几乎渐近拟非扩张型映象具混合误差的迭代逼近问题

通过引入一类新的几乎渐近拟非扩张型映象,研究了此映象的不动点具混合误差项的修正的Ishikawa迭代序列的迭代逼近问题,所得结果改进和推广了已有相关结果,且所用的证明方法也不全相同。     

φ-强伪压缩映象不动点的Ishikawa迭代逼近

在一般的Banach空间中,研究了φ-强伪压缩映象和φ-强增生映象的I shikawa迭代序列的收敛问题,去掉了通常文献中关于空间X的一致光滑或q-一致光滑的严格要求,改进了近年来文献中的一系列相应结果.     

ψ—强伪压缩映象不动点的Ishikawa迭代逼近

在一般的Banach空间中,研究了ψ－强伪压缩映象和ψ－强增生映象的Ishikawa迭代序列的收敛问题,去掉了通常文献中关于空间X的一致光滑或q-一致光滑的严格要求,改进了近年来文献中的一系列相应结果。     

概率度量空间中的两个定理

本文揭示了文[1]第九章中第(2)与第(4)型压缩映象的本质区别;在此基础上给出了一个定理,它是[1]中定理9、3、6与9、3、10的推广.做为该定理的一个应用、在稍强的条件下,给出[1]中定理9.3.13的一般形式。     

楔形上Altman不等式的推广

本文给出Bnnach空间中楔形上半紧1-集压缩映象A的方程Az=ux解的某些结果。其次,还扩充和改进几个具Altman型行列式的不等式的不动点定理。     

度量空间压缩映象的拟Picard迭代收敛性定理

游兆永在概率度量空间中首次研究了拟Picard迭代,获得了四个收敛性定理。本文讨论了度量空间中压缩映象的拟Picard迭代,非常有趣的是,我们所得定理的证明应用了概率度量空间理论。 下面出现的φ和Ψ,我们总假定是[0,+∞)→[0,+∞)的严格递增的连续函数,且φ(t)0,t—(φ(t))→+∞(t→+∞)。     

关于Banach空间中渐近非扩张型映象具混合误差的迭代序列的收敛问题

研究了Banach空间中渐近非扩张型映象不动点的迭代逼近问题，所得结果发展和改进了文[2]得到的最新成果。     

Lipschitz严格伪压缩映象的具误差的迭代逼近

设K是任意实Banach空间E的非空闭凸子集,T：K→K是Lipschitz严格伪压缩映象。本文给出一个新的具误差的Ishikawa迭代程序强收敛到T的唯一不动点,并给出一个涉及Lipschitz强增生映象T的非线性方程Tx=f的解的迭代逼近。本文结果通过去掉空间E的一致光滑或p-一致光滑的严格要求、K的有界性、lim^n→∞an=lim^n→∞βn=0和∑n=0^∞an^s＜∞(s＞1)的限制而得到。     

Banach空间中具误差的Reich-Takahashi迭代序列的强收敛性

本文在具一致Gteaux可微范数的Banach空间的框架下,得出了第一型和第二型修正的具误差的Reich-Takahashi迭代序列强收敛于非自渐近非扩张映象的不动点的充分必要条件。所得结果改进和推广了已有相关结果。     

渐近-伪压缩映像不动点的迭代逼近

通过构造Ishikawa迭代序列,研究了渐近(?)-伪压缩映像不动点的迭代收敛问题,所得的结果改进和发展了许多新近的结果。     

空间互异对Lotka-Volterra竞争模型的影响

本文讨论了在齐次Neumann边界条件下一类具有Lotka-Volterra的竞争模型.我们研究了两物种在拥有不同种间竞争能力情况下,空间互异对物种产生的影响.特别地,我们考虑了在弱竞争的条件下,一个物种资源分布分布不均匀,而另一个物种资源分布是均匀的且两物种具有不同的物种总资源.结果表明某些参数对模型起着非常重要的作用.我们研究了系统共存解的存在性和稳定性,进而在适当的条件下,我们建立了共存解的唯一性及共存解和半平凡解的全局动力学行为.进一步,我们讨论了共存解关于扩散的渐近行为.结果表明系统的动力学关于参数是非常复杂的.我们使用的方法包括谱分析和单调动力系统理论等.     

