1,721,005 research outputs found
{1,2}-semi-affine planar spaces.
No full textLet (S,L) be a finite linear space, that is, a finite set S whose elements we call points, and L a family of parts in S, whose elements we call lines, such that any line has at least two points, two distinct points are contained in just one line and |L|≥2. A subspace in (S,L) is a subset S′ in S such that for any X,Y∈S′, X≠Y, the line joining them belongs to S′. Suppose a family P of subspaces in (S,L) exists such that |P|≥2, every π∈P contains three noncollinear points and through three noncollinear points there is only one element of P. The triple (S,L,P) is called a planar space; the elements of P are called planes. Let (X,l) be a pair consisting of a point X∈S and a line l∈L with X∉l; let π(X,l) be the number of lines on X not meeting l and let H:={π(X,l):X∈S, l∈L, X∉l}. (S,L) is also called an H-semiaffine plane. Let n+1 be the maximum number of lines on a point; then the integer n is called the order of (S,L,P). In this paper the following result is proved: Let (S,L,P) be a finite planar space such that every plane of P is a {1,2}-semiaffine plane of order ≥5 and n+1 is the number of planes through every line of L. Then (S,L,P) is one of the following examples:(a) PG(3,n)∖π; (b) PG(3,n)∖{π∪X}, with X∉π; (c) PG(3,n)∖{π∪l}, with l⊄π; (d) PG(3,n)∖{π∪π′}, where X, l, π are a point, a line, and a plane of PG(3,n), respectively, and π′ is a plane of PG(3,n) different from π
Embedding semilinear and linear spaces in Grassmann spaces
No full textIn questo si articolo introduce la nozione di immersionedebole generalizzata per caratterizzare i sottospazi di G rassrnann Q (H)di spazi di Grassmann Q(K), con H sottocorpo del corpo K
OVOIDAL LINEAR SPACES
No full textAbstractIn this paper a suitable definition of ovoid in linear spaces is given and a characterization of the Galois space PG(3,q) as a finite linear space containing an ovoid is obtained
X-ray diffraction topographic study of twinning and growth of natural spinels
No full textTwo spinel twinned crystals coming from Pegu (Myanmar) have been studied by means of X-ray topographic methods,
optical microscopy and electron microprobe analysis.
Topographs, taken with conventional and synchrotron sources, showed the presence of a twin lamella in both samples as well as
the presence of cross-twinning in one of them. In particular, white beam synchrotron radiation source topography allowed to detect
the twin individuals, to identify and to locate the twin planes, and to determine spatial relationships and mutual orientations of the
twin components. By combining optical and topographic observations, an unusual morphology, flattened crosswise the twin planes
bounding the twin lamella, has been outlined in both samples and related to the growthmechanism.
Microchemical analyses showed that the twin individuals in each sample have nearly identical compositions,whereas the samples
differ mainly for the Mg and Zn contents. These observations suggest that they grew in similar and chemically closed microenvironments.
The results, taken as a whole, indicate that twinning and cross-twinning occurred since nucleation of the samples, and they mark
similar growth conditions
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