一个单峰函数族的模型

总的说来,人们对单峰函数族的动态性质已有较深刻的理解.如 MSS 序列的提出,周期窗口的发现,以及从不同角度对其动态性质的探讨都表明了这点.但是对参数所对应的函数拓扑熵大于零的混沌区域的结构还没有彻底研究清楚,本文讨论一个典型的单峰函数族,发现其混沌区域具有分层的结构,即可按层的次序把这个区域中的周期点、拟周期点和其他点的分布规律刻划出来.     

单峰函数族的捏制序列系列的不间断性

本文提出了关于Ｃ０－单峰函数族的局部渐变性及局部邻域吸引性等概念，得到了Ｃ０－单峰函数族具有捏制序列系列的不间断性的多个条件，推广了已有的一些结论，此外，本文还讨论了单峰函数族的捏制序列系列的ｍ－有限不间断性，得到了相应的一些结果。     

梯形映射族周期轨道的计算

运用符号动力学理论,研究一种特殊的一维分段线性映射族"梯形映射族"周期轨道的计算方法,确定其周期轨道的参数范围,给出了奇的最大周期序列对应参数的精确范围,以及偶的最大周期序列参数的近似范围.该方法可应用于更一般的单峰系统.     

单峰函数族中捏制轨道系列的完整性

本文考虑了两类单参数C~0-单峰函数族,其中一类是由满足Lipschitz条件且在峰顶处一致地可微的单峰函数组成,另一类是由一致平顶而不一定满足Li-pschitz条件的单峰函数组成。我们证明这两类函数族均具有捏制轨道系列的完整性,从而推广了文献[1]及[2]中的有关结论。本文还举例说明了,对于非平顶的单峰函数族来说,如果Lipschitz条件不成立的话,其捏制轨道系列的完整性可能不成立。     

单峰函数中具有指定的型的终于周期轨道的存在性

本文给出了捏制序列为ＢＣ的单峰函数具有ＢＣ＊Ｌ￣∞型周期轨道的几个充分条件。在此基础上，本文进一步讨论了一般的单峰函数ｆ中的终于周期轨道的存在性问题，证明了只要ｋ阶的终于ｎ－周期容许序列ＡＢ￣∞满足一定的要求，ｆ中就存在着ＡＢ￣∞型的ｋ阶终于ｎ－周期轨道。对广泛的一类单峰函数，本文减弱和简化了文献［１］的ＰａｒｔⅡ．３的主要定理的条件并加强了它的结论。对更一般的连续函数，本文亦充实了文献［８］的定理２的结论。     

双符号等长代换系统的序列熵

系统称为null的,如果对任意序列,它的序列熵为零.双符号等长代换及其对应的代换极小系统可分成三类:有限的、离散的和连续的.容易看出离散的代换极小系统是null的,Goodman证明了连续的代换极小系统不是null的.本文将完全刻画所有的双符号等长代换极小系统的序列墒.     

Clemens-Schmid序列的推广

本文把Clemens-Schmid正合序列推广到单参数族的奇异纤维具有任意奇性的情况。     

关于代换系统拓扑序列熵的注记

Goodman证明了对两符号等长代换系统, 如果代换规则中0和1对应的词只有一个位置不同,那么对应的代换系统为null的, 即此系统沿着任意正整数序列的序列熵均为0. 在本文中, 我们针对系统的结构特征, 通过考察因子系统, 给出了此经典结果的另外一种证明. 同时, 对此类代换系统沿着给定序列的复杂性, 我们得到了比Goodman更为精确的估计.     

基于广义分圆法的一类跳频序列族

平均汉明相关值是评价跳频序列族性能的一个重要参数.本文在Whiteman广义分圆法的基础上构造了一类新的跳频序列族,随后证明了其关于平均汉明相关界是最优的,并给出了各类汉明相关值的计算公式.     

基于符号序列方法的股价指数预测研究

用两种符号序列方法分别对上证指数进行实证统计分析。一种是以日收盘价计算的指数价差的符号序列,另一种是以每日5分钟高频数据计算的多重分形谱参数符号序列。统计结果表明,指数的涨落不是完全随机的,两种方法都能以一定的条件概率来预测指数的涨落;进一步地,在引入股价指数大涨落的阈值和条件平均增益后,发现大幅涨落时,条件与指数变化的关联性比小的涨落要强得多,而且将两种符号序列方法结合可以更好地预测指数的大涨落。     

一类推广的KdV方程的新行波解

本文研究了一类推广的Kd V方程的行波解求解的问题.利用新的G展开法,并借助Mathematica计算软件,获得了该方程的含有多个任意参数的新的行波解,分别为三角函数解、双曲函数解、有理函数解和指数函数解,扩大了该类方程的解的范围.     

