(2+1)维色散长波方程新的行波解

对偏微分方程解的研究主要有三个方向:1)解的数学理论研究.对于一些难以求出解的方程,借助数学理论(解的先验估计、算子理论等)证明解的适定性,属于基础数学研究的内容. 2)解的数值模拟.借助于计算机和计算数学知识,对解的变化态势进行分析和模拟,属于计算数学的内容. 3)求方程的显式解.通过适当的变换,构造出解的解析表达式.属于应用数学的范畴.微分方程的求解问题一直是人们关注的热点问题.本文以齐次平衡原则和试探函数法为基础求出(2+1)维色散长波方程的行波解.     

整合分数阶修正的等宽波动方程的所有单行波解的分类

利用多项式的完全判别法,构建了整合分数阶修正的等宽波动方程的所有单行波解的分类.基于所提出的方法,获得了许多新的精确解,这些解包括双曲函数解、三角函数解、有理函数解、隐式解和雅克比椭圆函数解.     

Variant Boussinesq方程组的精确解

F-展开法是近年提出的求非线性偏微分方程的精确解的一种简单而有效的方法.本文运用改进的F-展开法寻求Variant Boussinesq方程组的行波解,得到了该方程组多种类型的精确解,包括Jacobi椭圆函数解、孤立波解、三角函数解和有理函数解.     

上、下解与拟上下解的存在性

利用上、下解与拟上下解方法讨论常微分方程问题时,文献均是假设上、下解与拟上下解是存在的,进而讨论方程的解.给出一阶常微分方程初值问题的上、下解与拟上下解的存在性定理,为利用上、下解与拟上下解方法讨论一阶常微分方程初值问题提供充分的依据.     

一类“多项式型”初值问题的快速解法

对有解析解的偏微分方程定解问题 ,利用计算机系统有多种方法获得问题的数值 (近似 )解 ,但却无法给出解析解 (有限函数形式解 ) .经过深入研究 ,我们得出了“多项式型”初值问题解析解的计算机解法 ,并给出Mathematica语言源程序 .     

非线性薛定谔方程的稳态解及其稳定性研究

用行波变换方法和分叉理论研究里非线性薛定谔方程的定常解和定常解的稳定性.计算结果表明:非线性薛定谔方程存在两类定常解,静态解和平面波解.对于具有正阻尼和软特性的非线性薛定谔方程,稳定的平面解存在于正常色散媒质中;而对于具有正阻尼和硬特性的非线性薛定谔方程,稳态平面波解只存在于反常色散媒质中.此外,非线性薛定谔方程在行波变换下的派生系统在处发生Hopf分叉.     

Sharma-Tasso-Olver方程的新精确解研究

Sharma-Tasso-Olver方程广泛的应用于描述复杂非线性现象,构造其精确解有助于该方程相关物理背景的理解.应用exp(-φ(ζ))-展开方法,并借助计算系统-Maple,获得了Sharma-Tasso-Olver方程的多种精确解.这些解包括双曲函数解、三角函数解和有理函数解.     

Bogoyavlenskii-Kadontsev-Petviashili方程的新的显式解

利用直接对称方法,得到了Bogoyavlenskii-Kadontsev-Petviashili方程的对称约化和一些新的显式解,包括三角函数解、周期解等.并根据修正的CK直接方法的理论和已知解建立了新旧解之间的关系,由此也可得到原方程的某些新的显式解.     

群体决策问题的一种最优整体差解

引进了群体决策问题的一个最优解概念t*—最优整体差解,它可以作为群体决策问题的一种解,该解可以通过求解一个相应的数学规划问题得到.最后,讨论了t*—最优整体差解与s*—最优均衡解之间的联系.     

一类四阶微分方程边值问题的可解性条件

考虑了一类弱非线性的四阶常微分方程线性边界条件的边值问题.先利用渐近展开法,将弱非线性问题转化为线性问题.再利用格林函数将原问题的解变为伴随解的积分形式,讨论了伴随解的微分方程及边界条件.最后由伴随齐次问题的每一个非平凡解得到了问题的渐近解的可解条件.     

正态总体方差的贝叶斯区间估计

区间估计是数理统计的一个重要内容,分析了贝叶斯可信区间估计与经典置信区间估计的区别,推出了正态总体方差的贝叶斯可信区间,数值分析表明可信区间比置信区间更精确。     

M/G/c排队系统中顾客队长排队长的置信区间的Bootstrap估计

研究了M/G/c排队系统中顾客队长、排队长的置信区间的求解方法.利用Bootstrap原理,给出了正态区间法、枢轴量法和百分位区间法等三种计算方法.实际应用表明,三种方法都得到了较好的结果.以置信区间的长度为评价标准,正态区间法和百分位区间法较优.     

Serial position effects in social transmission of food preference: Retention/demonstration intervals

The effects of retention and demonstration intervals on serial position were evaluated in two experiments with Long-Evans rats. A list of 3 demonstrators that had eaten one of three flavored foods was presented to naive observers. In Experiment 1, there were four groups, three groups with a retention interval compared with one group with a zero retention interval or no retention interval. In Experiment 2, the demonstration interval was reduced. Intervals of 15, 5, 2, and 1 min were used. In Experiment 1, primacy decreased gradually in the four groups as the retention interval was increased in duration. In Experiment 2, primacy also decreased gradually, and recency occurred with the 1-min demonstrator interval. The increase in the duration of the retention interval reduced primacy. The reduction in the duration of the demonstration interval decreased primacy and produced recency.     

建筑工程流水施工中流水步距及工期计算的讨论

认为流水步距的定义应为相邻的两个施工班组相继投入施工的间隔时间 ,不包括组织间歇、技术间歇、搭接时间等时间间歇 .指出了计算全等节拍流水施工工期常用公式中的一些弊端 ,并给出了经验公式     

区间值随机变量的可积性与条件期望

首先在概率空间（Ω,A,P）上讨论了可测区间值函数,证明了区间值随机变量与二维随机变量的等价性.在此基础上又分别研究了区间值随机变量的可积性与条件期望.这两个性质对研究区间值马氏过程和区间值鞅有很大的帮助.     

Direct reliability-based design optimization of uncertain structures with interval parameters

In order to enhance the reliability of an uncertain structure with interval parameters and reduce its chance of function failure under potentially critical conditions, an interval reliability-based design optimization model is constructed. With the introduction of a unified formula for efficiently computing interval reliability, a new concept of the degree of interval reliability violation (DIRV) and the DIRV-based preferential guidelines are put forward for the direct ranking of various design vectors. A direct interval optimization algorithm integrating a nested genetic algorithm (GA) and the Kriging technique is proposed for solving the interval reliability-based design model, which avoids the complicated model transformation process in indirect ones and yields an interval solution that provides more insights into the optimization problem. The effectiveness of the proposed algorithm is demonstrated by a numeric example. Finally, the proposed direct reliability-based design optimization method is applied to the optimization of a press upper beam with interval uncertain parameters, the results of which demonstrate its feasibility and effectiveness in engineering.     

最优区间估计问题的探讨

文中讨论了区间估计的最优性，并证明了最优区间估计的存在性，同时给出了一种寻求最优区间估计的方法．     

Proactive interference in monkeys: Delay and intersample interval effects are noncomparable

Two prominent theories of proactive interference in animal memory predict that the effects of varying the interval between the interfering and to-be-remembered stimulus in a delayed-matching-to-sample paradigm ought to be comparable to the effects of manipulating the retention interval. To assess this prediction, monkeys were tested in a situation in which a sample was presented, followed by a variable intersample interval, whereupon a second sample was presented. After a delay interval, a choice test was given between the two stimuli that had served as samples. The correct choice was always the most recently presented sample stimulus, and the initial sample of a sequence provided a potential source of proactive interference. In two experiments, delay interval altered performance, whereas interstimulus interval had little or no effect. In a third experiment, using a small set of sample stimuli, intertriai interval altered proactive interference, but again interstimulus interval had no effect. One way of accounting for these data is in terms of distinct short- and long-term memory processes.     

多非线性区间Lurie系统的鲁棒绝对稳定性

考虑了关于模型变化的具有多非线性的区间Lurie控制系统的鲁棒绝对稳定性 ,用Lyapunov函数方法和区间分析技术 ,得到了区间Lurie系统鲁棒绝对稳定的一些充分条件 ,这些条件减少了绝对稳定鲁棒检测的保守性 ,这些鲁棒分析方法是基于区间矩阵的鲁棒稳定分析     

卷积积分区间的图解分段确定方法

本文给出了利用图解分段确定卷积积分区间的一种方法,并举例说明了其应用及推广.利用本方法,只要知道被卷积两函数的有值区间端点,就能有规律地快速确定卷积积分中自变量t和哑变量τ的取值区间,计算的结果为闭合形式.该方法能有效地克服积分区间(或求和区间)的重复和遗漏问题,特别是在多分段有值函数卷积的计算中更显示出其优越性.