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A Global Optimality Principle for Fully Coupled Mean-field Control Systems

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Acta Mathematicae Applicatae Sinica 2024年第2期40卷 379-413页

作者： Tao HAO school of Statistics and mathematics Shandong University of Finance and EconomicsJinan 250014China

This paper concerns a global optimality principle for fully coupled mean-field control *** the first-order and the second-order variational equations are fully coupled mean-field linear FBSDEs. A new linear relation is introduced, with which we successfully decouple the fully coupled first-order variational equations. We give a new second-order expansion of Y^(ε) that can work well in mean-field framework. Based on this result, the stochastic maximum principle is proved. The comparison with the stochastic maximum principle for controlled mean-field stochastic differential equations is supplied.

关键词： optimal control global maximum principle fully coupled general mean-field FBSDE adjoint equation recursive utility

Dynamical distribution of continuous service time model involving non-Maxwellian collision kernel and value functions

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Chinese Physics B 2024年第9期33卷 340-348页

作者： Minfang Zhao Lingting Kong Miao Liu Shaoyong Lai school of mathematics and Statistics Yili Normal UniversityYining 835000China Institute of Applied mathematics Yili Normal UniversityYining 835000China school of mathematics Southwestern University of Finance and EconomicsChengdu 611130China

The distribution of continuous service time in call centers is investigated.A non-Maxwellian collision kernel combining two different value functions in the interaction rule are used to describe the evolution of continuous service time,*** the statistical mechanical and asymptotic limit methods,Fokker–Planck equations are derived from the corresponding Boltzmann-type equations with non-Maxwellian collision *** steady-state solutions of the Fokker–Planck equation are obtained in exact *** experiments are provided to support our results under different parameters.

关键词： kinetic theory service time Fokker–Planck equation value function

Understanding inter-term fossil energy consumption pathways in China based on sustainable development goals

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Geoscience Frontiers 2024年第3期15卷 272-283页

作者： Xiaoxiao Zhou Fangyuan Xie Hui Li Chenbin Zheng Xin Zhao school of finance Anhui University of Finance and EconomicsBengbu 233030China school of Economics Shandong University of Finance and EconomicsJinan 250002China school of Economics Fujian Normal UniversityFuzhou 350117China school of Statistics and Applied mathematics Anhui University of Finance and EconomicsBengbu 233030China

Sustainable development goals(SDGs)and fossil energy are the core elements of almost all major challenges and opportunities for achieving social ***,energy sustainability has become one of the pivotal drivers of China’s *** study constructed a comprehensive evaluation index system for the provincial-level sustainable development of fossil energy in China covering three major dimensions(socio-economic,resource,and environmental).Moreover,a set of criteria for measuring the SDGs of fossil energy at the national level in China was *** on the provincial panel data collected from 30 provinces from 2010 through 2019,a spatial econometric model was applied to empirically evaluate the effects of SDGs on fossil energy *** results showed that the SDGs not only promote the reduction of fossil energy consumption with substantial negative spatial spillover effects,but also revealed differences between northern and southern *** promote the early achievement of sustainable fossil energy development in China,the transformation and upgradation of fossil energy systems should be conducted early and inter-regional cooperation should be strengthened according to local conditions to jointly achieve the SDGs.

关键词： Sustainable development goals Fossil energy consumption Spatial Durbin model Spillover effects

Matching Rota-Baxter Systems and Gröbner-Shirshov Bases

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Algebra Colloquium 2024年第3期31卷 389-406页

作者： Yi Zhang Shuangjian Guo school of mathematics and Statistics Nanjing University of Information Science and Technology Nanjing 210044China school of mathematics and Statistics Guizhou University of Finance and Economics Guiyang 550025China

Motivated by the concept of matching Rota-Baxter algebras arising from polarized associative Yang-Baxter equations and Volterra integral equations,we introduce the notion of a matching Rota-Baxter system,which generalizes the Rota-Baxter system proposed by *** show that this notion is also related to Yang-Baxter pairs and to matching pre-Lie *** then modify the definition of matching Rota-Baxter systems by adding a curvature term,and make a connection with matching pre-Lie algebras and with compatible associative ***,we study matching Rota-Baxter systems on a dendriform algebra and show how they induce matching quadri-algebra ***,we give a linear basis of free matching Rota-Baxter system by Grobner-Shirshov bases methods.

