Showing papers on "Affine transformation published in 1977"

Higher Order Contact of Submanifolds of Homogeneous Spaces

Abstract: The general theory.- Surfaces in R 3 under the Euclidean group of proper motions.- Curves in real Grassmannians.- Holomorphic curves in complex projective space.- Holomorphic curves in complex Grassmannians.- Special affine surface theory.

Tensor Geometry: The Geometric Viewpoint and Its Uses

Abstract: 0. Fundamental Not(at)ions.- I. Real Vector Spaces.- II. Affine Spaces.- III. Dual Spaces.- IV. Metric Vector Spaces.- V. Tensors and Multilinear Forms.- VI Topological Vector Spaces.- VII. Differentiation and Manifolds.- VIII. Connections and Covariant Differentiation.- IX. Geodesics.- X. Curvature.- XI. Special Relativity.- XII. General Relativity.- Index of Notations.

Deformations of cohen-macaulay schemes of codimension 2 and non-singular deformations of space curves.

Abstract: The following work deals with the deformations of embedded affine schemes of codimension 2, which locally have a resolution of length 2. The cases of immediate interest are curves in 3-space and 0-dimensional schemes in the plane. It is first shown that such a scheme X has a global resolution of length 2. Therefore, by a theorem of Burch, the functions defining the ideal of X can be obtained as the maximal minors of a matrix whose columns generate all the relations among these functions. All flat deformations of X can be obtained simply by deforming this matrix, and this permits the construction of the versal deformation space of X. Finally, for X of dimension 3 or less one can construct non-singular deformations of X by taking a parameter space sufficiently large to permit one to change the constant and linear terms of each entry in the matrix. For X of dimension 4, an example is given in XXX [11] in which the scheme not only has no non-singular deformations, but in fact has no non-isomorphic deformations at all. A brief review of the previous literature will help place these results in perspective. It has long been known, by Bertini's theorem, that the generic deformation of a scheme of codimension 1 is non-singular. As a consequence of the work of Fogarty [5], it was also known that every point, or rather, 0-dimensional scheme in the plane has non-singular deformations; Briancon and Galligo [3] give an explicit construction for such a deformation, splitting the scheme into distinct simple points. This led mathematicians interested in algebraic curves to ask if the generic deformation of a space curve is also non-singular, the question which is settled in this paper. Further direct extension of these results in the case of curves is impossible, since the work of Iarrobina [4] permits the construction of a non-reduced curve in affine 4-space which has no non-singular deformations; however, for reduced curves the question is still open as of this writing.

A Landsat digital image rectification system

Abstract: DIRS is a digital image rectification system for the geometric correction of Landsat multispectral scanner digital image data. DIRS removes spatial distortions from the data and brings it into conformance with the universal transverse mercator (UTM) map projection. Scene data in the form of landmarks or ground control points (GCP's) are used to drive the geometric correction algorithms. The system offers extensive capabilities for “shade printing” to aid in the determination of GCP's. Affine, two-dimensional least squares polynominal and spacecraft attitude modeling techniques for geometric mapping are provided. Entire scenes or selected quadrilaterals may be rectified. Resampling through nearest neighbor or cubic convolution at user designated intervals is available. The output products are in the form of digital tape in band-interleaved, single-band, or CCT format in a rotated UTM projection. The system was designed and implemented on large-scale IBM 360 computers with at least 300–500 kbytes of memory for user application programs and five 9-track tapes plus direct access storage.

Automorphisms of affine surfaces. ii

Abstract: Affine surfaces X completed by an irreducible rational curve C are studied. The integer m = (C2) is an invariant of X. It is shown that the set of all such surfaces with fixed invariant m is described in terms of orbits of a group action on the space of "tails"; moreover, the automorphism group Aut(X) is expressed by the stabilizers of the action. Explicit formulas for generators of the group Aut(X) are given for m ≤ 5. In particular, it is shown that in zero characteristic the invariant m uniquely determines the surface X; in the general case this is not so.Bibliography: 11 titles.

Pattern Matching Under Affine Transformations

Abstract: In the following we consider the action of the group of affine transformations on a class of patterns representable by continuous functions with compact support. It is first shown how to accomplish a reduction of the action of the affine group to that of the orthogonal group. In the two-dimensional case, it is shown how to find the particular orthogonal transformation necessary to complete a pattern match. Finally invariants under the orthogonal group are presented. Examples are given which present typical results obtained by implementing the techniques via a digital-optical scanner and minicomputer software.

Quasi-affine transforms of subnormal operators.

Abstract: For an operator T which is a quasi-affine transform of a subnormal operator S, we show that: (1) if 5* has no point spectrum and /: λ H> (T λ )~x is defined on an open set Π, then there is a dense subset fl(, of Ω such that /1 Ωo is analytic; and (2) if Σ is a spectral set of T and Q is a peak set of R (Σ), then the spectral manifold XT(Q) is a reducing subspace of T and Q is a spectral set of T |X T (Q).

Affine fields and the operator formulation of augmented scalar fields

Abstract: Affine fields, which can be used to replace the usual canonical fields, and which induce strictly homogeneous transformations of the underlying configuration space, are shown to be relevant in the operator formulation of augmented scalar field models. A characterization of the Hamiltonian and other basic generators by means of the expectation functional of the square of the field replaces the standard one based on the expectation functional of the field. Connection with previous work on augmented models is established through the form of the equation of motion for the field.

Affine open orbits, reductive isotropy groups, and dominant gradient morphisms; a theorem of Mikio Sato

Abstract: An algebraic proof is given for a theorem of M. Sato. The theorem gives criteria for the open orbit in a prehomogeneous vector space under a reductive group to be an affine variety. The following conditions are equivalent: 1. 0(G) the open orbit is an affine variety. 2. Gz the isotropy subgroup of X in O(G) is reductive. 3. There exists a semi-invariant form P of degree r ^ 2 such that gradP: V->V* is a dominant morphism of affine varieties.

Address designation circuit

Abstract: PURPOSE:To calculate the designation of video element address in high speed, based on the raster scanning and the equation of affine conversion in digital picture processing, and further, to efficiently execute the access to the video element in the vicinity without destructing the value of present address.

Some Aspects of Mann's Iterative Method for Approximating Fixed Points

Abstract: Some connections between summability theory and Mann's iterative process for affine mappings are exhibited and some questions are posed. Results are given for linear operator equations of the first and second kind using a special case of Mann's process and an iterative method for generalized solutions of singular linear operator equations of the first kind is studied.