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Stochastic maximum principle for optimal control problems involving delayed systems

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Science China(Information Sciences) 2021年第1期64卷 269-271页

作者： Feng ZHANG School of mathematics and quantitative economics Shandong University of Finance and Economics

Dear editor,The main objective of this study is to investigate one type of stochastic optimal control problem for a delayed system using the maximum principle *** existing research can be categorized into two *** the first category,the adjoint equation comprises two backward stochastic differential equations (BSDEs) and one backward ordinary differential equation (BODE),which is assumed to have a zero solution;see e.g.,[1-3].However,there is still scope for improvement in this research ***,a special setting is considered for the system parameters;see e.g.,(3.9)and (3.12) in *** BODE is assumed to result in a zero solution when the necessary maximum principle is strictly applied;see e.g.,Theorem 5.1 in *** the second category,a typee of anticipated/time-advanced BSDE is introduced as the adjoint equation;see e.g.,[1,4-7].

关键词： stochastic optimal control maximum principle delayed system anticipated BSDE linear quadratic problem

Unique Solvability for a Class of Non-newtonian Fluids for a Reacting Mixture with Vacuum

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Acta Mathematicae Applicatae Sinica 2016年第4期32卷 833-850页

作者： Hong-jun YUAN Jia-ning XIE College of mathematics Jilin University School of mathematics and quantitative economics Dongbei University of Finance and Economics

In this paper,we consider a class of non-Newtonian fluids for a reacting mixture in one-dimensional bounded interval, provided the initial data satisfying a compatibility condition. The main ingredient is that we allo... 详细信息

关键词： existence and uniqueness reactive gas flow vacuum non-Newtonian

Uniform partition extensions,a generating functions perspective

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Science China mathematics 2015年第12期58卷 2655-2670页

作者： LI ShanHai MA Jun YEH YeongNan School of mathematics and quantitative economics Shandong University of Finance and Economics department of mathematics Shanghai Jiao Tong University Institute of mathematics Academia Sinica

In this paper, a bivariate generating function CF(x, y) =f(x)-yf(xy)1-yis investigated, where f(x)= n 0fnxnis a generating function satisfying the functional equation f(x) = 1 + r j=1 m i=j-1aij xif(x)*** particular, we study lattice paths in which their end points are on the line y = 1. Rooted lattice paths are defined. It is proved that the function CF(x, y) is a generating function defined on some rooted lattice paths with end point on y = 1. So, by a simple and unified method, from the view of lattice paths, we obtain two combinatorial interpretations of this bivariate function and derive two uniform partitions on these rooted lattice paths.

关键词： Chung-Feller theorem Dyck path Motzkin path Schr¨oder path

A Jacobi-collocation method for solving second kind Fredholm integral equations with weakly singular kernels

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Science China mathematics 2014年第10期57卷 2163-2178页

作者： CAI Hao Tao School of mathematics and quantitative economics Shandong University of Finance and Economics

In this work,we propose a Jacobi-collocation method to solve the second kind linear Fredholm integral equations with weakly singular ***,we consider the case when the underlying solutions are sufficiently *** this case,the proposed method leads to a fully discrete linear *** show that the fully discrete integral operator is stable in both infinite and weighted square ***,we establish that the approximate solution arrives at an optimal convergence order under the two ***,we give some numerical examples,which confirm the theoretical prediction of the exponential rate of convergence.

关键词： second kind Fredholm integral equations with weakly singular kernels Jacobi-collocation methods stability analysis convergence analysis

RMB Appreciation, Output Growth, and Inflation

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Economic and Political Studies 2013年第2期1卷 3-17页

作者： YONGWEI CHEN DONG LI department of mathematics and quantitative economics Zhongnan University of Economics and Law the department of economics Kansas State University and Department of Mathematics and Quantitative Economics Zhongnan University of Economics and Law

Following Dibooglu and Kutan(2005),we construct a structural VAR model to investigate the impact of RMB(the Chinese currency)appreciation on growth and inflation in *** empirical results show that RMB appreciation has negative effects on output growth and inflation while neither effect is statistically ***,exchange rate shocks are important in the fluctuations of output growth and *** also simulate the scenario of a sharp currency appreciation compared to the gradual approach adopted by the Chinese *** the counterfactual analysis we find that a sharp appreciation would lead to more violent shocks in economic growth and inflation compared to the gradual approach.