关键词： Rota-Baxter systems curved matching Rota-Baxter systems Gröbner-Shirshov bases

A LOW-REGULARITY FOURIER INTEGRATOR FOR THE DAVEY-STEWARTSON II SYSTEM WITH ALMOST MASS CONSERVATION

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Acta Mathematica Scientia 2024年第4期44卷 1536-1549页

作者： Cui NING Chenxi HAO Yaohong WANG school of Financial mathematics and Statistics Guangdong University of FinanceGuangzhou 510521China Center for Applied mathematics Tianjin UniversityTianjin 300072China

In this work,we propose a low-regularity Fourier integrator with almost mass conservation to solve the Davey-StewartsonⅡsystem(hyperbolic-elliptic case).Arbitrary order mass convergence could be achieved by the suitable addition of correction terms,while keeping the first order accuracy in H~γ×H^(γ+1)for initial data in H^(γ+1)×H^(γ+1)withγ>*** main theorem is that,up to some fixed time T,there exist constantsτ_(0)and C depending only on T and‖u‖_(L^(∞)((0,T);H^(γ+1)))such that,for any 0<τ≤τ_(0),we have that‖u(t_(n),·)-u^(n)‖H_γ≤C_(τ),‖v(t_(n),·)-v^(n)‖_(Hγ+1)≤C_(τ),where u^(n)and v^(n)denote the numerical solutions at t_(n)=nτ.Moreover,the mass of the numerical solution M(u^(n))satisfies that|M(u^(n))-M(u_0)|≤Cτ~5.

关键词： Davey-StewartsonⅡsystem low-regularity exponential integrator first order accuracy mass conservation

Second-order error analysis of the averaged L1 scheme L1 for time-fractional initial-value and subdiffusion problems

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Science China mathematics 2024年第7期67卷 1641-1664页

作者： Jinye Shen Fanhai Zeng Martin Stynes school of mathematics Southwestern University of Finance and EconomicsChengdu611130China school of mathematics Shandong UniversityJinan250100China Applied and Computational mathematics Division Beijing Computational Science Research CenterBeijing100193China

Fractional initial-value problems(IVPs) and time-fractional initial-boundary value problems(IBVPs), each with a Caputo temporal derivative of order α ∈(0, 1), are considered. An averaged variant of the well-known L1 scheme is proved to be O(N^(-2)) convergent for IVPs on suitably graded meshes with N points, thereby improving the O(N^(-(2-α))) convergence rate of the standard L1 scheme. The analysis relies on a delicate decomposition of the temporal truncation error that yields a sharp dependence of the order of convergence on the degree of mesh grading used. This averaged L1 scheme can be combined with a finite difference or piecewise linear finite element discretization in space for IBVPs, and under a restriction on the temporal mesh width, one gets again O(N^(-2)) convergence in time, together with O(h^(2)) convergence in space,where h is the spatial mesh width. Numerical experiments support our results.

关键词： time-fractional subdiffusion averaged L1 scheme

Block Basis for Modular Coinvariants of Pseudo-Reflection Groups

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Algebra Colloquium 2024年第1期31卷 41-48页

作者： Ke Ou school of Statistics and mathematics Yunnan University of finance and Economics Kunming 650221China

We investigate the block basis for modular coinvariants of finite pseudo-reflection *** are particularly interested in the case of a subgroup G of the parabolic subgroups of GLn(q)which generalizes the Weyl groups of ... 详细信息

关键词： modular invariant theory pseudo-reflection group block basis coinvariant

Ergodicity of a Special Class of Markov Chains

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Acta Mathematicae Applicatae Sinica 2024年

作者： Xin-yu HU Ping HE school of mathematics Shanghai University of Finance and Economics

The paper focuses on the ergodicity of a φ-irreducible Markov chain {X_n, n ≥ 0} that is generated iteratively through the expression Xn+1= f（X_n） + ?n+1. Here, {?_n, n ≥ 1} is a sequence of independent identically distributed centralized random variables, f（·） is an R-valued continuous function, and X0is arbitrary but independent of {?_n, n ≥ 1}. Our main contribution is to provide necessary and sufficient conditions for ergodicity of this special class of Markov chains. We also present a generalized approach for f（·） in the end.

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Generalized Laws of Importation and Cross-Migrativity Based on(D, N)-Implications

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Journal of Mathematical Research with Applications 2024年第5期44卷 583-595页

作者： Nana MA school of mathematics Xi'an University of Finance and Economics

In the present article we study the generalized laws of importation and crossmigrativity based on(D, N)-implications. On the one hand, we consider the generalized law of importation I(T(x, α), y) = I(x, J(α, y)), when T is concretized as a fuzzy conjunction C, I and J are concretized as(D, N)-implications generated by a fuzzy disjunction D and a fuzzy negation N. On the other hand, we discuss the cross-migrativity of fuzzy disjunctions over fuzzy implications, that is, I(x, D(y, z)) = D(y, I(x, z)), where I is a fuzzy implication, D is a fuzzy disjunction. In addition, we study the relationship between the(α-)cross-migrative of(I, D) and the(α-)cross-law of importation(I, ID,N, C).

关键词： fuzzy implication generalized laws of importation cross-migrativity