1. Affine Geometry 1.1. Affine Space 1.2. Affine Lines 1.3. Affine transformations 1.4. Affine Collinearity 1.5. Conic Sections 2. Projective Geometry 2.1. Perspective 2.2. Projective Plane 2.3. Projective Transformations 2.4. Projective Collinearity 2.5. Conics 3. Geometries and Groups 3.1. Transformation Groups 3.2. Erlangen Program 4. Non-Euclidean Geometry 4.1. Elliptic Geometry 4.2. Hyperb...

In the present paper we obtain an intrinsic characterization of real locally C*-algebras (projective limits of projective families of real C*-algebras) among complete real lmc *-algebras, and of locally JB-algebras (projective limits of projective families of JB-algebras) among complete fine Jordan locally multiplicatively-convex topological algebras.

In this paper, we introduce and investigate the notions of ξ-strongly copure projective objects in a triangulated category. This extends Asadollahi’s notion of ξ-Gorenstein projective objects. Then we study the ξ-strongly copure projective dimension and investigate the existence of ξ-strongly copure projective precover.

Projective synchronization and generalized projective synchronization have recently been observed in the coupled hyperchaotic systems. In this paper a generalized projective synchronization technique is applied in the hyperchaotic Lorenz system and the hyperchaotic Lü. The sufficient conditions for achieving projective synchronization of two different hyperchaotic systems are derived. Numerical...

Image coding standards usually focus on storing and transmitting signals efficiently, in a frame based approach. The coming MPEG-4 standard [1] adds a new challenge, namely bringing new services to image communication users. It moves towards representing a scene as a composition of audiovisual objects rather than "just" a collection of pixels. MPEG-4 objects can be captured naturally by one (or...

Inspite of the fact that the study of suicidal behaviour has been the subject of an ever increasing body of li terature, re catch in the field of communication of suicidal intent has somehow not received due attention. Quite often pntient 's suicidal ideas may remain unnoticed during clinical interview in an overcrowded psychiatric outpatient and at times this inadvertent neglect might result i...

Projective texture-mapping is a powerful tool for image-based rendering. However, visibility information must be obtained in order to project correct textures onto the geometric sturcture. This paper presents a novel visibility algorithm for determining which polygons are visible from each camera position. It has object-space precision, but operates in both image-space and object-space to get b...

In this paper embeddings of projective Klingenberg planes in a 5-dimensional projective space are classified. It is proved that if a PK-plane is fully embedded in PG(5,K), for some skewfield K, then it is either isomorphic to the Desarguesian projective Klingenberg plane (projective Hjelmslev plane for bijective σ) PH(2,D(K, σ)) over a ring of ordinary or twisted dual numbers or it is a subgeom...

The first examples of complete projective connections are uncovered: normal projective connections on surfaces whose geodesics are all closed and embedded are complete, as are normal projective connections induced from complete affine connections with slowly decaying positive Ricci curvature. Moreover, I explain the relationship between projective and affine connections.

A graph G is outer projective planar if it can be embedded in the projective plane so that every vertex appears on the boundary of a single face We exhibit obstruction sets for outer projective planar graphs with respect to the subdivision minor and Y orderings Equivalently we nd the minimal non outer projective planar graphs under these orderings