We define discrete total differential forms on lattice space by. changing coefficients of discrete differential forms from functions only of n to functions also of dependent variables un and their partial differences....We define discrete total differential forms on lattice space by. changing coefficients of discrete differential forms from functions only of n to functions also of dependent variables un and their partial differences. And the discrete exterior derivative extends to be discrete total differential map which is also nilpotent. Then a discrete horizontal complex can be derived and be proved to be exact by constructing homotopy operators.展开更多
We present the noncommutative differential calculus on the function space of the infinite set and construct a homotopy operator to prove the analogue of the Poincare lemma for the difference complex. Then the horizont...We present the noncommutative differential calculus on the function space of the infinite set and construct a homotopy operator to prove the analogue of the Poincare lemma for the difference complex. Then the horizontal and vertical complexes are introduced with the total differential map and vertical exterior derivative. As the application of the differential calculus, we derive the schemes with the conservation of symplecticity and energy for Hamiltonian system and a two-dimensional integral models with infinite sequence of conserved currents. Then an Euler-Lagrange cohomology with symplectic structure-preserving is given in the discrete classical mechanics.展开更多
Let M be a connected complex manifold endowed with a Hermitian metric g.In this paper,the complex horizontal and vertical Laplacians associated with the induced Hermitian metric <·,·>on the holomorphic...Let M be a connected complex manifold endowed with a Hermitian metric g.In this paper,the complex horizontal and vertical Laplacians associated with the induced Hermitian metric <·,·>on the holomorphic tangent bundle T 1,0M of M are defined,and their explicit expressions are obtained.Using the complex horizontal and vertical Laplacians associated with the Hermitian metric <·,·>on T 1,0M,we obtain a vanishing theorem of holomorphic horizontal p forms which are compactly supported in T 1,0M under the condition that g is a Kaehler metric on M.展开更多
文摘We define discrete total differential forms on lattice space by. changing coefficients of discrete differential forms from functions only of n to functions also of dependent variables un and their partial differences. And the discrete exterior derivative extends to be discrete total differential map which is also nilpotent. Then a discrete horizontal complex can be derived and be proved to be exact by constructing homotopy operators.
基金The project supported by National Natural Science Foundation of China under Grant No.10626016China Postdoctor Science Foundation of Henan University under Grant No.05YBZR014
文摘We present the noncommutative differential calculus on the function space of the infinite set and construct a homotopy operator to prove the analogue of the Poincare lemma for the difference complex. Then the horizontal and vertical complexes are introduced with the total differential map and vertical exterior derivative. As the application of the differential calculus, we derive the schemes with the conservation of symplecticity and energy for Hamiltonian system and a two-dimensional integral models with infinite sequence of conserved currents. Then an Euler-Lagrange cohomology with symplectic structure-preserving is given in the discrete classical mechanics.
基金supported by the Program for New Century Excellent Talents in Fujian Province and National Natural Science Foundation of China(Grant Nos.10601040,10971170)
文摘Let M be a connected complex manifold endowed with a Hermitian metric g.In this paper,the complex horizontal and vertical Laplacians associated with the induced Hermitian metric <·,·>on the holomorphic tangent bundle T 1,0M of M are defined,and their explicit expressions are obtained.Using the complex horizontal and vertical Laplacians associated with the Hermitian metric <·,·>on T 1,0M,we obtain a vanishing theorem of holomorphic horizontal p forms which are compactly supported in T 1,0M under the condition that g is a Kaehler metric on M.
