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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 systems.Both 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

Balanced pairs and relative tilting objects in recollements of abelian categories

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Acta Mathematica Sinica,English Series 2024年

作者： Pei Yu ZHANG Meng Hui LIU Da Jun LIU Jia Qun WEI school of mathematics-physics and finance Anhui Polytechnic University Department of mathematics Zhejiang Normal University

In this paper, we study the relationship of balanced pairs in a recollement. As an application of balanced pairs, we introduce the notion of the relative tilting objects, and give a characterization of relative tilting objects, which is similar to Bazzoni characterization of n-tilting modules. Finally, we investigate the relationship of relative tilting objects in a recollement.

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Constraints on the primordial curvature power spectrum by pulsar timing array data:a polynomial parameterization approach

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Communications in Theoretical physics 2024年第1期76卷 96-104页

作者： Qin Fei school of mathematics and physics Hubei Polytechnic UniversityHuangshi 435003China

The recent stochastic signal observed jointly by NANOGrav,parkes pulsar timing array,European pulsar timing array,and Chinese pulsar timing array can be accounted for by scalarinduced gravitational waves(SIGWs).The source of the SIGWs is from the primordial curvature perturbations,and the main contribution to the SIGWs is from the peak of the primordial curvature power spectrum.To effectively model this peak,we apply the Taylor expansion to parameterize it.With the Taylor expansion parameterization,we apply Bayesian methods to constrain the primordial curvature power spectrum based on the NANOGrav 15 year data set.The constraint on the primordial curvature power spectrum possesses a degree of generality,as the Taylor expansion can effectively approximate a wide range of function profiles.

关键词： pulsar timing array scalar-induced gravitational waves inflation

A wealth distribution model with a non-Maxwellian collision kernel

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Chinese physics B 2024年第7期 234-242页

作者：孟俊周霞赖绍永 College of mathematics and Statistics Kashi University College of mathematics and physics Mianyang Teacher's College school of mathematics Southwestern University of Finance and Economics

A non-Maxwellian collision kernel is employed to study the evolution of wealth distribution in a multi-agent society.The collision kernel divides agents into two different groups under certain conditions. Applying the kinetic theory of rarefied gases, we construct a two-group kinetic model for the evolution of wealth distribution. Under the continuous trading limit, the Fokker–Planck equation is derived and its steady-state solution is obtained. For the non-Maxwellian collision kernel, we find a suitable redistribution operator to match the taxation. Our results illustrate that taxation and redistribution have the property to change the Pareto index.

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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

Annihilator Ideals of Indecomposable Modules of Finite-Dimensional Pointed Hopf Algebras of Rank One

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Algebra Colloquium 2024年第1期31卷 149-164页

作者： Yu Wang school of mathematics and physics Jiangsu University of Technology ChangzhouJiangsu 213001China

Let H be a finite-dimensional pointed Hopf algebra of rank one over an algebraically closed feld of characteristic zero.We describe all annihilator ideals of indecomposable H-modules by generators.In particular,we give the classification of all ideals of the finite-dimensional pointed rank one Hopf algebra of nilpotent type over the Klein 4-group.

关键词： indecomposable module annihilator ideal primitive central orthogonal idem-potent element

Parametric “non-nested” discriminants for multiplicities of univariate polynomials

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Science China mathematics 2024年第8期67卷 1911-1932页

作者： Hoon Hong Jing Yang Department of mathematics North Carolina State University SMS–HCIC–school of mathematics and physics Center for Applied Mathematics of GuangxiGuangxi Minzu University

We consider the problem of complex root classification, i.e., finding the conditions on the coefficients of a univariate polynomial for all possible multiplicity structures on its complex roots. It is well known that such conditions can be written as conjunctions of several polynomial equalities and one inequality in the coefficients. Those polynomials in the coefficients are called discriminants for multiplicities. It is also known that discriminants can be obtained using repeated parametric greatest common divisors. The resulting discriminants are usually nested determinants, i.e., determinants of matrices whose entries are determinants, and so on. In this paper, we give a new type of discriminant that is not based on repeated greatest common divisors. The new discriminants are simpler in the sense that they are non-nested determinants and have smaller maximum degrees.

关键词： parametric polynomial complex roots discriminant multiplicity resultant

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 groups.We are particularly interested in the case of a subgroup G of the parabolic subgroups of GLn(q)which generalizes the Weyl grou... 详细信息

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

Digital signal acquisition system for complex nuclear reaction experiments

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Nuclear Science and Techniques 2024年第1期35卷 124-133页

作者： Wei-Liang Pu Yan-Lin Ye Jian-Ling Lou Jia-Hao Chen school of physics and State Key Laboratory of Nuclear physics and Technology Peking UniversityBeijing 100871China Institute of Applied physics and Computational mathematics Beijing 100094China

A digital data-acquisition system based on XIA LLC products was used in a complex nuclear reaction experiment using radioactive ion beams.A flexible trigger system based on a field-programmable gate array(FPGA)parametrization was developed to adapt to different experimental sizes.A user-friendly interface was implemented,which allows converting script language expressions into FPGA internal control parameters.The proposed digital system can be combined with a conventional analog data acquisition system to provide more flexibility.The performance of the combined system was veri-fied using experimental data.

关键词： Digital signal acquisition system Trigger Programmable logic Timestamp