摘要：
Abstract: In the real life, many-valued situation information tables can describe the conflict problem better, but some conflict analysis models mainly focus on three-valued situa- tion information table. In this paper, for the many-valued situation information table, we first define the support function and the opposition function, and build two con- flict analysis models based on the support function and the opposition function. That is, the agent set is divided into support set and non-support set and opposition set and non-opposition set. Then, based on two two-way conflict analysis models, three conflict analysis models are obtained, which divide agent set into support set, neutral set and opposition set. An example is given to illustrate how to calculate support set, neutral set and opposition set based on support function and opposition function. Finally, a five-way model of conflict analysis is built based on support function and opposition function to divide agent set into support set, weak support set, neutral set, weak opposition set and opposition set, and an example is given to illustrate how to calculate support set, weak support set, neutral set, weak opposition set and opposition set.#@#@#摘要: 在现实生活中，多值形势信息表可以更好的刻画冲突问题，而已有的冲突分析模型主要关注于三 值形势信息表。在本文中，针对多值形势信息表，我们首先定义了支持度函数和反对度函数，并基 于支持度函数和反对度函数分别建立了二支冲突分析模型，即将Agent集分为支持集和非支持集 以及反对集和非反对集。然后，基于两个二支冲突分析模型得到三支冲突分析模型，其将Agent集 分为支持集、 中立集和反对集，并通过例子说明如何基于支持度函数和反对度函数计算支持集、 中立集和反对集。 最后，基于支持度函数和反对度函数建立五支冲突分析模型将Agent集分为支 持集、弱支持集、中立集、弱反对集和反对集，并通过例子说明如何计算支持集、弱支持集、中立 集、弱反对集和反对集。
摘要：
In this paper, we study the variable-order generalized time fractional Oldroyd-B fluid model, use the reduced order method and the L2-1 Sigma method to establish the differential format with second-order accuracy, prove the stability and conver-gence of the format, and give numerical examples to illustrate the effectiveness of the differential format.
期刊：
Mathematical Methods in the Applied Sciences,2023年47(6):- ISSN：0170-4214
通讯作者：
Zhang, JJ
作者机构：
[Li, Jing; Zhao, Haoyu] Changsha Univ Sci & Technol, Sch Math & Stat, Changsha, Hunan, Peoples R China.;[Zhao, Haoyu; Zhang, Jingjun] Jiaxing Univ, Coll Data Sci, Jiaxing, Zhejiang, Peoples R China.;[Zhang, Jingjun] Jiaxing Univ, Coll Data Sci, Jiaxing 314001, Zhejiang, Peoples R China.
通讯机构：
[Zhang, JJ ] J;Jiaxing Univ, Coll Data Sci, Jiaxing 314001, Zhejiang, Peoples R China.
关键词：
Fourier-splitting method;quasi-geostrophic model;upper and lower bounds
摘要：
This paper studies the fractional quasi‐geostrophic equation with modified dissipation term. We first prove the existence and uniqueness of smooth solution of the fractional quasi‐geostrophic equation by using the regularization method. Then, utilizing the Fourier‐splitting method, we obtain the long‐time behavior of the solution. More precisely, we show that under suitable assumptions on the initial data, for any multi‐index γ,m≥4$$ \gamma, m\ge 4 $$ and α∈12,1$$ \alpha \in \left(\frac{1}{2},1\right) $$, the solution ψ$$ \psi $$ satisfies C1(1+t)−1+|γ|2+2α≤∇γψ(·,t)L2≤C2(1+t)−1+|γ|2+2α,|γ|=0,1,…,m−1,t≥1,$$ {C}_1{\left(1+t\right)}^{-\frac{1+\mid \gamma \mid }{2+2\alpha }}\le {\left\Vert {\nabla}^{\gamma}\psi \left(\cdotp, t\right)\right\Vert}_{L^2}\le {C}_2{\left(1+t\right)}^{-\frac{1+\mid \gamma \mid }{2+2\alpha }},\mid \gamma \mid =0,1,\dots, m-1,t\ge 1, $$ and C3(1+t)−1+|γ|2+2α≤||∇γψ(·,t)||L2≤C4(1+t)−|γ|2+2α,|γ|=m,t≥1.$$ {C}_3{\left(1+t\right)}^{-\frac{1+\mid \gamma \mid }{2+2\alpha }}\le {\left\Vert {\nabla}^{\gamma}\psi \Big(\cdotp, t\Big)\right\Vert}_{L^2}\le {C}_4{\left(1+t\right)}^{-\frac{\mid \gamma \mid }{2+2\alpha }},\mid \gamma \mid =m,t\ge 1. $$
摘要：
The parabolic systems for migration of groundwater contaminants are studied through the semi-analytic method (SAM). For systems, a modification of the classic trigonometric basis function (TBF) is proposed that successfully obtains the solution on the available boundary data and improves accuracy. The method is based on a theory that removes instability and keeps the same accuracy. However, especially when using SAM schemes with acceptable stability properties, one is still faced with the considerable task of linearizing the systems, consequently, the linearization of the systems which approximate the nonlinear term with the first order derivative is introduced. The final approximation is given by the summation of the primary approximation, radial basis functions (RBFs), and the related TBFs which are determined by the homogeneous boundary conditions. Then the approximation is substituted back to the governing equations where the unknown coefficients can be determined. The efficiency of the algorithm is highlighted by numerical simulations relating to a model on test cases with analytical solutions and without an analytical solution.
