It has been shown, under certain conditions on the Gauss curvature, every totally real surface of the Cayley projective plane with parallel mean curvature vector is either flat or totally geodesic.
The most popular and representative classic waveform codes are referred to as orthogonal,bi-orthogonal,simplex,and etc,but the choice of waveform codes is essentially identical in error performance and cross correlati...The most popular and representative classic waveform codes are referred to as orthogonal,bi-orthogonal,simplex,and etc,but the choice of waveform codes is essentially identical in error performance and cross correlation characteristic.Though bi-orthogonal coding requires half the bandwidth of the others,such coding scheme is attractive only when large bandwidth is available.In this paper,a novel finite projective plane（FPP） based waveform coding scheme is proposed,which is with similar error performance and cross correlation.Nevertheless,the bandwidth requirement will grow in a quadratic way,but not in an exponential way with the values of message bit numbers（k）.The proposed scheme takes obvious advantages over the bi-orthogonal scheme when k ≥ 6.展开更多
In this paper,four pattern recognition methods are set forth.Based on plane projection of samples and analysis of typical samples along with the few pattern recognition methods,the PTR algorithm for recognizing variou...In this paper,four pattern recognition methods are set forth.Based on plane projection of samples and analysis of typical samples along with the few pattern recognition methods,the PTR algorithm for recognizing various structure samples is proposed.Also two examples are given and these show the PTR algorithm is effective.展开更多
Some models dealing with fibers and liquid crystals can be formulated probabilistically in terms of orientation distributions. Since the orientation of a thin object can be specified by a point in a real projective pl...Some models dealing with fibers and liquid crystals can be formulated probabilistically in terms of orientation distributions. Since the orientation of a thin object can be specified by a point in a real projective plane this approach leads to elliptic and parabolic problems in the real projective plane. In most previous works these kind of problems have been considered on the unit sphere which is a double cover of the real projective plane. However, numerically this is inefficient because the resulting systems of equations are unnecessarily big. We formulate the problem directly in the real projective plane using a certain parametrization with three coordinate domains. After reducing the computations to the coordinate domains we can then use finite elements almost in a standard way. In particular the standard error estimates with usual Sobolev spaces remain valid in this setting. We consider both elliptic and parabolic cases, and demonstrate the validity of our approach.展开更多
Both the circulant graph and the generalized Petersen graph are important types of graphs in graph theory. In this paper, the structures of embeddings of circulant graph C（2n ＋ 1; {1, n}） on the projective plane ar...Both the circulant graph and the generalized Petersen graph are important types of graphs in graph theory. In this paper, the structures of embeddings of circulant graph C（2n ＋ 1; {1, n}） on the projective plane are described, the number of embeddings of C（2n ＋ 1; {1, n}） on the projective plane follows, then the number of embeddings of the generalized Petersen graph P（2n ＋ 1, n） on the projective plane is deduced from that of C（2n ＋ 1; {1, n}）, because C（2n ＋ 1; {1, n}） is a minor of P（2n ＋ 1, n）, their structures of embeddings have relations. In the same way, the number of embeddings of the generalized Petersen graph P（2n, 2） on the projective plane is also obtained.展开更多
The enumerative functional equation of maps by the number of inner faces, the valency of root face and the number of non-rooted vertices on the projective plane is studied. An explicit expression for the generating fu...The enumerative functional equation of maps by the number of inner faces, the valency of root face and the number of non-rooted vertices on the projective plane is studied. An explicit expression for the generating function by the number of inner faces and the number of non-rooted vertices is obtained. From this result, the enumeration of rooted maps by the number of edges discussed in [1] is obtained as a corollary.展开更多
This paper thoroughly investigates the problem of robot self-location by line correspondences. The original contributions are three-fold: (1) Obtain the necessary and sufficient condition to determine linearly the rob...This paper thoroughly investigates the problem of robot self-location by line correspondences. The original contributions are three-fold: (1) Obtain the necessary and sufficient condition to determine linearly the robot's pose by two line correspondences. (2) Show that if the space lines are vertical ones, it is impossible to determine linearly the robot's pose no matter how many line correspondences we have, and the minimum number of line correspondences is 3 to determine uniquely (but non-linearly) the robot's pose. (3) Show that if the space lines are horizontal ones, the minimum number of line correspondences is 3 for linear determination and 2 for non-linear determination of the robot's pose.展开更多
文摘It has been shown, under certain conditions on the Gauss curvature, every totally real surface of the Cayley projective plane with parallel mean curvature vector is either flat or totally geodesic.
