In this article, we study the Lie supertriple system (LSTS) T over a field K admitting a nondegenerate invariant supersymmetric bilinear form (call such a Tmetrisable). We give the definition of T*ω-extension of...In this article, we study the Lie supertriple system (LSTS) T over a field K admitting a nondegenerate invariant supersymmetric bilinear form (call such a Tmetrisable). We give the definition of T*ω-extension of an LSTS T , prove a necessary and sufficient condition for a metrised LSTS (T ,Ф) to be isometric to a T*-extension of some LSTS, and determine when two T*-extensions of an LSTS are "same", i.e., they are equivalent or isometrically equivalent.展开更多
In this article, we study the (2+1)-extension of Burgers equation and the KPequation. At first, based on a known Baecklund transformation and corresponding Lax pair, aninvariance which depends on two arbitrary functio...In this article, we study the (2+1)-extension of Burgers equation and the KPequation. At first, based on a known Baecklund transformation and corresponding Lax pair, aninvariance which depends on two arbitrary functions for (2+1)-extension of Burgers equation isworked out. Given a known solution and using the invariance, we can find solutions of the(2+1)-extension of Burgers equation repeatedly. Secondly, we put forward an invariance of Burgersequation which cannot be directly obtained by constraining the invariance of the (2+1)-extension ofBurgers equation. Furthermore, we reveal that the invariance for finding the solutions of Burgersequation can help us find the solutions of KP equation. At last, based on the invariance of Burgersequation, the corresponding recursion formulae for finding solutions of KP equation are digged out.As the application of our theory, some examples have been put forward in this article and somesolutions of the (2+1)-extension of Burgers equation, Burgers equation and KP equation are obtained.展开更多
This paper,combined algebraical structure with analytical system,has studied the part of theory of C~*-modules over A by using the homolgical methods, where A is a commutative C~*-algebra over complex number field C. ...This paper,combined algebraical structure with analytical system,has studied the part of theory of C~*-modules over A by using the homolgical methods, where A is a commutative C~*-algebra over complex number field C. That is to say we have not only defined some relevant new concept,but also obtained some results about them.展开更多
In this paper, we discussed some improtant inequalities, such as young inequality, Holder inequality and Minkowski inequality,about the positive elements in C~*-Algebra.
We introduce a special tracial Rokhlin property for unital C~*-algebras. Let A be a unital tracial rank zero C~*-algebra(or tracial rank no more than one C~*-algebra). Suppose that α : G → Aut(A) is an actio...We introduce a special tracial Rokhlin property for unital C~*-algebras. Let A be a unital tracial rank zero C~*-algebra(or tracial rank no more than one C~*-algebra). Suppose that α : G → Aut(A) is an action of a finite group G on A, which has this special tracial Rokhlin property, and suppose that A is a α-simple C~*-algebra. Then, the crossed product C~*-algebra C~*(G, A, α) has tracia rank zero(or has tracial rank no more than one). In fact,we get a more general results.展开更多
文摘In this article, we study the Lie supertriple system (LSTS) T over a field K admitting a nondegenerate invariant supersymmetric bilinear form (call such a Tmetrisable). We give the definition of T*ω-extension of an LSTS T , prove a necessary and sufficient condition for a metrised LSTS (T ,Ф) to be isometric to a T*-extension of some LSTS, and determine when two T*-extensions of an LSTS are "same", i.e., they are equivalent or isometrically equivalent.
文摘In this article, we study the (2+1)-extension of Burgers equation and the KPequation. At first, based on a known Baecklund transformation and corresponding Lax pair, aninvariance which depends on two arbitrary functions for (2+1)-extension of Burgers equation isworked out. Given a known solution and using the invariance, we can find solutions of the(2+1)-extension of Burgers equation repeatedly. Secondly, we put forward an invariance of Burgersequation which cannot be directly obtained by constraining the invariance of the (2+1)-extension ofBurgers equation. Furthermore, we reveal that the invariance for finding the solutions of Burgersequation can help us find the solutions of KP equation. At last, based on the invariance of Burgersequation, the corresponding recursion formulae for finding solutions of KP equation are digged out.As the application of our theory, some examples have been put forward in this article and somesolutions of the (2+1)-extension of Burgers equation, Burgers equation and KP equation are obtained.
文摘This paper,combined algebraical structure with analytical system,has studied the part of theory of C~*-modules over A by using the homolgical methods, where A is a commutative C~*-algebra over complex number field C. That is to say we have not only defined some relevant new concept,but also obtained some results about them.
文摘In this paper, we discussed some improtant inequalities, such as young inequality, Holder inequality and Minkowski inequality,about the positive elements in C~*-Algebra.
文摘We introduce a special tracial Rokhlin property for unital C~*-algebras. Let A be a unital tracial rank zero C~*-algebra(or tracial rank no more than one C~*-algebra). Suppose that α : G → Aut(A) is an action of a finite group G on A, which has this special tracial Rokhlin property, and suppose that A is a α-simple C~*-algebra. Then, the crossed product C~*-algebra C~*(G, A, α) has tracia rank zero(or has tracial rank no more than one). In fact,we get a more general results.