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Infinitely many dichotomous solutions for the Schrödinger-Poisson system

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Science China mathematics 2024年第9期67卷 2049-2070页

作者： Yuke He Benniao Li Wei Long school of {1. and Statistics and Jiangxi Provincial Center for applied {1. Jiangxi Normal UniversityNanchang 330022China

In this paper,we consider the following Schrodinger-Poisson system{-ε^(2)Δu+V(x)u+K(x)Φ(x)u=|u|^(p-1.u in R^(N),-ΔΦ(x)=K(x)u^(2)in RN,,where e is a small parameter,1.p 详细信息

In this paper,we consider the following Schrodinger-Poisson system{-ε^(2)Δu+V(x)u+K(x)Φ(x)u=|u|^(p-1.u in R^(N),-ΔΦ(x)=K(x)u^(2)in RN,,where e is a small parameter,1.p

关键词： dichotomous solutions non-degeneracy Schrodinger-Poisson system

THE WEIGHTED KATO SQUARE ROOT PROBLEMOF ELLIPTIC OPERATORS HAVING A BMOANTI-SYMMETRICPART

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Acta Mathematica Scientia 2024年第2期44卷 532-550页

作者：马文贤杨四辈 school of {1. and Statistics Gansu Key Laboratory of Applied Mathematics and Complex SystemsLanzhou UniversityLanzhou730000China

Let n≥2 and let L be a second-order elliptic operator of divergence form with coefficients consisting of both an elliptic symmetric part and a BMO anti-symmetric part in ℝ^(n).In this article,we consider the weighted Kato square root problem for *** precisely,we prove that the square root L^(1.2)satisfies the weighted L^(p)estimates||L^(1.2)(f)||L_(ω)^p(R^(n))≤C||■f||L_(ω)^p(R^(n);R^(n))for any p∈(1.∞)andω∈Ap(ℝ^(n))(the class of Muckenhoupt weights),and that||■f||L_(ω)^p(R^(n);R^(n))≤C||L^(1.2)(f)||L_(ω)^p(R^(n))for any p∈(1.2+ε)andω∈Ap(ℝ^(n))∩RH_(2+ε/p),(R^(n))(the class of reverse Hölder weights),whereε∈(0,∞)is a constant depending only on n and the operator L,and where(2+ε/p)'denotes the Hölder conjugate exponent of 2+ε/***,for any given q∈(2,∞),we give a sufficient condition to obtain that||■f||L_(ω)^p(R^(n);R^(n))≤C||L^(1.2)(f)||L_(ω)^p(R^(n))for any p∈(1.q)andω∈A_(p)(R^(n))∩pRH_(q/p),(R^(n)).As an application,we prove that when the coefficient matrix A that appears in L satisfies the small BMO condition,the Riesz transform∇L^(−1.2)is bounded on L_(ω)^(p)(ℝ^(n))for any given p∈(1.∞)andω∈Ap(ℝ^(n)).Furthermore,applications to the weighted L^(2)-regularity problem with the Dirichlet or the Neumann boundary condition are also given.

关键词： elliptic operator Kato square root problem Muckenhoupt weight Riesz transform reverse Hölder inequality

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 {1. Southwestern University of Finance and EconomicsChengdu611130China school of {1. Shandong UniversityJinan250100China applied and Computational {1. 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

Intercultural Trust in Global Contexts:Synthesizing a Western Nomological Approach with a Chinese Systems Approach

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Journal of Systems Science and Systems Engineering 2024年第2期33卷 162-186页

作者： Rong Du Mingqian Li Shizhong Ai Cathal MacSwiney Brugha Uirike Reisach school of Economics and {1. Xidian UniversityXi'an 710071China UCD school of Business University College DublinDublinIreland Information management Department Neu-Ulm University of Applied SciencesBavariaGermany

Intercultural trust in global contexts plays a central role in helping people from different cultures to communicate comfortably,which is essential for *** to construct a framework that might foster international cooperation,and thus be helpful for coping with global emergencies,we relate a Western nomological approach to an Eastern systems approach to analyse intercultural trust in global *** cultural impacts on intercultural trust and the nomological framework of cultural differences,we propose an intercultural trust model to interpret how cultural differences influence trust.A qualitative study of Chinese-Irish interactions was conducted to interpret this *** organized 1. seminars on intercultural trust,and interviewed 1. people to further explore the respondents'deeper feelings and experiences about intercultural trust in global *** this study,we have identified factors impacting on intercultural trust,and found that intercultural trust can be developed and improved in various *** llustrate these ways,we have provided tactics and methods for building intercultural trust in global *** are highlighted for organizations to avoid cultural clashes and relevant political or economic risks.

