In this paper, we present a general approach to the construction of the Said-type generalized Ball basis functions. The advantage of our approach lies in the fact that it can be used to derive the expressions for poly...In this paper, we present a general approach to the construction of the Said-type generalized Ball basis functions. The advantage of our approach lies in the fact that it can be used to derive the expressions for polynomials of not only odd degrees but also even degrees in terms of the Said-type generalized Ball basis functions. We then define dual functionals for the Said-type generalized Ball basis in a very natural manner and bring to light the integral property of the Said-type generalized Ball basis functions. Last but not least, new polynomial basis functions are defined which include the Said-type generalized Ball basis functions as their special case, and the corresponding dual functionals and Marsden-like identity are obtained.展开更多
A conclusive teleportation protocol of a d-dimensional two-particle unknown quantum state using three d- dimensional particles in an arbitrary pure state is proposed. A sender teleports the unknown state conclusively ...A conclusive teleportation protocol of a d-dimensional two-particle unknown quantum state using three d- dimensional particles in an arbitrary pure state is proposed. A sender teleports the unknown state conclusively to a receiver by using the positive operator valued measure（POVM） and introducing an ancillary qudit to perform the generalized Bell basis measurement, We calculate the optimal teleportation fidelity. We also discuss and analyse the reason why the information on the teleported state is lost in the course of the protocol,展开更多
A family of Said-Bézier type generalized Ball （SBGB） bases and surfaces with a parameter H over triangular domain is introduced,which unifies Bézier surface and Said-Ball surface and includes several inter...A family of Said-Bézier type generalized Ball （SBGB） bases and surfaces with a parameter H over triangular domain is introduced,which unifies Bézier surface and Said-Ball surface and includes several intermediate surfaces. To convert different bases and surfaces,the dual functionals of bases are presented. As an application of dual functionals,the subdivision formulas for surfaces are established.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.61472466)
文摘In this paper, we present a general approach to the construction of the Said-type generalized Ball basis functions. The advantage of our approach lies in the fact that it can be used to derive the expressions for polynomials of not only odd degrees but also even degrees in terms of the Said-type generalized Ball basis functions. We then define dual functionals for the Said-type generalized Ball basis in a very natural manner and bring to light the integral property of the Said-type generalized Ball basis functions. Last but not least, new polynomial basis functions are defined which include the Said-type generalized Ball basis functions as their special case, and the corresponding dual functionals and Marsden-like identity are obtained.
基金Project supported by the National Natural Science Foundation of China （Grant No 60373059）, the Major Research Plan of the National Natural Science Foundation of China （Grant No 90604023） and the Doctoral Foundation of the State Education Ministry of China（Grant No 20040013007）.
文摘A conclusive teleportation protocol of a d-dimensional two-particle unknown quantum state using three d- dimensional particles in an arbitrary pure state is proposed. A sender teleports the unknown state conclusively to a receiver by using the positive operator valued measure（POVM） and introducing an ancillary qudit to perform the generalized Bell basis measurement, We calculate the optimal teleportation fidelity. We also discuss and analyse the reason why the information on the teleported state is lost in the course of the protocol,
文摘A family of Said-Bézier type generalized Ball （SBGB） bases and surfaces with a parameter H over triangular domain is introduced,which unifies Bézier surface and Said-Ball surface and includes several intermediate surfaces. To convert different bases and surfaces,the dual functionals of bases are presented. As an application of dual functionals,the subdivision formulas for surfaces are established.
