年龄等级结构两种群系统模型解的存在唯一性

本文提出一类新的显示等级差异的两种群系统框架模型,它是具有全局反馈边界条件的偏微分-积分方程组,能描述种群内部和种群之间的竞争、合作、捕食等各种关系.基于一组较为自然的参数条件,运用不动点方法建立了无穷时域中模型非负解的存在唯一性,借助特征线和积分不等式导出解对初始年龄分布的一致连续性.所获结果为研究系统稳定性、能控性及各类最优控制问题奠定了基础.     

采用复合规则约束的多种群自适应进化算法

针对种群固定的进化算法容易使个体集中分布在局部区域,不利于处理大尺度空间和多峰类型的优化问题,提出了一种多种群分布并且动态变化的种群自适应进化算法.采用Logistic模型模拟多个种群在有限资源下的竞争关系,设计了稳定性规则、熵规则和精英规则以确定不同种群的Logistic模型参数,从而控制种群数量的变化.同时,算法引入了算术内插和外插两种交叉算子,使得各个种群依据自身类型来缩小或扩展搜索空间.此外,算法还通过周期性的调整规则重新构建种群和分配资源.通过5组大尺度和多峰优化问题的测试结果表明,所提的种群自适应方法能够有效改善算法的寻优性能,在达到同等优化水平时所提算法消耗的函数调用次数为对比算法的61.08%～91.55%.     

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.     

带环境污染的与年龄相关的非线性种群动力系统的最优控制

研究带环境污染的与年龄相关的非线性种群动力系统的最优控制问题,利用不动点定理得出系统非负解的存在性和唯一性,利用极大化序列及紧性证明最优控制的存在性,利用法锥方法得到控制问题的最优条件.     

基于种群自适应调整的多目标差分进化算法

为提高已有多目标进化算法在求解复杂多目标优化问题上的收敛性和解集分布性,提出一种基于种群自适应调整的多目标差分进化算法。该算法设计一个种群扩增策略,它在决策空间生成一些新个体帮助搜索更优的非支配解;设计了一个种群收缩策略,它依据对非支配解集的贡献程度淘汰较差的个体以减少计算负荷,并预留一些空间给新的带有种群多样性的扰动个体;引入精英学习策略,防止算法陷入局部收敛。通过典型的多目标优化函数对算法进行测试验证,结果表明所提算法相对于其他算法具有明显的优势,其性能优越,能够在保证良好收敛性的同时,使获得的Pareto最优解集具有更均匀的分布性和更广的覆盖范围,尤其适合于高维复杂多目标优化问题的求解。     

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.     

依赖个体尺度结构的种群资源开发模型理论分析

研究一类具有个体尺度结构的非线性种群控制模型.确立了状态系统模型非负解的存在唯一性,以及状态关于控制变量的连续依赖性.应用紧性推理和极值化序列法证明了最优策略的存在性,借助切锥法锥和共轭系统技巧导出了最优性条件.     

基于Leslie种群模型的城市流浪猫数量模型研究

城市中日益增多的流浪猫正在成为一个人们关注的问题.其种群个体数量有不同的模型可用于描述,这里应用Leslie种群模型建立了城市雌性流浪猫数量模型,并在此基础上推导了整体数量模型;分析了随时间发展流浪猫数量的性态.根据有关资料数据,给出模型算例,预测了发展趋势.     

两种群竞争和合作模型的全局渐近稳定性

其中R=r/K,r为种群的内禀自然增长率,K为环境容纳量,N为种群数量(或密度)。 考虑在周期环境中两种群竞争(合作),此时每一种群的生长由于另一种群的存在而减少(增加),可设这时i种群的环境容纳量为     

生物种群在污染环境中的生灭过程

建立了生物种群在污染环境中的一个线性生灭过程模型.利用马尔可夫过程的理论和方法,得到生物种群数量变化的概率分布,最后讨论了各模型参数的变化对生物种群生存的影响.     

