一类具有加权总规模的非线性种群扩散系统的最优控制

讨论了一类与年龄相关的非线性种群扩散系统的最优控制问题,其生死率依赖于个体年龄和加权总规模.利用不动点原理确立了系统的适定性,借助于法锥概念得到了控制问题最优解存在的必要条件.这些结果可为种群扩散系统最优控制问题的实际研究提供理论基础.     

一类具有年龄分布的非线性种群系统的最优控制

研究了一类非线性种群系统的最优控制问题.利用Ekeland变分原理和共轭系统证明了最优收获的存在性,并借助于法锥概念得到了最优控制的必要性条件.     

污染环境中具有尺度结构的周期种群系统的最优控制

本文研究污染环境中具有尺度结构的周期种群系统的最优控制问题.首先,利用积分方程及算子理论证明非负解的存在唯一性,接着利用Mazur定理确定最优策略的存在性,又借助切锥法锥的技巧,导出控制问题的最优条件.     

具有年龄结构两竞争种群系统的适定性和最优控制

本文研究了具有年龄结构两竞争种群系统的适定性和最优控制问题.利用不动点定理,证明了系统解的存在唯一性,并利用法锥原理得到最优控制所满足的必要条件,推广了一些文献的工作.     

污染环境中具有年龄结构的非线性时变种群扩散系统的最优控制

本文研究污染环境中具有年龄结构的非线性时变种群扩散系统的最优控制问题.利用不动点定理得到该系统非负解的存在性和唯一性.利用极小化序列及紧性证明最优控制的存在性.利用法锥性质,得到最优控制的必要性条件.     

考虑污染和种内关系的种群扩散最优控制模型

针对污染和种内关系均影响细菌种群扩散这一管理生态学问题,本文建立了基于非线性拟抛物方程的最优控制模型,将外界环境向细菌种群输入的毒素率作为控制变量,运用控制理论和方法探讨污染和种内关系双重影响下种群扩散系统的最优控制问题。利用Schauder不动点定理证明了该种群扩散系统的适定性;同时,通过建立新的Carleman型估计,给出了容许控制和最优控制的存在性。最后,通过数值算例分析了理论推导的结果,在算例中都找到一对时间最优控制,验证了种群扩散系统最优控制模型的有效性。该研究结果对现代传染病预防具有借鉴意义,也为有效控制瘟疫的爆发和流行提供理论参考。     

年龄相关的种群扩散系统广义解的正则性

证明了年龄相关的种群扩散系统广义解的正则性,为进一步讨论该系统最优控制的存在性奠定了理论基础,也为种群系统控制问题的实际研究提供了数学理论和方法.     

年龄相关的非线性时变种群扩散系统最优分布控制的存在性

讨论了一类非线性时变种群扩散系统的最优分布控制问题,利用LionsJL的偏微控制理论和先验估计,证明了系统最优分布控制的存在性.所得结果可为非线性种群扩散系统中的最优控制问题的实际研究提供必要的理论基础.     

一类种群系统的适定性及最优收获问题

本文研究了一类非线性时变种群扩散系统的适定性及最优收获问题.利用压缩不 动点原理讨论了该种群系统的解的存在唯一性.证明了最优收获控制的存在性,并且获 得了最优控制的唯一性和所满足的必要条件.     

一类改进的非线性种群系统的最优控制

研究某一类改进的关于年龄结构的非线性种群系统的最优控制问题.首先利用常用的极小化序列方法证明最优控制问题的最优解存在;其次定义原系统对应的共轭系统,借助于法锥定义,得到最优解所要满足的必要条件.     

On small perturbations of a nonlinear periodic system with degenerate equilibrium

This paper considers the reducibility and existence of periodic solutions for a class of nonlinear periodic system with a degenerate equilibrium point under small perturbations. By introducing some parameter, we consider an equivalent periodic system. Then we prove that by an affine linear periodic transformation the parameterized periodic system is reducible to one with zero as an equilibrium. Topological degree theorem ensures that for some parameter the result can go back to the original system. Then, we obtain a small periodic solution.     

The Rayleigh-Ritz method, refinement and Arnoldi process for periodic matrix pairs

We extend the Rayleigh-Ritz method to the eigen-problem of periodic matrix pairs. Assuming that the deviations of the desired periodic eigenvectors from the corresponding periodic subspaces tend to zero, we show that there exist periodic Ritz values that converge to the desired periodic eigenvalues unconditionally, yet the periodic Ritz vectors may fail to converge. To overcome this potential problem, we minimize residuals formed with periodic Ritz values to produce the refined periodic Ritz vectors, which converge under the same assumption. These results generalize the corresponding well-known ones for Rayleigh-Ritz approximations and their refinement for non-periodic eigen-problems. In addition, we consider a periodic Arnoldi process which is particularly efficient when coupled with the Rayleigh-Ritz method with refinement. The numerical results illustrate that the refinement procedure produces excellent approximations to the original periodic eigenvectors.     

