By our count, 245 projective planes of order less than 32 are currently known. This list is dominated by the 193 known planes of order 25. Most of these are either translation planes or Hughes planes, or planes obtained from these by the well-known process of repeatedly dualizing and deriving. We describe two new planes obtainable by the quite different method of ‘lifting quotients’. 2000 Mathe...

An unobstructedness theorem is proved for deformations of compact holomorphic Poisson manifolds and applied to a class of examples. These include certain rational surfaces and Hilbert schemes of points on Poisson surfaces. We study in particular the Hilbert schemes of the projective plane and show that a generic deformation is determined by two parameters—an elliptic curve and a translation on ...

As an extension of projective homology, stereohomology is proposed via an extension of Desargues theorem and the extended Desargues configuration. Geometric transformations such as reflection, translation, central symmetry, central projection, parallel projection, shearing, central dilation, scaling , and so on are all included in stereohomology and represented as modified Householder elementar...

This paper presents a generative probabilistic dependency model of parallel texts that can be used for statistical machine translation and parallel parsing. Unlike syntactic models that are based on context-free dependency grammars, the dependency model proposed in this paper is based on a sophisticated notion of dependency grammar that is capable of modelling non-projective word order and isla...

In this paper, we introduce the notion of {bf K}-flat projective fuzzy quantales, and give an elementary characterization in terms of a fuzzy binary relation on the fuzzy quantale. Moreover, we  prove that {bf K}-flat projective fuzzy quantales are precisely the coalgebras for a certain comonad on the category of fuzzy quantales. Finally, we present two special cases of {bf K} as examples.

We present three families of multiple blocking sets in Desarguesian projective planes of even characteristic. The first and the third construction apply to any translation hyperoval. The second construction applies to arbitrary hyperovals. ∗The second and third authors were partially supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by th...

This paper presents a self-calibration and pose estimation method that uses two cameras which only diier by focal length. The estimation of the rotation and focal lengths is independent of the translation recovery. Unlike most methods, we do not initialize our recovery with the projective camera. Instead we estimate the ego-motion and calibration from 3 homographies. These homographies can be e...

The estimation of parametric global motion using non-linear optimization is a fundamental technique in computer vision. Such schemes are able to recover various motion models (translation, rotation, affine, projective) with subpixel accuracy. The parametric motion is computed using a first order Taylor expansions of the registered images. But, it is limited to the estimation of small motions, a...

By using an extension of Desargues theorem, and the extended Desarguesian configuration thereof, the analytical definition for the stereohomology geometric transformation in projective geometry is proposed in this work. A series of such commonly used geometric transformations in computer graphics as central projection, parallel projection, centrosymmetry, reflection and translation transformati...

in this paper, lie group structure and lie algebra structure of unit complex 3-sphere     are studied. in order to do this, adjoint representations of unit biquaternions (complexified quaternions) are obtained. also, a correspondence between the elements of     and the special complex unitary matrices    (2) is given by expressing biquaternions as 2-dimensional bicomplex numbers    .  the relat...