots, and roots of Tn(x) interlace those of Tn+1(x), as well as those of Tn+2(x), which gives an affirmative answer to an open question of Fisk. We establish necessary and sufficient conditions such that the generalized central trinomial coefficients Tn(b, c) form a log-convex sequence or a Stieltjes moment *** Codes 26C10, 60F0, 05A15, 15B48 © 2023, CC BY.

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