Let A = F [x, y] be the polynomial algebra on two variables x, y over an algebraically closed field F of characteristic zero. Under the Poisson bracket, A is equipped with a natural Lie algebra structure. It is proven...Let A = F [x, y] be the polynomial algebra on two variables x, y over an algebraically closed field F of characteristic zero. Under the Poisson bracket, A is equipped with a natural Lie algebra structure. It is proven that the maximal good subspace of A* induced from the multiplication of the associative commutative algebra A coincides with the maximal good subspace of A* induced from the Poisson bracket of the Poisson Lie algebra A. Based on this, structures of dual Lie bialgebras of the Poisson type are investigated. As by-products,five classes of new infinite-dimensional Lie algebras are obtained.展开更多
This work represents a formalized description of information and communicative interac- tions of individuals on the basis of theory of information images （II）. It also demonstrates how important it is to choose the ...This work represents a formalized description of information and communicative interac- tions of individuals on the basis of theory of information images （II）. It also demonstrates how important it is to choose the models type adequate to the systems under research. It also introduces an explication of the possibility to create the model of information and communication interactions that can illustrate transmission of information between two and more individuals. Methods and approaches suggested in this paper allow us to compare different levels of the described processes depending on the chosen architecture of the model; the methods and approaches mentioned in the current work can be also used to simulate the processes of distortion and generation of information images while information and communication social interaction. Expansion and addition of informa- tion images theory in terms of transmission of information among individuals enables us to speak about the space of individual II. The existence of such a space and creation of correct formalized model help us to explain a number of characteristic phenomena of human thinking processes. As a result of this research, the authors introduce an equa- tion that describes the spatial and structural evolution of individual II. There is also an example of modeling on the basis of this theory taking into account the results of the experiment （bilingual Stroop test）.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.11071147,11431010 and 11371278)Natural Science Foundation of Shandong Province(Grant Nos.ZR2010AM003and ZR2013AL013)+1 种基金Shanghai Municipal Science and Technology Commission(Grant No.12XD1405000)Fundamental Research Funds for the Central Universities
文摘Let A = F [x, y] be the polynomial algebra on two variables x, y over an algebraically closed field F of characteristic zero. Under the Poisson bracket, A is equipped with a natural Lie algebra structure. It is proven that the maximal good subspace of A* induced from the multiplication of the associative commutative algebra A coincides with the maximal good subspace of A* induced from the Poisson bracket of the Poisson Lie algebra A. Based on this, structures of dual Lie bialgebras of the Poisson type are investigated. As by-products,five classes of new infinite-dimensional Lie algebras are obtained.
基金The theoretical part of the research was performed with support by the Grant of the Russian Science Foundation （Project No. 15-18-00047）. The experimental part of the research was performed with support by Grants from the Board President of the Russian Federation （Project MK-7165.2015.6）.
文摘This work represents a formalized description of information and communicative interac- tions of individuals on the basis of theory of information images （II）. It also demonstrates how important it is to choose the models type adequate to the systems under research. It also introduces an explication of the possibility to create the model of information and communication interactions that can illustrate transmission of information between two and more individuals. Methods and approaches suggested in this paper allow us to compare different levels of the described processes depending on the chosen architecture of the model; the methods and approaches mentioned in the current work can be also used to simulate the processes of distortion and generation of information images while information and communication social interaction. Expansion and addition of informa- tion images theory in terms of transmission of information among individuals enables us to speak about the space of individual II. The existence of such a space and creation of correct formalized model help us to explain a number of characteristic phenomena of human thinking processes. As a result of this research, the authors introduce an equa- tion that describes the spatial and structural evolution of individual II. There is also an example of modeling on the basis of this theory taking into account the results of the experiment （bilingual Stroop test）.