摘要：
Abstract Forecasting equity risk premium is notoriously difficult due to a mass of data noise in the raw series and the absence of clear tendency. Using the monthly S&P 500 excess returns from 1927:01 to 2018:12, we first de‐noise the in‐sample original returns series via wavelet method to capture the basic trend of equity risk premium, and then propose forecasting models to obtain one‐step forward out‐of‐sample predicted values based on the de‐noised returns. Our new models can provide substantially superior out‐of‐sample performance compared with other competing models and the historical average. Sizeable economic gains can be realized by a mean–variance investor if they allocate their asset through the new approach. Our findings are robust under different settings from both statistical and economic perspectives.
摘要：
Nowadays, the researches of conflict analysis are increasing with the development of three-way decisions, and three-way decisions with rankings and reference tuples provides new perspectives for conflict analysis. In this paper, we first divide a whole set of issues into a bundle of supported issues and a bundle of non-supported issues, and a bundle of opposed issues and a bundle of non-opposed issues, respectively, from the perspectives of support and opposition. Accordingly, we give two ranking orders and two reference tuples. Then, we put forward alliance and conflict measures by considering weights of issues, and develop models of three-way conflict analysis with ideas of rankings and reference tuples. Finally, we show how to compute the alliance, neutral and conflict coalitions with the proposed models. It provides an attempt to study conflict problems with thoughts of rankings and reference tuples.
摘要：
Pawlak conflict analysis focuses on three-valued ratings of a set of agents on a set of issues, in which the three values +, 0, and - indicate, respectively, that an agent is positive, neutral, and negative about an issue. According to their shared ratings, we can form different types of agent coalitions and, similarly, different types of issue bundles (i.e., families of issues to be considered together). The main objective of this paper is to introduce and investigate connections of agent coalitions and issue bundles from Wille formal concept analysis perspectives. By interpreting a three-valued rating table as four different formal contexts, we introduce four types of agent coalitions, namely, support, non-opposition, opposition, and non-support coalitions, the corresponding four types of issue bundles, and four lattices of coalition-bundle couplings. The lattices reveal structural information of agents and issues in a conflict situation. To demonstrate the usefulness of the proposed model, we analyze the problem of development planning of the Gansu Province of China.(c) 2022 Elsevier Inc. All rights reserved.
期刊：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS,2023年16(11):2980-3013 ISSN：1078-0947
通讯作者：
Lin, Q
作者机构：
[Zhang, Fubao; Cai, Li] Southeast Univ, Sch Math, Nanjing 210096, Peoples R China.;[Lin, Qiang] Changsha Univ Sci & Technol, Sch Math & Stat, Changsha 410004, Peoples R China.;[Zhang, Fubao] Southeast Univ, Chengxian Coll, Nanjing 210088, Peoples R China.;[Lin, Qiang; Cai, Li] Univ Craiova, Dept Math, Craiova 200585, Romania.;[Lin, Qiang; Cai, Li] China Romania Res Ctr Appl Math, Craiova, Romania.
通讯机构：
[Lin, Q ] C;Changsha Univ Sci & Technol, Sch Math & Stat, Changsha 410004, Peoples R China.;Univ Craiova, Dept Math, Craiova 200585, Romania.;China Romania Res Ctr Appl Math, Craiova, Romania.
关键词：
Coupled Kirchhoff system;high energy solutions;Linking theorem;Nehari manifold method;topological degree theory
摘要：
In this paper, we consider the coupled Kirchhoff system in subcrit-ical case and critical case. For subcritical case, we first study the least energy of coupled Kirchhoff system and the limit system by using the Nehari manifold method and exclude the existence of semi-trivial solutions. Then we improve the global compactness lemma of coupled Kirchhoff system to overcome the loss of compactness. Combining with the linking theorem and topological de-gree, we construct a Palais-Smale sequence in the high energy level and prove the existence of high energy positive solutions. Moreover, the results of the subcritical case are extended to the critical case.
