Totally Real Surfaces of the Cayley Projective Plane with Parallel Mean Curvature Vector

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.

Evaluations of Novel Waveform Coding Signals Based on Finite Projective Plane

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.

THE PROJECTIVE PLANE CROSSING NUMBERS OF CIRCULAR GRAPHS

The authors give an upper bound for the projective plane crossing number of a circular graph. Also, the authors prove the projective plane crossing numbers of circular graph C （8, 3） and C （9, 3） are 2 and 1, respectively.

Gorenstein Q-homology projective planes

We present the complete list of all singularity types on Gorenstein Q-homology projective planes,i.e.,normal projective surfaces of second Betti number one with at worst rational double points.The list consists of 58 possible singularity types,each except two types supported by an example.

A fake projective plane constructed from an elliptic surface with multiplicities (2,4)

Given any (2,4)-elliptic surface with nine smooth rational curves,eight (2)-curves and one (3)-curve,forming a Dynkin diagram of type [2,2][2,2][2,2][2,2,3],we show that a fake projective plane can be constructed from it by taking a degree 3 cover and then a degree 7 cover.We also determine the types of singular fibres of such a (2,4)-elliptic surface.

ON THE NUMERICAL SOLUTION OF ELLIPTIC AND PARABOLIC PDE IN THE REAL PROJECTIVE PLANE

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.

Embedding generalized of circulant graphs and Petersen graphs on projective plane

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.

Exotic structures arising from fake projective planes

We present examples of exotic structures on pPC2#qPC2 for some small p and q obtained naturally from quotients of fake projective planes in complex geometry,which are classified by the work of Prasad-Yeung and Cartwright-Steger.

ENUMERATION OF MAPS ON THE PROJECTIVE PLANE

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.

Novel method for extraction of ship target with overlaps in SAR image via EM algorithm

The quality of synthetic aperture radar(SAR)image degrades in the case of multiple imaging projection planes(IPPs)and multiple overlapping ship targets,and then the performance of target classification and recognition can be influenced.For addressing this issue,a method for extracting ship targets with overlaps via the expectation maximization(EM)algorithm is pro-posed.First,the scatterers of ship targets are obtained via the target detection technique.Then,the EM algorithm is applied to extract the scatterers of a single ship target with a single IPP.Afterwards,a novel image amplitude estimation approach is pro-posed,with which the radar image of a single target with a sin-gle IPP can be generated.The proposed method can accom-plish IPP selection and targets separation in the image domain,which can improve the image quality and reserve the target information most possibly.Results of simulated and real mea-sured data demonstrate the effectiveness of the proposed method.

The study and application of PTR algorithm on recognizing various structure samples

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.

The maximal size of 6-and 7-arcs in projective Hjelmslev planes over chain rings of order 9 Dedicated to Professor Feng Keqin on the Occasion of his 70th Birthday

We complete the determination of the maximum sizes of （k,n）-arcs, n ≤ 12, in the projective gjelmslev planes over the two （proper） chain rings Z9 = Z/9Z and S3 = F3[X]/（X2） of order 9 by resolving the hitherto open cases n = 6 and n = 7. Parts of our proofs rely on decidedly geometric properties of the planes such as Desargues＇ theorem and the existence of certain subplanes.

The Bonnesen isoperimetric inequality in a surface of constant curvature

We first estimate the containment measure of a convex domain to contain in another in a surface X of constant curvature.Then we obtain the analogue of the known Bonnesen isoperimetric inequality for convex domain in X.Finally we strengthen the known Bonnesen isoperimetric inequality.

Robot Self-Location by Line Correspondences

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.