具有时滞三斑块扩散捕食模型的全局稳定性

引入辅助系统、应用比较原理及Lyapunov函数，讨论具有连续无限时滞三斑块扩散捕食系统解的正性和有界性，给出了正平衡点全局渐近稳定的充分条件。     

A discrete dynamical system for the greedy strategy at collective Parrondo games

We consider a collective version of Parrondo's games with probabilities parameterized by ρ?∈?(0,?1) in which a fraction φ?∈?(0,?1] of an infinite number of players collectively choose and individually play at each turn the game that yields the maximum average profit at that turn. Dinís and Parrondo [L. Dinís and J.M.R. Parrondo, Optimal strategies in collective Parrondo games, Europhys. Lett. 63 (2003), pp. 319–325] and Van den Broeck and Cleuren [C. Van den Broeck and B. Cleuren, Parrondo games with strategy, in Noise in Complex Systems and Stochastic Dynamics II, Z. Gingl, J.M. Sancho, L. Schimansky-Geier, and J. Kertesz, eds., SPIE, Bellingham, WA, 2004, pp. 109–118.] studied the asymptotic behaviour of this greedy strategy, which corresponds to a piecewise-linear discrete dynamical system in a subset of the plane, for ρ?=?1/3 and three choices of φ. We study its asymptotic behaviour for all (ρ, φ)?∈?(0,?1)?×?(0,?1], finding that there is a globally asymptotically stable equilibrium if φ?≤?2/3 and, typically, a unique (asymptotically stable) limit cycle if φ?>?2/3 (‘typically’ because there are rare cases with two limit cycles). Asymptotic stability results for φ?>?2/3 are partly conjectural.     

Liapunov稳定性理论若干定理的推广

讨论了矢量微分方程dx/dt=f(t,x)的零解的稳定性，对Liapunov函数V（t,x)的限制条件作了改进，推广了扰动微分方程零解稳定性的若干判定定理。     

关于相依随机阵列的一类强偏差定理

随机变量序列的强偏差定理是经典概率论强大数定理的自然推广。引入渐近广义对数似然比概念作为任意相依随机阵列与行独立随机阵列之间偏差的随机性度量。采用随机变量的截尾技术，构造带一个参数且期望为 1 的似然比，然后借助 Borel-Cantelli 引理获得随机变量序列的几乎处处收敛性。在一类钟开莱型条件下，给出了任意相依随机阵列的部分和与随机变量关于参考测度的期望之间的偏差的上、下界，并且其上、下界是广义相对熵的函数。定理的证明过程没有用复杂的测度论理论，仅采用简单的纯分析方法。所得结果推广了已有的结论，使强极限定理的应用范围更加广泛。     

The relationship between stimulus-response mappings and the detection of novel stimuli in a simulated luggage screening task

Automaticity research suggests that consistent mapping leads to better skill acquisition than varied mapping. Other research demonstrates that in some situations varied mapping leads to better transfer. The effect of stimulus-response mappings in complex visual inspection tasks, wherein transfer stimuli might differ from training stimuli, has seldom been studied. Therefore, the effects of consistency vs variability of practice on learning and transfer in a simulated luggage screening task were compared. Consistent mapping led to faster and more accurate initial skill acquisition. However, during transfer, varied mapping led to higher levels of sensitivities and confidence and fewer deviations from optimal response criteria. Consistent mapping assists initial skill acquisition; however, in tasks where the physical identity of transfer stimuli might differ from those used in training, varied mapping leads to more efficient transfer. The results provide an important starting point for training individuals to achieve optimal transfer of learning in complex tasks. This research demonstrates that a combination of variables influence transfer of learning in real-world visual inspection tasks wherein transfer conditions may not be identical to training conditions. Acquisition of skills during training is facilitated by consistent stimulus-response mappings; however, in order to ensure optimal transfer of skills to situations involving novel stimuli, training should incorporate varied mapping of stimulus-response elements.     

Logistic增长的时滞SIS模型分析

本文研究了一类具有生理阶段结构的Logistic增长的SIS传染病模型,给出了系统边界平衡点和正平衡点全局渐近稳定的条件。即得到了传染病最终消除和成为地方病的阈值。