Single periodic Riemann problems for null-solutions to polynomially Cauchy–Riemann equations

In this paper, we focus on single periodic Riemann problems for a class of meta-analytic functions, i.e. null-solutions to polynomially Cauchy–Riemann equation. We first establish decomposition theorems for single periodic meta-analytic functions. Then, we give a series expansion of single periodic meta-analytic functions, and derive generalised Liouville theorems for them. Next, we introduce a definition of order for single periodic meta-analytic functions at infinity, and characterise their growth at infinity. Finally, applying the decomposition theorem for single periodic meta-analytic functions, we get explicit expressions of solutions and condition of solvability to Riemann problems for single periodic meta-analytic functions with a finite order at infinity.     

一种广义周期Besov类的多元周期多项式样条逼近

本文证明多元多项式周期样条空间是某些多元周期光滑函数类的关于Kolmogorov n-宽度的弱渐近极子空间．给出了广义周期Besov类的一种推广，得到了空间元素的一种表示定理，不仅给出了一种多元周期多项式样条算子．而且证明了所得的结果．     

Bochner’s theorem and Stepanov almost periodic functions

Motivated by a renewed interest in generalizations of classical almost periodicity (originally due to Harald Bohr), we develop a theorem of Bochner within the framework of almost periodic functions in the sense of Stepanov. As a result we establish some conditions that guarantee the existence of Stepanov almost periodic solutions to differential equations with Stepanov almost periodic coefficients. Finally, we extend a now classic theorem of Favard originally stated for classical almost periodic functions to the Stepanov almost periodic case.      

周期B样条基转换矩阵的表示和计算

周期B样条基以一种简洁的形式表示闭B样条曲线.周期B样条基转换矩阵为闭B样条曲线及相关曲面的不同表示间的转换提供了一个数学模型.本文给出了周期B样条基转换矩阵的存在性条件,给出并证明了周期B样条基转换矩阵的一个简单的递归表示式.在此基础上,本文进一步给出了周期B样条基转换矩阵的计算公式和高效算法.周期B样条基转换矩阵为闭B样条曲线的节点插入、升阶、节点删除和降阶等基本运算提供了一个统一而简单的解决方法,本文给出了一些应用例子.     

Periodic solution of a stochastic SIQR epidemic model incorporating media coverage

In this paper, we propose a stochastic SIQR epidemic model with periodic parameters and media coverage. Firstly, we study that the stochastic non-autonomous periodic system has a unique global positive solution. Secondly, by using the Khasminskii''s theory, we prove that this stochastic periodic system has a nontrivial positive periodic solution. Then, we obtain the sufficient condition for extinction of the disease. Finally, numerical simulations are employed to illustrate our theoretical analysis.     

The New Method for the Searching Periodic Solutions of Periodic Differential Systems

In the paper we are giving the new method for searching periodic solutions of periodic differential systems. For this we construct a differential system with the same Reflecting Function as the Reflecting Function of the given system and with a known periodic solution. Then the initial data of the periodic solutions of this two systems coincide. In such a way the problem of existance periodic solutions goes to the Cauchy problem.     

Quadratic control for linear periodic systems

We propose a new quadratic control problem for linear periodic systems which can be finite or infinite dimensional. We consider both deterministic and stochastic cases. It is a generalization of average cost criterion, which is usually considered for time-invariant systems. We give sufficient conditions for the existence of periodic solutions.Under stabilizability and detectability conditions we show that the optimal control is given by a periodic feedback which involves the periodic solution of a Riccati equation. The optimal closed-loop system has a unique periodic solution which is globally exponentially asymptotically stable. In the stochastic case we also consider the quadratic problem under partial observation. Under two sets of stabilizability and detectability conditions we obtain the separation principle. The filter equation is not periodic, but we show that it can be effectively replaced by a periodic filter. The theory is illustrated by simple examples.This work was done while this author was a visiting professor at the Scuola Normale Superiore, Pisa.     

On the module containment of the almost periodic solution for a class of differential equations with piecewise constant delays

In the first part of this paper, we obtain a new property on the module containment for almost periodic functions. Based on it, we establish the module containment of an almost periodic solution for a class of differential equations with piecewise constant delays. In the second part, we investigate the existence, uniqueness and exponential stability of a positive almost periodic and quasi-periodic solution for a certain class of logistic differential equations with a piecewise constant delay. The module containment for the almost periodic solution is established.