完备稠序线性序拓扑空间上的奇周期轨序关系

研究完备稠序线性序拓扑空间上连续自映射的周期轨,指出当连续自映射有（2n＋1）-周期轨而没有（2n-1）-周期轨时,该（2n＋1）-周期轨上各点的序关系.利用这个关系将Sharkovskii定理从实直线推广到完备稠序线性序拓扑空间上。     

Some characterizations of discrete unimodality

Let F be a discrete distribution function on $\text{|Z}$. This paper gives a characterization of discrete unimodal distribution functions (Theorem 5.1) and a representation theorem for those distribution functions (Theorem 6.3), both in terms of their Lévy concentration functions.     

Nonlinear coordinate transformations for unconstrained optimization II. Theoretical background

In this two-part article, nonlinear coordinate transformations are discussed in order to simplify global unconstrained optimization problems and to test their unimodality on the basis of the analytical structure of the objective functions. If the transformed problems can be quadratic in some or all the variables, then the optimum can be calculated directly, without an iterative procedure, or the number of variables to be optimized can be reduced. Otherwise, the analysis of the structure can serve as a first phase for solving global unconstrained optimization problems.The first part treats real-life problems where the presented technique is applied and the transformation steps are constructed. The second part of the article deals with the differential geometrical background and the conditions of the existence of such transformations.The paper was presented at the II. IIASA Workshop on Global Optimization, Sopron (Hungary), December 9–14, 1990.     

Nonlinear coordinate transformations for unconstrained optimization I. Basic transformations

In this two-part article, nonlinear coordinate transformations are discussed to simplify unconstrained global optimization problems and to test their unimodality on the basis of the analytical structure of the objective functions. If the transformed problems are quadratic in some or all the variables, then the optimum can be calculated directly, without an iterative procedure, or the number of variables to be optimized can be reduced. Otherwise the analysis of the structure can serve as a first phase for solving unconstrained global optimization problems.The first part treats real-life problems where the presented technique is applied and the transformation steps are constructed. The second part of the article deals with the differential geometrical background and the conditions of the existence of such transformations.The paper was presented at the II. IIASA Workshop on Global Optimization, Sopron (Hungary), December 9–14, 1990.     

Renormalization of binary trees derived from one-dimensional unimodal maps

For one-dimensional unimodal mapsh (x):I I, whereI=[x ₀,x ₁] when =_max, a binary tree which includes all the periodic windows in the chaotic regime is constructed. By associating each element in the tree with the superstable parameter value of the corresponding periodic interval, we define a different unimodal map. After applying a certain renormalization procedure to this new unimodal map, we find the period-doubling fixed point and the scaling constant. The period-doubling fixed point depends on the details of the maph (x), whereas the scaling constant equals the derivative . The thermodynamics and the scaling function of the resulting dynamical system are also discussed. In addition, the total measure of the periodic windows is calculated with results in basic agreement with those obtained previously by Farmer. Up to 13 levels of the tree have been included, and the convergence of the partial sums of the measure is shown explicitly. A new scaling law has been observed, i.e., the product of the length of a periodic interval characterized by sequenceQ and the scaling constant ofQ is found to be approximately 1.     

马尔可夫随机过程中移动对象的空间特征分析及近似逼近研究

研究一类移动对象在马尔可夫（马氏）随机过程中的空间逼近问题.首先运用数学推理方式获得时空网络马尔可夫随机模型的一种状态转移函数.定义时空网络为移动对象及其移动轨迹形成的三维空间,建立马尔可夫随机过程的距离空间,证明了相应环境下的不动点理论.通过分析和扩展状态转移函数得到距离空间的自映射算子,从原节点映射到目标节点,达到对象的移动,并对此进行了理论证明和仿真实验验证.在此基础上从应用层面出发,尝试性地进行了移动对象的空间粒度分解,利用不动点映射更好地定位移动对象,实时满足移动对象的需求.相关实验进一步验证了空间分析的可行性和有效性. 关键词： 马尔可夫随机过程 距离空间 不动点 自映射算子     

区间上反N型函数的迭代根

讨论了区间I＝[0,1]上的所有反N型（即减－增－减型）函数的迭代根问题。     

ABUNDANCE OF UNIMODAL MAPS WITH DENSE CRITICAL ORBIT AND PREFIXED CRITICAL ORBIT

ＩｎｔｒｏｄｕｃｔｉｏｎＡｍａｊｏｒｐｒｏｂｌｅｍｏｆｏｎｅｄｉｍｅｎｓｉｏｎａｌｄｙｎａｍｉｃｓｉｓｔｏｓｔｕｄｙｔｈｅａｔｔｒａｃｔｏｒｓｏｆｉｎｔｅｒｖａｌｍａｐｓ,ｉ.ｅ.ｔｈｅｃｌａｓｓｉｆｉｃａｔｉｏｎａｎｄｓｔｒｕｃｔｕｒｅｏｆａｔｔｒａｃｔｏｒｓ.ＦｏｌｌｏｗｉｎｇＭｉｌｎｏｒ’ｓｄｅｆｉｎｉｔｉｏｎｏｎａｔｔｒａｃｔｏｒｓ[1],ｉｆｆｉｓａｕｎｉｍｏｄａｌｍａｐｗｉｔｈｎｅｇａｔｉｖｅＳｃｈｗａｒｚｉａｎｄｅｒｉｖａｔｉｖｅ ,ｔｈｅｎｂｙＧｕｃｋｅｎｈｅｉｍｅｒ’ｓｔｈｅｏｒｅｍ[2 ]…     

具有稠密临界轨道和预不动临界轨道的单峰映射的丰富性

证明了对于实二次族在参数空间存在正Ｌｅｂｅｓｇｕｅ测度集合Ｅ,使得Ｅ中几乎所有的参数,相应的映射在不变测度的支集上具有稠密的临界轨道;还证明了Ｅ中存在稠密集合使得相应映射的临界轨道进入它的反向不动点。     

р阶Feigenbaum函数方程的解的拓扑熵

р阶Feigenbaum函数方程的解的拓扑熵@范钦杰...