CONSTRUCTION OF CONCEPTUAL KNOWLEDGE: THE CASE OF COMPUTER-AIDED EXPLORATION OF PERIOD DOUBLING

This research focuses on students using an experimental approach with computer software to give visual meaning to symbolic ideas and to provide a basis for further generalisation. They use computer software that draws orbits of x=f(x) iteration and are encouraged to investigate the iterations of f_λ(x)=λx(1-x) as λ increases. The iterations pass through successive acts of period-doubling as λ=λ₀, λ₁, λ₂, …,. students are invited to estimate the values of λ and to compare their experimental results with the theory of geometric convergence. The supervisor acts as a mentor, using various styles of questioning to provoke links between different ideas. A variety of data is collected to give evidence for the ways in which students develop conceptual links between symbolic theory and the visual and numeric aspects of computer experiment.     

有限型子集的Hausdorff测度

给出了有限型子集的Hausdorff测度的一个估计,改进了已有的结果。     

ON A LEMMA OF BOWEN

We are concerned with the sets of quasi generic points in finite symbolic space. We estimate the sizes of the sets by the Billingsley dimension defined by Gibbs measures. A dimension formula of such set is given, which generalizes Bowen＇s result. An application is given to the level sets of Birkhoff average.     

加权Besicovitch集的Hausdorff维数

本文引入并研究符号空间上的加权Besicoritch集.通过构造一个伯努利测度,得到此集的Hausdorff维数,结果符合一个变分原理.     

Symbolic models for infinite networks of control systems: A compositional approach

This paper presents a compositional framework for the construction of symbolic models for a network composed of a countably infinite number of finite-dimensional discrete-time control subsystems. We refer to such a network as infinite network. The proposed approach is based on the notion of alternating simulation functions. This notion relates a concrete network to its symbolic model with guaranteed mismatch bounds between their output behaviors. We propose a compositional approach to construct a symbolic model for an infinite network, together with an alternating simulation function, by composing symbolic models and alternating simulation functions constructed for subsystems. Assuming that each subsystem is incrementally input-to-state stable and under some small-gain type conditions, we present an algorithm for orderly constructing local symbolic models with properly designed quantization parameters. In this way, the proposed compositional approach can provide us a guideline for constructing an overall symbolic model with any desired approximation accuracy. A compositional controller synthesis scheme is also provided to enforce safety properties on the infinite network in a decentralized fashion. The effectiveness of our result is illustrated through a road traffic network consisting of infinitely many road cells.     

共振长短波方程的孤波解

本文研究了共振长短波方程的孤波解.利用扩展映射法和符号计算,得到许多新的孤波解.这些孤波解能很好地模拟水波,辅助方程用更一般方程代替的扩展映射法能更有效找到这些孤波解.

Abstract：

In this article,soliton solutions of the long-short wave resonance equations are investigated.By the extended mapping method and symbolic computation,many new exact soliton solutions are obtained.These soliton solutions are fascinating in modeling water waves.The extended mapping method,with the auxiliary ordinary equations replaced by more general ones,is more effective to find these soliton solutions.     

INVESTIGATING THE VIABILITY OF SQUIRREL POPULATIONS; A MODELING APPROACH FOR THE ISLAND OF LESVOS,GREECE

ABSTRACT. Habitat loss and fragmentation are considered to be the most important factors responsible for population decreases in small mammal populations. Particularly important is also the effect of insularity that can act syn‐ergistically with the previous factors. Population Viability Analysis (PVA) combines the spatial component of the problem with the species population structure offering an integrated platform for testing and assessing the effects of critical parameters upon the population viability. Various management options can also be quantified and tested. In the case of Sciurus anomalous, a vulnerable squirrel species endemic in Lesvos, a series of threats and management problems were identified and assessed. A stochastic simulation model was developed and parameterized with field data for the species using the program Ramas/GIS. The results suggested that special attention has to be paid to the planning of road system networks and to stopping illegal hunting, especially when extinction risks for vulnerable populations are higher with the above threats.     

多项式判别矩阵的若干性质及其应用

具有文字系数的多项式f(x)，其判别矩阵是f与f′的Sylvester矩阵通过添加一行一列而得，已经知道，判别矩阵的偶数阶主子式的符号确定了f(x)的相异根(实根、复根)的数目，这里介绍如何将奇数阶与偶数阶主子式相结合用以判定该多项式的相异负根或正根的数目，并进一步判定其在区间上的实根数，本文还研究了与判别矩阵相关的一些实用性质，并应用这些性质给出了4次键合多项式不能正分解的一组简洁的充分必要条件。     

振动杆有限差分模型的一类特征值反问题

1引言杆是重要的工程构件之一,具有分布质量的杆的纵向振动由下面的偏微分方程描述: