In this paper we study the properties of homotopy inverses of comultiplications and Mgebraic loops of co-H-spaces based on a wedge of spheres. We also investigate a method to construct new comultiplications out of old...In this paper we study the properties of homotopy inverses of comultiplications and Mgebraic loops of co-H-spaces based on a wedge of spheres. We also investigate a method to construct new comultiplications out of old ones by using a group action. We are primarily interested in the algebraic loops which have inversive, power-associative and Moufang properties for some comultiplications.展开更多
On condition that the basic equations set of atmospheric motion possesses the best stability in the smooth function classes, the structure of solution space for local analytical solution is discussed, by which the thi...On condition that the basic equations set of atmospheric motion possesses the best stability in the smooth function classes, the structure of solution space for local analytical solution is discussed, by which the third-class initial value problem with typ- icality and application is analyzed. The calculational method and concrete expressions of analytical solution about the well-posed initial value problem of the third-kind are given in the analytic function classes. Near an appointed point, the relevant theoretical and computational problems about analytical solution of initial value problem are solved completely in the meaning of local solution. Moreover, for other type ofproblems for determining solution, the computational method and process of their stable analytical solution can be obtained in a similar way given in this paper.展开更多
We propose a representation of the basic laws, namely the zeroth, first, second and third law, in quantum thermodynamics. The zeroth law is represented by some parameters () that specify respective quantum states. The...We propose a representation of the basic laws, namely the zeroth, first, second and third law, in quantum thermodynamics. The zeroth law is represented by some parameters () that specify respective quantum states. The parameters are the elements of thermodynamic state space. The introduction of such parameters is based on a probabilistic nature of quantum theory. A quantum analog of the first law can be established by utilizing these parameters. The notion of heat in quantum systems is clarified from the probabilistic point of view in quantum theory. The representation of the second law can be naturally described in terms of these parameters introduced for the respective quantum systems. In obtaining the representation of quantum thermodynamics, consistency between quantum theory and classical thermodynamics should have been preserved throughout our formulation of quantum thermodynamics. After establishing the representation of the second law, the third law is discussed briefly. The relationship between thermodynamic temperatures and the parameters in is also discussed.展开更多
基金supported by Basic Science Research Program through the National Research Foundation of Korea (NRF)the Ministry of Education,Science and Technology (2010-0022035)
文摘In this paper we study the properties of homotopy inverses of comultiplications and Mgebraic loops of co-H-spaces based on a wedge of spheres. We also investigate a method to construct new comultiplications out of old ones by using a group action. We are primarily interested in the algebraic loops which have inversive, power-associative and Moufang properties for some comultiplications.
基金Project supported by the National Natural Science Foundation of China (Major Program of the Tenth Five-Year Plan) (No.90411006).
文摘On condition that the basic equations set of atmospheric motion possesses the best stability in the smooth function classes, the structure of solution space for local analytical solution is discussed, by which the third-class initial value problem with typ- icality and application is analyzed. The calculational method and concrete expressions of analytical solution about the well-posed initial value problem of the third-kind are given in the analytic function classes. Near an appointed point, the relevant theoretical and computational problems about analytical solution of initial value problem are solved completely in the meaning of local solution. Moreover, for other type ofproblems for determining solution, the computational method and process of their stable analytical solution can be obtained in a similar way given in this paper.
文摘We propose a representation of the basic laws, namely the zeroth, first, second and third law, in quantum thermodynamics. The zeroth law is represented by some parameters () that specify respective quantum states. The parameters are the elements of thermodynamic state space. The introduction of such parameters is based on a probabilistic nature of quantum theory. A quantum analog of the first law can be established by utilizing these parameters. The notion of heat in quantum systems is clarified from the probabilistic point of view in quantum theory. The representation of the second law can be naturally described in terms of these parameters introduced for the respective quantum systems. In obtaining the representation of quantum thermodynamics, consistency between quantum theory and classical thermodynamics should have been preserved throughout our formulation of quantum thermodynamics. After establishing the representation of the second law, the third law is discussed briefly. The relationship between thermodynamic temperatures and the parameters in is also discussed.
