The aim of this work is mathematical education through the knowledge system and mathematical modeling. A net model of formation of mathematical knowledge as a deductive theory is suggested here. Within this model the ...The aim of this work is mathematical education through the knowledge system and mathematical modeling. A net model of formation of mathematical knowledge as a deductive theory is suggested here. Within this model the formation of deductive theory is represented as the development of a certain informational space, the elements of which are structured in the form of the orientated semantic net. This net is properly metrized and characterized by a certain system of coverings. It allows injecting net optimization parameters, regulating qualitative aspects of knowledge system under consideration. To regulate the creative processes of the formation and realization of mathematical know- edge, stochastic model of formation deductive theory is suggested here in the form of branching Markovian process, which is realized in the corresponding informational space as a semantic net. According to this stochastic model we can get correct foundation of criterion of optimization creative processes that leads to “great main points” strategy (GMP-strategy) in the process of realization of the effective control in the research work in the sphere of mathematics and its applications.展开更多
文献^([1-9])提出了血液循环在大脑处理信息的过程中具有时序控制作用,并用量化模型结合结构风险最小化相关理论说明时序控制作用的意义。文献^([10-24])汇总介绍量化模型中的一些细节。为方便同行阅读,我们在2013年也发表了系列综合报...文献^([1-9])提出了血液循环在大脑处理信息的过程中具有时序控制作用,并用量化模型结合结构风险最小化相关理论说明时序控制作用的意义。文献^([10-24])汇总介绍量化模型中的一些细节。为方便同行阅读,我们在2013年也发表了系列综合报告^([25-29])。文献^([31-32])介绍我们开发的一个算法,这一算法实现将一个有向网络分解为一系列前向网络集合。分解出来的前向网络集合可用于分析各种情况对任一细胞活动情况的影响,也可用于搭建精细的神经网络模型,进而用于辅助医学等方面的研究。算法的网络分解能力能符合文献^([1-28])所介绍的大脑处理信息量化方案的要求。算法的设计用到了笔者在2004年论文^([30])中总结的一种算法设计思路,采用这一思路设计的算法有好的可扩展性,文献^([33])将文献^([31-32])介绍的算法升级为DG-FFN SR Trees算法,本文介绍了怎样将文献^([33])介绍的DG-FFN SR Trees算法升级扩展为DG-FFN SR TreesEI算法,升级成的DG-FFN SR Trees-EI算法可用于多种用途。展开更多
文摘The aim of this work is mathematical education through the knowledge system and mathematical modeling. A net model of formation of mathematical knowledge as a deductive theory is suggested here. Within this model the formation of deductive theory is represented as the development of a certain informational space, the elements of which are structured in the form of the orientated semantic net. This net is properly metrized and characterized by a certain system of coverings. It allows injecting net optimization parameters, regulating qualitative aspects of knowledge system under consideration. To regulate the creative processes of the formation and realization of mathematical know- edge, stochastic model of formation deductive theory is suggested here in the form of branching Markovian process, which is realized in the corresponding informational space as a semantic net. According to this stochastic model we can get correct foundation of criterion of optimization creative processes that leads to “great main points” strategy (GMP-strategy) in the process of realization of the effective control in the research work in the sphere of mathematics and its applications.
文摘文献^([1-9])提出了血液循环在大脑处理信息的过程中具有时序控制作用,并用量化模型结合结构风险最小化相关理论说明时序控制作用的意义。文献^([10-24])汇总介绍量化模型中的一些细节。为方便同行阅读,我们在2013年也发表了系列综合报告^([25-29])。文献^([31-32])介绍我们开发的一个算法,这一算法实现将一个有向网络分解为一系列前向网络集合。分解出来的前向网络集合可用于分析各种情况对任一细胞活动情况的影响,也可用于搭建精细的神经网络模型,进而用于辅助医学等方面的研究。算法的网络分解能力能符合文献^([1-28])所介绍的大脑处理信息量化方案的要求。算法的设计用到了笔者在2004年论文^([30])中总结的一种算法设计思路,采用这一思路设计的算法有好的可扩展性,文献^([33])将文献^([31-32])介绍的算法升级为DG-FFN SR Trees算法,本文介绍了怎样将文献^([33])介绍的DG-FFN SR Trees算法升级扩展为DG-FFN SR TreesEI算法,升级成的DG-FFN SR Trees-EI算法可用于多种用途。
