Results 251 to 260 of about 401,072 (287)
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Projective and Affine Quadrics
2020Dupin ring cyclide with a three-web consisting of Villarceau circles of both kinds and of isogonal trajectories of the circular curvature lines. In a conformal model of elliptic geometry, the cyclide represents a Clifford surface, where each kind of Villarceau circles is a family of Clifford parallels, while the isogonal trajectories play the role of ...
Boris Odehnal +2 more
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2013
In Definitions 5.2.1 and 5.1.1, projective and affine spaces were introduced by means of axioms, and in Propositions 5.2.2 and 5.1.3, the spaces ℙ(V) and \(\mathbb {A}(V)\), where V is a vector space, were shown to be examples. In this chapter we show that by and large there are no further examples.
Francis Buekenhout, Arjeh M. Cohen
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In Definitions 5.2.1 and 5.1.1, projective and affine spaces were introduced by means of axioms, and in Propositions 5.2.2 and 5.1.3, the spaces ℙ(V) and \(\mathbb {A}(V)\), where V is a vector space, were shown to be examples. In this chapter we show that by and large there are no further examples.
Francis Buekenhout, Arjeh M. Cohen
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Affine and Projective Geometry
1977In this chapter we shall introduce two different (but closely related) geometrical languages. The first of these, the language of affine geometry, is the one which appeals most closely to our intuitive ideas of geometry. In this language the subspaces of a vector space of dimensions 0, 1 and 2 are called “points”, “lines” and “planes”, respectively ...
K. W. Gruenberg, A. J. Weir
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2020
This chapter gives fundamental results on finite affine and projective planes. It provides detailed proofs on various counting results concerning these planes such as the number of points, lines, points on a line, and lines through a point. It describes the canonical relation between affine planes and mutually orthogonal Latin squares.
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This chapter gives fundamental results on finite affine and projective planes. It provides detailed proofs on various counting results concerning these planes such as the number of points, lines, points on a line, and lines through a point. It describes the canonical relation between affine planes and mutually orthogonal Latin squares.
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Affine and Projective Transformations
2010In addition to isometries, there are two kinds of mappings that preserve lines: affine (Section 3.1) and projective (Section 3.2) transformations. Affine transformations f of \({\mathbb{R}}^{n}\) have the following property: If l is a line then f(l) is also a line, and if l ∥ k then f(l) ∥ f(k). A line in \({\mathbb{R}}^{n}\) means a set of the form {r
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2015
The normalized least-mean-squares (NLMS) algorithm has a problem that the convergence slows down for correlated input signals. The reason for this phenomenon is explained by looking at the algorithm from a geometrical point of view. This observation motivates the affine projection algorithm (APA) as a natural generalization of the NLMS algorithm.
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The normalized least-mean-squares (NLMS) algorithm has a problem that the convergence slows down for correlated input signals. The reason for this phenomenon is explained by looking at the algorithm from a geometrical point of view. This observation motivates the affine projection algorithm (APA) as a natural generalization of the NLMS algorithm.
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Switching Mechanism on the Order of Affine Projection Algorithm
Electronics (Switzerland), 2022Jindong Xu, Shifeng Ou
exaly
Projective and Affine Geometries
2011The present chapter deals mainly with projective and affine geometries. In Sect. 2, the notions pregeometry and geometry are introduced. In Sects. 3–6, affine and projective spaces are discussed in detail. In particular, the affine and projective spaces are endowed with a structure of subspaces, and the relation between affine and projective spaces is ...
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2012
The historical roots of algebraic geometry lie in the study of curved lines in the plane, or as we would prefer to say today, planar curves. The treatment of modern algebraic geometry offered in the present book takes a starting point which is more general and at the same time more restricted: More general in the sense that we will study geometric ...
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The historical roots of algebraic geometry lie in the study of curved lines in the plane, or as we would prefer to say today, planar curves. The treatment of modern algebraic geometry offered in the present book takes a starting point which is more general and at the same time more restricted: More general in the sense that we will study geometric ...
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