基金supported by MOST under Grant MOST 103-2633-E-242-002
文摘The most popular and representative classic waveform codes are referred to as orthogonal,bi-orthogonal,simplex,and etc,but the choice of waveform codes is essentially identical in error performance and cross correlation characteristic.Though bi-orthogonal coding requires half the bandwidth of the others,such coding scheme is attractive only when large bandwidth is available.In this paper,a novel finite projective plane（FPP） based waveform coding scheme is proposed,which is with similar error performance and cross correlation.Nevertheless,the bandwidth requirement will grow in a quadratic way,but not in an exponential way with the values of message bit numbers（k）.The proposed scheme takes obvious advantages over the bi-orthogonal scheme when k ≥ 6.
文摘In this paper,four pattern recognition methods are set forth.Based on plane projection of samples and analysis of typical samples along with the few pattern recognition methods,the PTR algorithm for recognizing various structure samples is proposed.Also two examples are given and these show the PTR algorithm is effective.
文摘Some models dealing with fibers and liquid crystals can be formulated probabilistically in terms of orientation distributions. Since the orientation of a thin object can be specified by a point in a real projective plane this approach leads to elliptic and parabolic problems in the real projective plane. In most previous works these kind of problems have been considered on the unit sphere which is a double cover of the real projective plane. However, numerically this is inefficient because the resulting systems of equations are unnecessarily big. We formulate the problem directly in the real projective plane using a certain parametrization with three coordinate domains. After reducing the computations to the coordinate domains we can then use finite elements almost in a standard way. In particular the standard error estimates with usual Sobolev spaces remain valid in this setting. We consider both elliptic and parabolic cases, and demonstrate the validity of our approach.
文摘Both the circulant graph and the generalized Petersen graph are important types of graphs in graph theory. In this paper, the structures of embeddings of circulant graph C（2n ＋ 1; {1, n}） on the projective plane are described, the number of embeddings of C（2n ＋ 1; {1, n}） on the projective plane follows, then the number of embeddings of the generalized Petersen graph P（2n ＋ 1, n） on the projective plane is deduced from that of C（2n ＋ 1; {1, n}）, because C（2n ＋ 1; {1, n}） is a minor of P（2n ＋ 1, n）, their structures of embeddings have relations. In the same way, the number of embeddings of the generalized Petersen graph P（2n, 2） on the projective plane is also obtained.
基金the National Natural Foundation of China (Grant No. 19831080),
文摘The enumerative functional equation of maps by the number of inner faces, the valency of root face and the number of non-rooted vertices on the projective plane is studied. An explicit expression for the generating function by the number of inner faces and the number of non-rooted vertices is obtained. From this result, the enumeration of rooted maps by the number of edges discussed in [1] is obtained as a corollary.
基金the National '863' High-Tech Programme of China under the grant No. 863-512-9915-01 and the National Natural Science Foundatio
文摘This paper thoroughly investigates the problem of robot self-location by line correspondences. The original contributions are three-fold: (1) Obtain the necessary and sufficient condition to determine linearly the robot's pose by two line correspondences. (2) Show that if the space lines are vertical ones, it is impossible to determine linearly the robot's pose no matter how many line correspondences we have, and the minimum number of line correspondences is 3 to determine uniquely (but non-linearly) the robot's pose. (3) Show that if the space lines are horizontal ones, the minimum number of line correspondences is 3 for linear determination and 2 for non-linear determination of the robot's pose.
