Let H be a separable infinite dimensional complex Hilbert space, and L（H） the algebra of all bounded linear operators on 3-t＇. The class of finite operators is the class of operators for which the distance of the i...Let H be a separable infinite dimensional complex Hilbert space, and L（H） the algebra of all bounded linear operators on 3-t＇. The class of finite operators is the class of operators for which the distance of the identity operator I and the derivation range is maximal; where the derivation range of the operator A is defined by δA;δA ： L（H） -L（H） X- AX - XA. In this paper we present some properties of finite operators and give some classes of operators which are in the class of finite operators, and find for witch condition A ~ W is a finite operator in L（2-H H）, and gave a g6neralisation of Stampflli theorem.展开更多
We consider even factors with a bounded number of components in the n-times iterated line graphs L^n(G). We present a characterization of a simple graph G such that L^n(G) has an even factor with at most k components,...We consider even factors with a bounded number of components in the n-times iterated line graphs L^n(G). We present a characterization of a simple graph G such that L^n(G) has an even factor with at most k components, based on the existence of a certain type of subgraphs in G. Moreover, we use this result to give some upper bounds for the minimum number of components of even factors in L^n(G) and also show that the minimum number of components of even factors in L^n(G) is stable under the closure operation on a claw-free graph G, which extends some known results. Our results show that it seems to be NP-hard to determine the minimum number of components of even factors of iterated line graphs. We also propose some problems for further research.展开更多
The phonon thermal contribution to the melting temperature of nano-particles is inspected. The discrete summation of phonon states and its corresponding integration form as an approximation for a nano-particle or for ...The phonon thermal contribution to the melting temperature of nano-particles is inspected. The discrete summation of phonon states and its corresponding integration form as an approximation for a nano-particle or for a bulk system have been analyzed. The discrete phonon energy levels of pure size effect and the wave-vector shifts of boundary conditions are investigated in detail. Unlike in macroscopic thermodynamics, the integration volume of zero-mode of phonon for a nano-particle is not zero, and it plays an important role in pure size effect and boundary condition effect. We find that a nano-particle will have a rising melting temperature due to purely finite size effect; a lower melting temperature bound exists for a nano-particle in various environments, and the melting temperature of a nano-particle with free boundary condition reaches this lower bound. We suggest an easy procedure to estimation the melting temperature, in which the zero-mode contribution will be excluded, and only several bulk quantities will be used as input. We would like to emphasize that the quantum effect of discrete energy levels in nano-particles, which is not present in early thermodynamic studies on finite size corrections to melting temperature in small systems, should be included in future researches.展开更多
文摘Let H be a separable infinite dimensional complex Hilbert space, and L（H） the algebra of all bounded linear operators on 3-t＇. The class of finite operators is the class of operators for which the distance of the identity operator I and the derivation range is maximal; where the derivation range of the operator A is defined by δA;δA ： L（H） -L（H） X- AX - XA. In this paper we present some properties of finite operators and give some classes of operators which are in the class of finite operators, and find for witch condition A ~ W is a finite operator in L（2-H H）, and gave a g6neralisation of Stampflli theorem.
基金supported by National Natural Science Foundation of China (Grant Nos. 11471037 and 11171129)Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20131101110048)
文摘We consider even factors with a bounded number of components in the n-times iterated line graphs L^n(G). We present a characterization of a simple graph G such that L^n(G) has an even factor with at most k components, based on the existence of a certain type of subgraphs in G. Moreover, we use this result to give some upper bounds for the minimum number of components of even factors in L^n(G) and also show that the minimum number of components of even factors in L^n(G) is stable under the closure operation on a claw-free graph G, which extends some known results. Our results show that it seems to be NP-hard to determine the minimum number of components of even factors of iterated line graphs. We also propose some problems for further research.
基金Supported by National Natural Science Foundation of China under Grant No.1121403
文摘The phonon thermal contribution to the melting temperature of nano-particles is inspected. The discrete summation of phonon states and its corresponding integration form as an approximation for a nano-particle or for a bulk system have been analyzed. The discrete phonon energy levels of pure size effect and the wave-vector shifts of boundary conditions are investigated in detail. Unlike in macroscopic thermodynamics, the integration volume of zero-mode of phonon for a nano-particle is not zero, and it plays an important role in pure size effect and boundary condition effect. We find that a nano-particle will have a rising melting temperature due to purely finite size effect; a lower melting temperature bound exists for a nano-particle in various environments, and the melting temperature of a nano-particle with free boundary condition reaches this lower bound. We suggest an easy procedure to estimation the melting temperature, in which the zero-mode contribution will be excluded, and only several bulk quantities will be used as input. We would like to emphasize that the quantum effect of discrete energy levels in nano-particles, which is not present in early thermodynamic studies on finite size corrections to melting temperature in small systems, should be included in future researches.
