Showing papers on "Affine transformation published in 1973"

Quasihomogeneous affine algebraic varieties of the group sl(2)

Abstract: We classify up to G-isomorphism all normal affine irreducible quasihomogeneous (i.e. containing a dense orbit) varieties of the group G = SL(2) which are defined over an algebraically closed field of characteristic zero.

On $\mu$-Resolvable and Affine $\mu$-Resolvable Balanced Incomplete Block Designs

Abstract: The concept of resolvability and affine resolvability was generalized to $\mu$-resolvability and affine $\mu$-resolvability by Shrikhande and Raghavarao (1964). In this paper, a representation of parameters of an affine $\mu$-resolvable BIB design is given and necessary conditions for the existence of this design are derived. Some methods of constructing (affine) $\mu$-resolvable BIB designs are given and some inequalities for these designs are obtained. Finally, some information on the block structure of $\mu$-resolvable BIB designs is provided.

Positive linear extension operators for spaces of affine functions

Abstract: The following result is proved: letE be anF-space (that is, the space of all continuous affine functions defined on a compact universal cap van shing at zero) and letMχE be anM-ideal. Then, ifE/M is a π1 with positive defining projections, then there is a positive linear operator ϱ:E/M→E of norm one such that ϱ lifts the canonical mapE→E/M. In the proof, which heavily depends on work of Ando, we study ensor products of certain convex cones with compact bases, and we calculate the norm of a positive linear operator defined on a finite dimensional space with range in aF-space. Various corollaries are deduced for split faces of compact convex sets and for morphisms ofC*-algebras.

Fundamental groups of compact complete locally affine complex surfaces

Abstract: The fundamental group of a compact complete locally affine complex manifold of two complex dimensions is a solvable group which is a finite cyclic extension of a nilpotent or abelian group. Such a manifold has vanishing Euler characteristic and is finitely covered by a nilmanifold. A description of these manifolds and their fundamental groups is obtained in the course of the proofs of these facts.

Geometric Transformations III: Affine and Projective Transformations

Abstract: This book is the sequel to Geometric Transformations I and II, volumes 8 and 21 in this series, but can be studies independently. It is devoted to the treatment of affine and projective transformations of the plane these transformations include the congruencies and similarities investigated in the previous volumes. The simple text and the many problems are designed mainly to show how the principles of affine and projective geometry may be used to furnish relatively simple solutions of large classes of problems in elementary geometry, including some straight edge construction problems. In the Supplement, the reader is introduced to hyperbolic geometry. The latter part of the book consists of detailed solutions of the problems posed throughout the text.

The structure of $n$-uniform translation Hjelmslev planes

Abstract: Affine or projective Hjelmslev planes are called 1-uniform (also strongly 1-uniform) if they are finite customary affine or projective planes. If n > 1, an n-uniform affine or projective Hjelmslev plane is a (finite) Hjelmslev plane U with the following property: for each point P of ?, the substructure n1 p of all neighbor points of P is an (n 1)-uniform affine Hjelmslev plane. Associated with each point P is a sequence of neighborhoods lp C 2p C ... C np = 2X. For i k, ('i)j and (i k -).k are isomorphic. Then if 2I(i) denotes (i?)i_ 1(1), q... , I(n) is a periodic sequence of ordinary translation planes (all of order r) whose period is divisible by k. It is proved that if T 1 . 9 Tk is an arbitrary sequence of translation planes with common order and if n > k, then there exists a strongly n-uniform translation Hjelmslev plane U of width k such that I(i) T. for i < k. The proof of this result depends heavily upon a characterization of the class of strongly n-uniform translation Hjelmslev planes which is given in this paper. This characterization is given in terms of the constructibility of the n-uniform planes from the (n 1)-uniform planes by means of group congruences. Introduction. Hjelmslev planes are generalizations of customary affine and projective planes in which distinct lines may intersect in more than a single point. Throughout this paper, we will refer to a Hjelmslev plane as an H-plane. One calls a finite H-plane 1-uniform if it is a customary affine or projective H-plane: Received by the editors May 14, 1971. AMS (MOS) subject classifications (1970). Primary 05B25, 50D35; Secondary 05B30.

ISomorphismen verallgemeinerter Parallelstrukturen

Abstract: Incidencestructures with an equivalence relation on the set of blocks or lines, satisfying the euclidean axiom of parallelism, are called generalised parallel structures, if on each line are at least two points and if through two different points passes at most one line. In this paper we give a coordinatization for a class of generalised parallel structures. Isomorphisms of desarguesian affine spaces induce in a well known manner regular semilinear mappings of the corresponding vector spaces. We prove an analogous theorem for generalised parallel structures and the corresponding algebraic structures.

Eine Kennzeichnung der schwach affinen Räume über Skalarensystemen

Abstract: Weak affine spaces have been introduced in [6] and [7] by E. SPERNER. They can be algebraically described by quasimodules. in [8] E. SPERNER constructed quasimodules by nearfields. In [9] and [10] he used more general algebraic structures for this construction and in [5] the author described a generalisation of this method. In this note we give a geometric and algebraic characterization of those weak affine spaces which can be constructed in this way.

A characterization of projective and affine 3-schemes /

Abstract: 3. When a map, drawing or chart, etc., was part of the material being photographed the photographer followed a definite method in "sectioning" the material. It is customary to begin photoing at the upper left hand corner of a large sheet and to continue photoing from left to right in equal sections with a small overlap. If necessary, sectioning is continued again — beginning below the first row and continuing on until complete.

Geometric aspects in digital analysis of Multi-Spectral Scanner (MSS) data

Abstract: Present automated systems of interpretation which apply pattern recognition techniques on MSS data do not fully consider the geometry of the acquisition system. In an effort to improve the usefulness of the MSS data when digitally treated, geometric aspects are analyzed and discussed. Attempts to correct for scanner instabilities in position and orientation by affine and polynomial transformations, as well as by modified collinearity equations are described. Methods of accounting for panoramic and relief effects are also discussed. It is anticipated that reliable area as well as position determinations can be accomplished during the process of automatic interpretation. A concept for a unified approach to the treatment of remote sensing data, both metric and nonmetric is presented.

Formulae for estimating extreme changes of lengths in spatial affine transformation

Abstract: Formulae (27) and (28) which make it possible to estimate the minimum and maximum value of the deformation in length in affine transformation in space have been derived. Both values are determined by means of the elements of the given transformation matrixA without having to form the productAA T, or compute the corresponding eigenvalues explicitly. The derived formulae hold true under the assumption that both extreme values do not differ from each other too much.