Banach空间中一类强非线性发展方程的反周期解

本文讨论一类强非线性发展方程的反周期解的存在性。针对一大类既含有单调非线性算子又含有非单调非线性算子的发展方程。我们巧妙地结合单调算子理论与Leray-Schauder不动点理论，证明了其反周期解的存在性。最后，举例说明理论结果在2m阶拟线性抛物型方向的时间反周期问题中的应用。     

Banach空间n阶非线性积分-微分方程初值问题解的存在性

用Tonelli方法研究了Banach空间中n阶非线性积分—微分方程初值问题，在非线性增长条件下，获得了初值问题解的存在性及其Tonelli迭代逼近。     

MM教育方式下常微分方程教学实验研究

研究高师MM教育方式下常微分方程教学实验方案的设计框架、实施措施和效果分析，初步摸索出一条MM方式下“问题探究型”(创设问题情景——巧用思想方法——探究‘自主发现’——推证新知结论——获得‘问题解决’——开发实际应用)的创新教学途径。     

关于差分式放大器输入电阻的研究

差分式放大器在实际应用方面非常广泛,其理论分析方法的深入研究,对生产实践和教学都有重要的意义。采用电路理论分析、差放理论分析、“虚短”理论分析及实验的方法对差分式放大电路进行了研究。     

High precision topographic data on Lop Nor basin's Lake "Great Ear" ? and the timing of its becoming a dry salt lake

High precision elevation measurements using DGPS were carried out along three representative tran- sects for the "Great Ear" area, a dry salt lake within the Lop Nor basin. Results indicate that the Lop Nor basin is only 5.2 m deep and its lowest point occurs at the center of the "Great Ear". In addition, the basin is asymmetric - steeper in the southwest (0.19‰) and gentler in the northeast (0.09‰). Points along the same "Great Ear" ring were found to have an identical elevation value, but different when from different ones (lower towards the center). The spacing of the "Great Ear" rings was found to be closely related with the surface steepness. The closer the "Great Ear" rings are spaced, the steeper the ground surface, and vice versa. These findings support the argument that the "Great Ear" rings are the former shoreline trails left behind by Lop Nor water during the last few episodes of recession towards its total dry up. A comprehensive analysis of the high precision elevation data, historical accounts, aerial and satellite photographs and imagery, and official topographic maps of the study area suggests that the "Great Ear" area in the Lop Nor basin was incorrectly mapped as being covered by a great body of water on the 1963 topographic maps. A re-interpretation of the 1958 aerial photographs and newer remote sensing imagery indicated that the "Great Ear" ring structure was already in place in 1958 and it continued to appear on the subsequent remote sensing data without any major changes. It is estimated that lake water in the "Great Ear" area of the Lop Nor basin disappeared between the late 1930s and early 1940s.     

Long term monitoring of urban subsidence by Permanent Scatterer DInSAR

When using differential SAR interferometry (DInSAR) to monitor the surface deformation over a long time scale, it is often strongly affected by the spatial and temporal decorrelations and atmospheric dishomogeneities. The recently developed Permanent Scatterers (PS) technique proposed by Fertti et al. can overcome these difficulties by interpreting time-series of interferometric phase only at coherent point scatterers. In this study, we apply this PS technique using 25 ERS-1/2 scenes from 1992 to 2000 to monitor the subsidence in Suzhou. By using the linear deformation model, the deformation map in Suzhou urban area over the eight years is obtained. And the calculated results are in good agreement with the measurements of leveling.     

中立型时滞双曲微分方程的振动准则

建立了一类中立型非线性时滞双曲微分方程的若干新的振动准则,结论推广和改进了一些文献中的定理.     

不连续二阶周期边值问题的可解性

考察了一类非线性项含有一阶导数的二阶周期边值问题的解的存在性,其中非线性项是Carathèodory函数.通过构造非线性项的高度函数并且利用Leray-Schauder不动点定理建立了两个存在定理.第一个定理表明只要高度函数的积分是适当的,这类问题至少有一个解.第二个定理表明当非线性项在无穷远处增长的极限是一个无界函数时在适当条件下这问题仍可能有一个解.     

多维函数全局寻优的团队进步算法

通过模仿团队进步需要的学习、探索行为和成员更新规则,提出了一种新颖的双群体演化算法,称为团队进步算法(TPA).算法将一个团队的成员分为精英和普通组,建立了两组的学习样板,定义了学习和探索运算,并合理设定了成员更新规则.两组成员在搜索过程中出现了明显分工,使算法兼备了全局搜索、局部搜索和定向搜索的能力.数值试验结果验证了新算法具有实现简单、全局寻优成功率高、收敛快、计算量少、坚韧性强和参数选择相对容易等特性,对解决优化应用问题具有较大的价值.     

绿洲-荒漠生态系统演化因素及其非线性探讨——以新疆为例

对立统一于干旱区的绿洲—荒漠生态系统在降水等自然因素和人类活动等人为因素的影响下不断进行着演化.从长期看,这一演化过程具有不可预测性,短期内却有细微可预见性.现如今在绿洲扩展同时,荒漠也在扩展,整体趋势仍是荒漠在扩展.为维持绿洲的稳定性,促使绿洲—荒漠系统处于一种稳定的发展趋势,本文从分析绿洲-荒漠这对对立统一的生态系统入手,在探讨引起这对生态系统演化的自然因素和人为因素的基础上,确定了自然因素中的降水和人为因素中的政府调控行为为演化的主导因素,初步探索了促使这对生态系统统演化的主导因素作用所具有的非线性关系,这对维持绿洲的稳定性,抑制荒漠扩展有一定的实际意义.