The electronic and optical properties of TiS2 are studied of density functional theory. A linearized and augmented by using an ab-initio calculation within the frame plane wave basis set with the generalized gradient ...The electronic and optical properties of TiS2 are studied of density functional theory. A linearized and augmented by using an ab-initio calculation within the frame plane wave basis set with the generalized gradient approximation as proposed by Perdew et al. is used for the energy exchange-correlation determination. The results show a metallic character of TiS2, and the plots of total and partial densities of states of TiS2 show the metallic character of the bonds and a strong hybridization between the states d of Ti and p of S below the Fermi energy. The optical properties of the material such as real and imaginary parts of dielectric constant （ε（w） = ε1（w） ＋ iε2（w））, refractive index n（w）, optical reflectivity R（w）, for E / /x and E / /z are performed for the energy range of 0-.14 eV.展开更多
Taking a coupled system of wave equations with Dirichlet boundary controls as an example,by splitting and merging some synchronization groups of the state variables cor-responding to a given generalized synchronizatio...Taking a coupled system of wave equations with Dirichlet boundary controls as an example,by splitting and merging some synchronization groups of the state variables cor-responding to a given generalized synchronization matrix,this paper introduces two kinds of induced generalized exact boundary synchronizations to better determine its generalized exactly synchronizable states.展开更多
In this paper we define tensor modules （sheaves） of Schur type and of generalized Schur type associated with given modules （sheaves）, using the so-called Schur functors. According to the functorial property, we gi...In this paper we define tensor modules （sheaves） of Schur type and of generalized Schur type associated with given modules （sheaves）, using the so-called Schur functors. According to the functorial property, we give a series of tensor modules （sheaves） of Schur types in a categorical description. The main conclusion is that, by using basic ideas of algebraic geometry, there exists a canonical isomorphism of different tensor modules （sheaves） of Schur types if the original sheaf is locally free, which is in fact a generalization of results in linear algebra into locally free sheaves.展开更多
Suppose that x is a complex number and i is a non negative integer. Define N - i(x)=|x| i if i is even and N - i(x)=x|x| i-1 if i is odd. Let V - n(x 1, ...,x n) denote the ...Suppose that x is a complex number and i is a non negative integer. Define N - i(x)=|x| i if i is even and N - i(x)=x|x| i-1 if i is odd. Let V - n(x 1, ...,x n) denote the n× n matrix whose (i,j) th entry is N - i-1 (x j) . This paper presents a computation formula for det V - n(x 1, ...,x n) , which can be considered as a generalized that of Vandermonde determinant, and some its important theoretical applications.展开更多
文摘The electronic and optical properties of TiS2 are studied of density functional theory. A linearized and augmented by using an ab-initio calculation within the frame plane wave basis set with the generalized gradient approximation as proposed by Perdew et al. is used for the energy exchange-correlation determination. The results show a metallic character of TiS2, and the plots of total and partial densities of states of TiS2 show the metallic character of the bonds and a strong hybridization between the states d of Ti and p of S below the Fermi energy. The optical properties of the material such as real and imaginary parts of dielectric constant （ε（w） = ε1（w） ＋ iε2（w））, refractive index n（w）, optical reflectivity R（w）, for E / /x and E / /z are performed for the energy range of 0-.14 eV.
文摘Taking a coupled system of wave equations with Dirichlet boundary controls as an example,by splitting and merging some synchronization groups of the state variables cor-responding to a given generalized synchronization matrix,this paper introduces two kinds of induced generalized exact boundary synchronizations to better determine its generalized exactly synchronizable states.
文摘In this paper we define tensor modules （sheaves） of Schur type and of generalized Schur type associated with given modules （sheaves）, using the so-called Schur functors. According to the functorial property, we give a series of tensor modules （sheaves） of Schur types in a categorical description. The main conclusion is that, by using basic ideas of algebraic geometry, there exists a canonical isomorphism of different tensor modules （sheaves） of Schur types if the original sheaf is locally free, which is in fact a generalization of results in linear algebra into locally free sheaves.
文摘Suppose that x is a complex number and i is a non negative integer. Define N - i(x)=|x| i if i is even and N - i(x)=x|x| i-1 if i is odd. Let V - n(x 1, ...,x n) denote the n× n matrix whose (i,j) th entry is N - i-1 (x j) . This paper presents a computation formula for det V - n(x 1, ...,x n) , which can be considered as a generalized that of Vandermonde determinant, and some its important theoretical applications.
