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Applied mathematics(A Journal of Chinese Universities) 2024年第1期39卷 98-113页

作者： LIU Zai-ming GENG Bing-zhen WANG Shi-jie school of mathematics and statistics Central South UniversityChangsha 410083China school of Big Data and statistics Anhui UniversityHefei 230601China

Consider a nonstandard continuous-time bidimensional risk model with constant force of interest,in which the two classes of claims with subexponential distributions satisfy a general dependence structure and each pair of the claim-inter-arrival times is arbitrarily *** some mild conditions,we achieve a locally uniform approximation of the finite-time ruin probability for all time horizon within a finite *** we further assume that each pair of the claim-inter-arrival times is negative quadrant dependent and the two classes of claims are consistently-varying-tailed,it shows that the above obtained approximation is also globally uniform for all time horizon within an infinite interval.

关键词： bidimensional risk model asymptotic formula subexponential distribution consistently varying tail ruin probability

On Existence of the Even L_(p)Gaussian Minkowski Problem for p>n

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Chinese Annals of mathematics,Series B 2024年第2期45卷 179-192页

作者： Hejun WANG school of mathematics and statistics Shandong Normal UniversityJi'nan 250014China

This paper concerns the even L_(p)Gaussian Minkowski problem in n-dimensional Euclidean space R^(n).The existence of the solution to the even L_(p)Guassian Minkowski problem for p>n is obtained.

关键词： Convex body Existence L_(p)Gaussian surface area measure The even L_(p)Gaussian Minkowski problem

WEAK APPROXIMATIONS OF STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS WITH FRACTIONAL NOISE

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Journal of Computational mathematics 2024年第3期42卷 735-754页

作者： Meng Cai Siqing Gan Xiaojie Wang school of mathematics and statistics HNP-LAMACentral South UniversityChangshaChina

This paper aims to analyze the weak approximation error of a fully discrete scheme for a class of semi-linear parabolic stochastic partial differential equations(SPDEs)driven by additive fractional Brownian motions with the Hurst parameter H∈(1/2,1).The spatial approximation is performed by a spectral Galerkin method and the temporal discretization by an exponential Euler *** far as we know,the weak error analysis for approximations of fractional noise driven SPDEs is absent in the literature.A key difficulty in the analysis is caused by the lack of the associated Kolmogorov *** the present work,a novel and efficient approach is presented to carry out the weak error analysis for the approximations,which does not rely on the associated Kolmogorov equations but relies on the Malliavin *** the best of our knowledge,the rates of weak convergence,shown to be higher than the strong convergence rates,are revealed in the fractional noise driven SPDE setting for the first *** examples corroborate the claimed weak orders of convergence.

关键词： Parabolic SPDEs Fractional Brownian motion Weak convergence rates Spec-tral Galerkin method Exponential Euler method Malliavin calculus

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 mathematics and statistics and Jiangxi Provincial Center for Applied mathematics 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 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

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

An Approximation Algorithm Based on Seeding Algorithm for Fuzzy k-Means Problem with Penalties

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Journal of the Operations Research Society of China 2024年第2期12卷 387-409页

作者： Wen-Zhao Liu Min Li school of mathematics and statistics Shandong Normal UniversityJinan 250014ShandongChina

As a classic NP-hard problem in machine learning and computational geometry,the k-means problem aims to partition the given dataset into k clusters according to the minimal squared Euclidean *** from k-means problem and most of its variants,fuzzy k-means problem belongs to the soft clustering problem,where each given data point has relationship to every center *** to fuzzy k-means problem,fuzzy k-means problem with penalties allows that some data points need not be clustered instead of being paid *** this paper,we propose an O(αk In k)-approximation algorithm based on seeding algorithm for fuzzy k-means problem with penalties,whereαinvolves the ratio of the maximal penalty value to the minimal ***,we implement numerical experiments to show the effectiveness of our algorithm.

关键词： Approximation algorithm Seeding algorithm Fuzzy k-means problem with penalties

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

The Perturbed Compound Poisson Risk Model with Proportional Investment

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Acta Mathematicae Applicatae Sinica 2024年第1期40卷 109-128页

作者： Nai-dan Deng Chun-wei Wang Jia-en Xu school of mathematics and statistics Henan University of Science and TechnologyLuoyang471023China

In this paper, the insurance company considers venture capital and risk-free investment in a constant proportion. The surplus process is perturbed by diffusion. At first, the integro-differential equations satisfied by the expected discounted dividend payments and the Gerber-Shiu function are derived. Then, the approximate solutions of the integro-differential equations are obtained through the sinc method. Finally, the numerical examples are given when the claim sizes follow different distributions. Furthermore, the errors between the explicit solution and the numerical solution are discussed in a special case.

关键词： expected discounted dividend payments lognormal distribution proportional investment perturbed risk model sinc numerical method

Neighbor Sum Distinguishing Total Choosability of Planar Graphs with Maximum Degree at Least 10

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Acta Mathematicae Applicatae Sinica 2024年第1期40卷 211-224页

作者： Dong-han Zhang You Lu Sheng-gui Zhang Li Zhang school of mathematics and statistics Northwestern Polytechnical UniversityXi’an710129China school of mathematics and Computer Application Shangluo UniversityShangluo726000China

A neighbor sum distinguishing(NSD)total coloringφof G is a proper total coloring of G such thatΣz∈EG(u)U{u}φ(z)≠Σz∈EG(v)U{v}φ(z)for each edge uv∈E(G),where EG(u)is the set of edges incident with a vertex *** 2015,Pilśniak and Wozniak conjectured that every graph with maximum degreeΔhas an NSD total(Δ+3)-***,Yang et *** that the conjecture holds for planar graphs withΔ≥10,and Qu et *** that the list version of the conjecture also holds for planar graphs withΔ≥*** this paper,we improve their results and prove that the list version of the conjecture holds for planar graphs withΔ≥10.

关键词： planar graphs neighbor sum distinguishing total choosibility combinatorial nullstellensatz discharging method

MIXED DISCONTINUOUS GALERKIN METHOD FOR QUASI-NEWTONIAN STOKES FLOWS

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Journal of Computational mathematics 2024年第3期42卷 885-910页

作者： Yanxia Qian Fei Wang Wenjing Yan school of mathematics and statistics Xi'an Jiaotong UniversityXi'an 710049China school of mathematics and statistics&State Key Laboratory of Multiphase Flow in Power Engineering Xi'an Jiaotong UniversityXi'an 710049China

In this paper,we introduce and analyze an augmented mixed discontinuous Galerkin(MDG)method for a class of quasi-Newtonian Stokes *** the mixed formulation,the unknowns are strain rate,stress and velocity,which are approximated by a discontinuous piecewise polynomial triplet ■for k≥***,the discontinuous piecewise polynomial function spaces for the field of strain rate and the stress field are designed to be *** addition,the pressure is easily recovered through simple *** the benefit of the analysis,we enrich the MDG scheme with the constitutive equation relating the stress and the strain rate,so that the well-posedness of the augmented formulation is obtained by a nonlinear functional *** k≥0,we get the optimal convergence order for the stress in broken ■(div)-norm and velocity in L^(2)-***,the error estimates of the strain rate and the stress in-norm,and the pressure in L^(2)-norm are optimal under certain ***,several numerical examples are given to show the performance of the augmented MDG method and verify the theoretical *** evidence is provided to show that the orders of convergence are sharp.

关键词： Quasi-Newtonian fows Mixed discontinuous Galerkin method Symmetric strain rate Symmetric stress Optimal convergence orders

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 mathematics 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