Using the technique of integration within an ordered product of operators and the intermediate coordinatemomentum representation in quantum optics, as well as the excited squeezed state we derive a new form of Legendr...Using the technique of integration within an ordered product of operators and the intermediate coordinatemomentum representation in quantum optics, as well as the excited squeezed state we derive a new form of Legendre polynomials.展开更多
In this paper, an explicit expression of the blossom by the means of the B-form of B-B polynomial defined on a simplex is given. With its help, new but very short and simple blossom proofs of the most important theore...In this paper, an explicit expression of the blossom by the means of the B-form of B-B polynomial defined on a simplex is given. With its help, new but very short and simple blossom proofs of the most important theorems on B-B polynomials are derived, such as the degree elevation formula, the subdivision and the change of the underlying simplex procedure, the control points convergence property, the Marsden's identity.展开更多
Water waves are one of the most common phenomena in nature, the studies of which help energy development, marine/offshore engineering, hydraulic engineering, mechanical engineering, etc. Hereby, symbolic computation i...Water waves are one of the most common phenomena in nature, the studies of which help energy development, marine/offshore engineering, hydraulic engineering, mechanical engineering, etc. Hereby, symbolic computation is performed on the Boussinesq–Burgers system for shallow water waves in a lake or near an ocean beach. For the water-wave horizontal velocity and height of the water surface above the bottom, two sets of the bilinear forms through the binary Bell polynomials and N-soliton solutions are worked out, while two auto-B?cklund transformations are constructed together with the solitonic solutions, where N is a positive integer. Our bilinear forms, N-soliton solutions and B?cklund transformations are different from those in the existing literature. All of our results are dependent on the waterwave dispersive power.展开更多
The following problem is called the everywhere-cover problem:“Given a set of dependencies over a database scheme,is the set of dependencies explicitly given for each relation scheme equivalent to the dependencies imp...The following problem is called the everywhere-cover problem:“Given a set of dependencies over a database scheme,is the set of dependencies explicitly given for each relation scheme equivalent to the dependencies implied for that relation scheme?”It is shown that when the everywhere-cover problem has a ‘yes’ answer,examining only the dependencies explicitly given will suffice to test 3NF,BCNF and 4NF of a database scheme.But this does not hold for 2NF.Consequently,in such cases,tests of BCNF and 4NF all take polynomial time.Then a proof is given that test of 3NF of a database scheme is Co-NP-complete,and from this result it is shown that everywhere-cover is also Co-NP-complete when only functional dependencies are allowed.These results lead to doubt the truth of the well believed conjec- ture that no polynomial time algorithm for designing a Iossless BCNF database scheme is likely to exist.展开更多
To enhance the expressive power and the declarative ability of a deductive database, various CWA (Closed World Assumption) formalizations including the naive CWA, the generalized CWA and the careful CWA are extended ...To enhance the expressive power and the declarative ability of a deductive database, various CWA (Closed World Assumption) formalizations including the naive CWA, the generalized CWA and the careful CWA are extended to multi-valued logics. The basic idea is to embed logic formulas into some polynomial ring. The extensions can be applied in a uniform manner to any finitely multi-valued logics. Therefore they are also of computational significance.展开更多
文摘Using the technique of integration within an ordered product of operators and the intermediate coordinatemomentum representation in quantum optics, as well as the excited squeezed state we derive a new form of Legendre polynomials.
文摘In this paper, an explicit expression of the blossom by the means of the B-form of B-B polynomial defined on a simplex is given. With its help, new but very short and simple blossom proofs of the most important theorems on B-B polynomials are derived, such as the degree elevation formula, the subdivision and the change of the underlying simplex procedure, the control points convergence property, the Marsden's identity.
基金supported by the National Nature Science Foundation of China under Grant No.11871116Fundamental Research Funds for the Central Universities of China under Grant No. 2019XD-A11。
文摘Water waves are one of the most common phenomena in nature, the studies of which help energy development, marine/offshore engineering, hydraulic engineering, mechanical engineering, etc. Hereby, symbolic computation is performed on the Boussinesq–Burgers system for shallow water waves in a lake or near an ocean beach. For the water-wave horizontal velocity and height of the water surface above the bottom, two sets of the bilinear forms through the binary Bell polynomials and N-soliton solutions are worked out, while two auto-B?cklund transformations are constructed together with the solitonic solutions, where N is a positive integer. Our bilinear forms, N-soliton solutions and B?cklund transformations are different from those in the existing literature. All of our results are dependent on the waterwave dispersive power.
基金Supported by the National Natural Science Foundation of China.
文摘The following problem is called the everywhere-cover problem:“Given a set of dependencies over a database scheme,is the set of dependencies explicitly given for each relation scheme equivalent to the dependencies implied for that relation scheme?”It is shown that when the everywhere-cover problem has a ‘yes’ answer,examining only the dependencies explicitly given will suffice to test 3NF,BCNF and 4NF of a database scheme.But this does not hold for 2NF.Consequently,in such cases,tests of BCNF and 4NF all take polynomial time.Then a proof is given that test of 3NF of a database scheme is Co-NP-complete,and from this result it is shown that everywhere-cover is also Co-NP-complete when only functional dependencies are allowed.These results lead to doubt the truth of the well believed conjec- ture that no polynomial time algorithm for designing a Iossless BCNF database scheme is likely to exist.
文摘To enhance the expressive power and the declarative ability of a deductive database, various CWA (Closed World Assumption) formalizations including the naive CWA, the generalized CWA and the careful CWA are extended to multi-valued logics. The basic idea is to embed logic formulas into some polynomial ring. The extensions can be applied in a uniform manner to any finitely multi-valued logics. Therefore they are also of computational significance.
