In this paper, Leibniz' formula of generalized divided difference with respect to a class of differential operators whose basic sets of solutions have power form, is considered. The recurrence formula of Green fun...In this paper, Leibniz' formula of generalized divided difference with respect to a class of differential operators whose basic sets of solutions have power form, is considered. The recurrence formula of Green function about the operators is also given.展开更多
Based on the Kubo formula for an electron tunneling junction, we revisit the nonequilibrium transport properties through a quantum dot. Since the Fermi level of the quantum dot is set by the conduction electrons of th...Based on the Kubo formula for an electron tunneling junction, we revisit the nonequilibrium transport properties through a quantum dot. Since the Fermi level of the quantum dot is set by the conduction electrons of the leads, we calculate the electron current from the left side by assuming the quantum dot coupled to the right lead as another side of the tunneling junction, and the other way round is used to calculate the current from the right side. By symmetrizing these two currents, an effective local density states on the dot can be obtained, and is discussed at high and low temperatures, respectively.展开更多
In this paper, we use the Mittag-Leffler addition formula to solve the Green function of generalized time fractional diffusion equation in the whole plane and prove the convergence of the Green function.
In this article, we establish the Gauss Green type theorems for Clifford-valued functions in Clifford analysis. The boundary conditions in theorems obtained are very general by using the geometric measure theoretic me...In this article, we establish the Gauss Green type theorems for Clifford-valued functions in Clifford analysis. The boundary conditions in theorems obtained are very general by using the geometric measure theoretic method. The Cauchy-Pompeiu formula for Clifford-valued functions under the weak condition will be derived as their simple application. Furthermore, Cauchy formula for monogenic functions under the weak condition is derived directly from the Cauchy-Pompeiu formula.展开更多
文摘In this paper, Leibniz' formula of generalized divided difference with respect to a class of differential operators whose basic sets of solutions have power form, is considered. The recurrence formula of Green function about the operators is also given.
基金国家自然科学基金，the Special Fund for State Key Basic Research Projects of China under
文摘Based on the Kubo formula for an electron tunneling junction, we revisit the nonequilibrium transport properties through a quantum dot. Since the Fermi level of the quantum dot is set by the conduction electrons of the leads, we calculate the electron current from the left side by assuming the quantum dot coupled to the right lead as another side of the tunneling junction, and the other way round is used to calculate the current from the right side. By symmetrizing these two currents, an effective local density states on the dot can be obtained, and is discussed at high and low temperatures, respectively.
文摘In this paper, we use the Mittag-Leffler addition formula to solve the Green function of generalized time fractional diffusion equation in the whole plane and prove the convergence of the Green function.
基金Supported by the NNSFC(11161030)the Specialized Research Fund for the Doctoral Program of Higher Education of China(20121501120003)the Doctoral Science Foundation of Hubei University for Nationalities(2014)
基金Supported by the National Nature Science Foundation of China(11161030)the Specialized Research Fund for the Doctoral Program of Higher Education of China(20121501120003)the Doctoral Science Foundation of Hubei University for Nationalities(2014)
基金supported by NNSF of China(11171260)RFDP of Higher Education of China(20100141110054)
文摘In this article, we establish the Gauss Green type theorems for Clifford-valued functions in Clifford analysis. The boundary conditions in theorems obtained are very general by using the geometric measure theoretic method. The Cauchy-Pompeiu formula for Clifford-valued functions under the weak condition will be derived as their simple application. Furthermore, Cauchy formula for monogenic functions under the weak condition is derived directly from the Cauchy-Pompeiu formula.