关键词： growth inflation RMB structural VAR

Two 8-node quadrilateral spline elements by B-net method

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Acta Mechanica Sinica 2012年第6期28卷 1620-1629页

作者： Juan Chen Chong-Jun Li School of mathematics and quantitative economics Dongbei University of Finance and Economics School of Mathematical Sciences Dalian University of Technology

Isoparametric quadrilateral elements are widely used in the finite element method, but the accuracy of the isoparametric quadrilateral elements will drop obviously deteriorate due to mesh distortions. Spline functions have some properties of simplicity and conformality. Two 8-node quadrilateral elements have been developed using the trian- gular area coordinates and the B-net method, which can ex- actly model the quadratic field for both convex and concave quadrangles. Some appropriate examples are employed to evaluate the performance of the proposed elements. The nu- merical results show that the two spline elements can obtain solutions which are highly accurate and insensitive to mesh distortions.

关键词： Spline finite element B-net method Quadri-lateral element - Bivariate spline interpolation The secondorder completeness

Development of quadrilateral spline thin plate elements using the B-net method

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Acta Mechanica Sinica 2013年第4期29卷 567-574页

作者： Juan Chen Chong-Jun Li School of mathematics and quantitative economics Dongbei University of Finance and Economics School of Mathematical Sciences Dalian University of Technology

The quadrilateral discrete Kirchhoff thin plate bending element DKQ is based on the isoparametric element Q8, however, the accuracy of the isoparametric quadrilateral elements will drop significantly due to mesh distortions. In a previous work, we constructed an 8-node quadrilateral spline element L8 using the triangular area coordinates and the B- net method, which can be insensitive to mesh distortions and possess the second order completeness in the Cartesian co- ordinates. In this paper, a thin plate spline element is devel- oped based on the spline element L8 and the refined tech- nique. Numerical examples show that the present element indeed possesses higher accuracy than the DKQ element for distorted meshes.

关键词： Spline finite element ~ Refined quadrilateral el-ement ~ Discrete Kirchhoff plate element ~ Triangular areacoordinates ~ B-net method

Four Forbidden Subgraph Pairs for Hamiltonicity of 3-connected Graphs

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Acta Mathematicae Applicatae Sinica 2016年第2期32卷 469-476页

作者： Hou-yuan LIN Zhi-quan HU School of mathematics and quantitative economics Shandong University of Finance and Economics Faculty of mathematics and Statistics Central China Normal University

For non-negative integers i,j and k, we denote the generalized net as Ni,j,k, which is a triangle with disjoint paths of length i, j and k, attached to distinct vertices of the triangle. In this paper, we prove that e... 详细信息

关键词： hamiltonian cycle forbidden subgraphs claw-free graphs closure

Approximate Solutions of Nonlinear Fractional Kolmogorov-Petrovskii-Piskunov Equations Using an Enhanced Algorithm of the Generalized Two-Dimensional Differential Transform Method

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Communications in Theoretical Physics 2012年第8期58卷 182-188页

作者：宋丽哪王维国 Center for Econometric Analysis and Forecasting School of Mathematics and Quantitative Economics Dongbei University of Finance and Economics

By constructing the iterative formula with a so-called convergence-control parameter, the generalized two-dimensional differential transform method is improved. With the enhanced technique, the nonlinear fractional Kolmogorov-Petrovskii-Piskunov equations are dealt analytically and approximate solutions are derived. The results show that the employed approach is a promising tool for solving many nonlinear fractional partial differential equations. The algorithm described in this work is expected to be employed to solve more problems in fractional calculus.

关键词： differential transform method fractional differential equation approximate solution