关键词： Intercultural trust global contexts systems approach Western approach Chinese approach

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 {1. and Statistics Guangdong University of FinanceGuangzhou 510521China Center for applied {1. 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 01.≤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

Acyclic Edge Coloring of 1.planar Graphs without 4-cycles

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Acta Mathematicae Applicatae Sinica 2024年第1期40卷 35-44页

作者： Wei-fan Wang Yi-qiao Wang Wan-shun Yang Department of mathematics Zhejiang Normal UniversityJinhua321004China school of {1. Beijing University of Chinese MedicineBeijing100029China school of {1. and Information Science Weifang UniversityWeifang261061China

An acyclic edge coloring of a graph G is a proper edge coloring such that there are no bichromatic cycles in *** acyclic chromatic index χ'α(G) of G is the smallest k such that G has an acyclic edge coloring using k *** was conjectured that every simple graph G with maximum degree Δ has χ'_α(G) ≤Δ+2.A1.planar graph is a graph that can be drawn in the plane so that each edge is crossed by at most one other *** this paper,we show that every 1.planar graph G without 4-cycles has χ'_α(G)≤Δ+22.

关键词： 1.planar graph acyclic edge coloring acyclic chromatic index

Evolution of the rare earth trade network:A perspective of dependency and competition

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Geoscience Frontiers 2024年第3期15卷 183-191页

作者： Jilan Xu Jiahao Li Vincent Charles Xin Zhao school of Urban and Regional Science Shanghai University of Finance and EconomicsShanghai 200433China school of Business East China University of Science and TechnologyShanghai 200237China school of {1. University of BradfordBradford BD71DPUnited Kingdom school of Statistics and {1. mathematics Anhui University of Finance and EconomicsBengbu 233030China

As a global strategic reserve resource,rare earth has been widely used in important industries,such as military equipment and ***,existing analyses based solely on the total volume of rare earth trade fail to uncover the underlying competition and dependency *** address this gap,this paper employs the principles of trade preference and import similarity to construct dependency and competition *** network analysis is then employed to study the evolution of the global rare earth trade network from 2002 to *** main conclusions are as *** global rare earth trade follows the Pareto principle,and the trade network shows a scale-free *** has emerged as the world’s largest importer and exporter of rare earth since *** the dependency network,China has become the most dependent country since *** result of community division shows that China has separated from the American community and formed new communities with the Association of Southeast Asian Nations(ASEAN)*** United States of America has formed a super-strong community with European and Asian *** the competition network,the distribution of competition intensity follows a scale-free *** countries face low-intensity competition,but there are numerous competing *** competition related to China has increased ***,the competition source for the United States of America has shifted from Mexico to China,resulting in China,the USA,and Japan becoming the core participants in the competition network.

关键词： Rare earth Trade network Dependency Competition Complex network analysis

VARIABLE STEP-SIZE BDF3 METHOD FOR ALLEN-CAHN EQUATION

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Journal of Computational mathematics 2024年第5期42卷 1380-1406页

作者： Minghua Chen Fan Yu Qingdong Zhang Zhimin Zhang school of {1. and Statistics Gansu Key Laboratory of Applied Mathematics and Complex SystemsLanzhou UniversityLanzhou 730000China Department of mathematics Wayne State UniversityDetroitMI 48202USA

In this work,we analyze the three-step backward differentiation formula(BDF3)method for solving the Allen-Cahn equation on variable *** BDF2 method,the discrete orthogonal convolution(DOC)kernels are positive,the stability and convergence analysis are well established in[Liao and Zhang,***.,90(2021.,1.07–1.26]and[Chen,Yu,and Zhang,arXiv:21.8.0291.,2021..However,the numerical analysis for BDF3 method with variable steps seems to be highly nontrivial due to the additional degrees of freedom and the non-positivity of DOC *** developing a novel spectral norm inequality,the unconditional stability and convergence are rigorously proved under the updated step ratio restriction rk:=τk/τk−1.1.405 for BDF3 ***,numerical experiments are performed to illustrate the theoretical *** the best of our knowledge,this is the first theoretical analysis of variable steps BDF3 method for the Allen-Cahn equation.

关键词： Variable step-size BDF3 method Allen-Cahn equation Spectral norm inequality Stability and convergence analysis

Weak type(1. 1. of the Riesz transform on some direct product manifolds with exponential volume growth

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Science China mathematics 2024年第7期67卷 1599-1622页

作者： Hong-Quan Li Jie-Xiang Zhu school of Mathematical Sciences Fudan UniversityShanghai200433China Center for applied {1. Tianjin UniversityTianjin300072China

In this paper, we are concerned with the Riesz transform on the direct product manifold H^(n)× M,where H^(n) is the n-dimensional real hyperbolic space, and M is a connected complete non-compact Riemannian manifold satisfying the volume doubling property and generalized Gaussian or sub-Gaussian upper estimates for the heat kernel. We establish its weak type(1. 1. property. In addition, we obtain the weak type(1. 1. of the heat maximal operator in the same setting. Our arguments also work for a large class of direct product manifolds with exponential volume growth. Particularly, we provide a simpler proof of weak type(1. 1. boundedness of some operators considered in the work of Li et al.(201.).

关键词： Riesz transform heat kernel direct product real hyperbolic space