通讯机构：
[Di Liu; Ximeng Liu] 1;1 School of Mathematics and Statistics, Changsha University of Science and Technology , Changsha 410114, People’s Republic of China
摘要：
In this paper, we consider the long-time behavior of the nonclassical diffusion equation with perturbed parameter and memory on a bounded domain Ω⊂Rn(n≥3) . The main feature of this model is that the equation contains a dissipative term with perturbation parameters −νΔu and the nonlinearity f satisfies the polynomial growth of arbitrary order. By using the nonclassical operator method and a new analytical method (or technique) (Lemma 2.7), the existence and regularity of uniform attractors generated for this equation are proved. Furthermore, we also get the upper semicontinuity of the uniform attractors when the perturbed parameter ν → 0. It is remarkable that if ν = 0, we can get the same conclusion as in the works of Toan et al. [Acta Appl. Math. 170, 789–822 (2020)] and Conti et al. [Commun. Pure Appl. Anal. 19, 2035–2050 (2020)], but the nonlinearity is critical.
通讯机构：
[Wang, C ] C;Changsha Univ Sci & Technol, Sch Math & Stat, Changsha 410114, Peoples R China.
关键词：
filtering evidence;GAT;Natural language inference;program-like evidence;table-based fact verification
摘要：
Table-based fact verification requests parsing table and statement structure and performing numerical and logical reasoning. Previous methods may select erroneous programs and ignore the interpretability of table-based fact verification. Thus, we propose a double graph attention network reasoning method based on filtering and program-like evidence (DGMFP). In detail, we initially obtain the filtering evidence based on tables and the program-like evidence based on logical forms to incorporate the semantic and symbolic information of evidence. Then, we construct an evidence graph with statement-evidence pairs as nodes and use the kernel in graph neural network to conduct more fine-grained joint reasoning and improve the interpretability of table-based fact verification. We also construct a connected graph with all entities and functions in the program-like evidence as nodes and use the graph attention network (GAT) to capture more fine-grained relationships within the program-like evidence. Finally, we connect the outputs of two GAT models and BERT model to predict labels. Experimental results on TABFACT show that DGMFP outperforms all baselines with 76.1% accuracy. Ablation studies further indicate that constructed two graphs, filtering evidence, and program-like evidence play an important role in better understanding the semi-structured table.
摘要：
Abstract: The purpose of this article is to extend the dynamic results of SD oscillators with dry friction on a plane to an inclined plane. The analysis results indicate that the system will have one or two equilibrium sets. And the stability of the equilibrium set was proved through non smooth Lyapunov functions. Finally, we provided numerical simulations to illustrate the dynamics and validate the results.#@#@#摘要: 本文的目的是将平面上带干摩擦的SD振子的动力学结果推广至斜面上。 分析结果表明，系统会有 一个或两个平衡集。 并通过非光滑李雅普诺夫函数证明了平衡集的稳定性。 最后我们给出了数值 模拟图来说明动力学并验证结果。
作者：
Xian Zhao*;Chuangxia Huang;Bingwen Liu;Jinde Cao
期刊：
Mathematics and Computers in Simulation,2023年 ISSN：0378-4754
通讯作者：
Xian Zhao
作者机构：
[Xian Zhao; Chuangxia Huang] School of Mathematics and Statistics, Changsha University of Science and Technology;Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha, 410114, Hunan, China;[Bingwen Liu] College of Data Science, Jiaxing University, Jiaxing, 314001, Zhejiang, China;School of Mathematics, Southeast University, Nanjing, 210096, Jiangsu, China;Yonsei Frontier Lab, Yonsei University, Seoul, 03722, South Korea
通讯机构：
[Xian Zhao] S;School of Mathematics and Statistics, Changsha University of Science and Technology;Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha, 410114, Hunan, China
摘要：
For delay patch-constructed periodic Nicholson’s blowflies system, the global stability on positive periodic solutions remains imperfectly understood at best. In this paper, by combining the fluctuation lemma with elementary inequality techniques, we build up several novel criteria to ensure the global asymptotic stability of positive periodic solutions of the proposed model, which have essentially novelty and supplement some existing literature. In particular, we afford some numerical simulations to substantiate the validness and efficacy of the obtained theoretic results.
作者机构：
School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha, China;College of Data Science, Jiaxing University, Zhejiang, China;[Haoyu Zhao] School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha, China<&wdkj&>College of Data Science, Jiaxing University, Zhejiang, China
摘要：
In this paper, we study the long-time behavior of solutions of the single-layer quasi-geostrophic model arising from geophysical fluid dynamics. We obtain the lower bound of the decay estimate of the solution. Utilizing the Fourier splitting method, under suitable assumptions on the initial data, for any multi-index α, we show that the solution Ψ satisfies
