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
Squeezed quantum vacua seems to violate the averaged null energy conditions (ANEC’s), because they have a negative energy density. When treated as a perfect fluid, rapidly rotating Casimir plates will create vorticit...Squeezed quantum vacua seems to violate the averaged null energy conditions (ANEC’s), because they have a negative energy density. When treated as a perfect fluid, rapidly rotating Casimir plates will create vorticity in the vacuum bounded by them. The geometry resulting from an arbitrarily extended Casimir plates along their axis of rotation is similar to van Stockum spacetime. We observe closed timelike curves (CTC’s) forming in the exterior of the system resulting from frame dragging. The exterior geometry of this system is similar to Kerr geometry, but because of violation of ANEC, the Cauchy horizon lies outside the system unlike Kerr blackholes, giving more emphasis on whether spacetime is multiply connected at the microscopic level.展开更多
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Squeezed quantum vacua seems to violate the averaged null energy conditions (ANEC’s), because they have a negative energy density. When treated as a perfect fluid, rapidly rotating Casimir plates will create vorticity in the vacuum bounded by them. The geometry resulting from an arbitrarily extended Casimir plates along their axis of rotation is similar to van Stockum spacetime. We observe closed timelike curves (CTC’s) forming in the exterior of the system resulting from frame dragging. The exterior geometry of this system is similar to Kerr geometry, but because of violation of ANEC, the Cauchy horizon lies outside the system unlike Kerr blackholes, giving more emphasis on whether spacetime is multiply connected at the microscopic level.