Spectral Mapping Theorem for Fractional Powers of Linear Relations

In this paper, we give the fractional powers version of spectral mapping theorems for various essential spectra of non-negative linear operators and non-negative linear relations.     

Separating inequalities for non-negative covariances

We demonstrate explicit inequalities which separate covariances generated by non-negative stochastic processes from the class consisting of all non-negative covariances. The first class of covariances corresponds to completely positive matrices whereas the second class corresponds to doubly non-negative matrices. A key ingredient in our analysis is a new result the "convexity" of quatratic functions defined on the surface of a sphere.     

L 1 ergodic behavior of non-negative kernels

Some results that have been obtained in the study of strongly and weakly ergodic behavior of non-homogeneous stochastic kernels are generalized to the case of non-negative kernels. The first generalization simply involves extending the definitions of weakly and strongly ergiodic behavior to the case of non-negative kernels and using the ergodic coefficient which was first defined for stochastic kernels by Dobrushin and extended to non-negative kernels by Blum and Reichaw. It happens that this straightforward extension excludes many cases of non-negative kernels which do exhibit a types of ergodic behavior. In order to study these cases a definition ofL ₁ weakly and strongly ergodic behavior is given in which normalizing by constants is allowed. Sufficient conditions for these types of ergodic behavior are given.     

四阶边值问题的非负解

讨论了一类四阶非线性常微分方程两点边值问题非负解的存在性.利用锥不动点指数理论得到了方程存在非负解的充分条件.     

Separating inequalities for non-negative covariances

We demonstrate explicit inequalities which separate covariances generated by non-negative stochastic processes from the class consisting of all non-negative covariances. The first class of covariances corresponds to completely positive matrices whereas the second class corresponds to doubly non-negative matrices. A key ingredient in our analysis is a new result the "convexity" of quatratic functions defined on the surface of a sphere.     

Existence of large solutions of a class of quasilinear elliptic equations with singular boundary

We study a class of quasilinear elliptic equations with boundary blow-up. Based on super and sub-solution arguments and certain comparison principle, we prove the existence of non-negative solutions of (1.1). Moreover, we show the existence of maximal and minimal non-negative solutions of (1.1).     

Entrywise relative perturbation bounds for exponentials of essentially non-negative matrices

A real square matrix is said to be essentially non-negative if all of its off-diagonal entries are non-negative. We establish entrywise relative perturbation bounds for the exponential of an essentially non-negative matrix. Our bounds are sharp and contain a condition number that is intrinsic to the exponential function. As an application, we study sensitivity of continuous-time Markov chains. J. Xue was supported by the National Science Foundation of China under grant number 10571031, the Program for New Century Excellent Talents in Universities of China and Shanghai Pujiang Program. Q. Ye was supported in part by NSF under Grant DMS-0411502.     

模糊Choquet-可积函数空间的凸锥结构

在一般有限模糊测度空间上研究了非负模糊Choquet-可积函数的模糊测度表示, 进而获得了非负模糊Choquet-可积函数空间和一般模糊Choquet-可积函数空间构成凸锥的充要条件.     

Sur certaines martingales de Mandelbrot

We consider a non-negative martingale, defined by sums of product of non-negative random weights indexed by nodes of a Galton-Watson tree. In case the limit variable is not degenerate, we study the asymptotic behaviour at infinity of its distribution; in the contrary case, we prove that there is an associated natural martingale which converges to a non-negative random variable with infinite mean. The two limit variables satisfy the same distributional equation.     

Some new results for demimartingales

Harremoёs obtained some new maximal inequalities for non-negative martingales. In this paper, we get some new maximal and minimal inequalities for non-negative demimartingales which generalize the results of Harremoёs. We also obtain an inequality for non-negative demimartingales which generalizes the result of Iksanov and Marynych. Finally we obtain a strong law of large numbers, strong growth rate and integrability of supremum for demimartingales which generalize and improve the result of Chow.