• 主题
高级搜索  >
历史搜索 清空历史
首页> 外文期刊>Russian mathematics >Statistical Characteristics of Continuous Functions and Statistically Weakly Invariant Sets of Controllable System
【24h】

Statistical Characteristics of Continuous Functions and Statistically Weakly Invariant Sets of Controllable System

机译：连续功能的统计特性和统计上弱不变集合系统

获取原文
获取原文并翻译 | 示例
           
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

We continue the investigation of expansion of a concept of invariance for sets which consists in studying statistically invariant sets with respect to control systems and differential inclusions. We consider the statistical characteristics of continuous functions: Upper and lower relative frequency of containing for graph of a function in a given set. We obtain conditions under which statistical characteristics of two various asymptotical equivalent functions coincide; then by the value of one of them it is possible to calculate the value of another one. We adduce the equality for finding relative frequencies of hitting functions the given set in the case when the distance from the graph of one of functions to the given set is a periodic function. A consequence of these statements are conditions of statistically weak invariance of a set with respect to controlled system. For some almost periodic functions we obtain the formulas by which we can calculate the mean values and the statistical characteristics. We also consider the following problem. Let the number λ_0 ∈ [0, 1] be given. It is necessary to find the value c(λ_0) such that the upper solution z(t) of the Cauchy problem does not exceed c(λ_0) with the relative frequency being equal λ_0. Depending on statement of the problem, a value z(t) can be interpreted as the size of population, energy of a particle, concentration of substance, size of manufacture or the price of production.
机译：我们继续调查扩展的集合的不变性概念，该概念包括关于控制系统和差分夹杂物的统计上不变集。我们考虑连续功能的统计特征：上下和较低的相对频率，用于在给定集中函数的曲线图。我们获得两个各种渐近等效功能的统计特征的条件重合;然后通过其中一个值，可以计算另一个的值。我们涉及查找给定函数的相对频率的平等在与给定集合之一的曲线图中的距离是周期性的情况下的情况下。这些陈述的结果是对受控系统的一个集合的统计上弱不变性的条件。对于一些几乎定期的功能，我们获得了可以计算平均值和统计特征的公式。我们还考虑以下问题。提供数字λ_0∈[0,1]。有必要找到值C（λ_0），使得Cauchy问题的上解Z（t）不超过C（λ_0），相对频率等于λ_0。根据问题的陈述，值Z（t）可以被解释为群体的尺寸，粒子的能量，物质浓度，制造规模或生产价格。

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号