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Improved Approximation Schemes for Early Work Scheduling on Identical Parallel Machines with a Common Due Date

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Journal of the Operations Research Society of China 2024年第2期12卷 341-350页

作者： Wei-Dong Li school of mathematics and statistics Yunnan UniversityKunming650504YunnanChina

We study the early work scheduling problem on identical parallel machines in order to maximize the total early work,i.e.,the parts of non-preemptive jobs that are executed before a common due *** preprocessing and constructing an auxiliary instance which has several good properties,for any desired accuracy,we propose an efficient polynomial time approximation scheme with running time O(f(1/ε)n),where n is the number of jobs and f(1/ε)is exponential in 1/ε,and a fully polynomial time approximation scheme with running time O(1/ε^(2m+1)+n)when the number of machines is fixed.

关键词： Scheduling Early work Polynomial time approximation scheme Effcient polynomial time approximation scheme Fully polynomial time approximation scheme

Local Hamilton type Gradient Estimates and Harnack Inequalities for Nonlinear Parabolic Equations on Riemannian Manifolds

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Acta Mathematicae Applicatae Sinica 2024年第2期40卷 539-546页

作者： Wen WANG Da-peng XIE Hui ZHOU school of mathematics and statistics Hefei Normal UniversityHefei 230601China

In this paper,we prove a local Hamilton type gradient estimate for positive solution of the nonlinear parabolic equation ut(x,t)=Δu(x,t)+au(x,t) ln u(x,t)+bu^(α)(x,t),on M×(-∞,∞) with α∈R,where a and b are *** ... 详细信息

关键词： nonlinear parabolic equation gradient estimate Harnack inequality

A dynamical neural network approach for distributionally robust chance-constrained Markov decision process

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Science China mathematics 2024年第6期67卷 1395-1418页

作者： Tian Xia Jia Liu Zhiping Chen school of mathematics and statistics Xi’an Jiaotong UniversityXi’an710049China

In this paper,we study the distributionally robust joint chance-constrained Markov decision *** the logarithmic transformation technique,we derive its deterministic reformulation with bi-convex terms under the moment-based uncertainty *** cope with the non-convexity and improve the robustness of the solution,we propose a dynamical neural network approach to solve the reformulated optimization *** results on a machine replacement problem demonstrate the efficiency of the proposed dynamical neural network approach when compared with the sequential convex approximation approach.

关键词： Markov decision process chance constraints distributionally robust optimization moment-based ambiguity set dynamical neural network

Eventually homological isomorphisms and Gorenstein projective modules

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Science China mathematics 2024年第8期67卷 1719-1734页

作者： Yongyun Qin Dawei Shen school of mathematics Yunnan Normal UniversityKunming 650500China school of mathematics and statistics Henan UniversityKaifeng 475004China

We prove that a certain eventually homological isomorphism between module categories induces triangle equivalences between their singularity categories,Gorenstein defect categories and stable categories of Gorenstein projective ***,we show that the Auslander-Reiten conjecture and the Gorenstein symmetry conjecture can be reduced by eventually homological *** these results to arrow removal and vertex removal,we describe the Gorenstein projective modules over some non-monomial algebras and verify the Auslander-Reiten conjecture for certain algebras.

关键词： singularity categories Gorenstein defect categories Gorenstein projective modules AuslanderReiten conjecture Gorenstein symmetry conjecture eventually homological isomorphisms

Optimal Model Average Prediction in Orthogonal Kriging Models

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Journal of Systems Science & Complexity 2024年第3期37卷 1080-1099页

作者： WANG Jun HE Jiabei LIANG Hua LI Xinmin school of mathematics and statistics Qingdao UniversityQingdao 266071China Department of statistics George Washington UniversityWashington DC 20052USA

The main objective of this paper is to consider model averaging methods for kriging *** paper proposes a Mallows model averaging procedure for the orthogonal kriging model and demonstrate the asymptotic optimality of the model averaging estimators in terms of mean square *** studies are conducted to evaluate the performance of the proposed method and compare it with the competitors to demonstrate its *** authors also analyse a real dataset for an illustration.

关键词： Asymptotic optimality Mallows criterion optimal model averaging orthogonal kriging model

Locally and globally uniform approximations for ruin probabilities of a nonstandard bidimensional risk model with subexponential claims

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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

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

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