Showing papers on "Affine transformation published in 1984"

An embedding theorem of complete Kähler manifolds of positive bisectional curvature onto affine algebraic varieties

Abstract: We prove that a complete noncompact Kahler manifold X of positive bisectional curvature satisfying suitable growth conditions can be biholomorphicaUy embedded onto an affine algebraic variety. In case X is a complex surface of positive Riemannian sectional curvature satisfying the same growth conditions, we show that X is biholomorphic toC. The following conjectures concerning the complex structure of noncompact complete Kahler manifolds of positive curvature, formulated by GREENE and Wu [9], Siu [22] and Wu [32] are central to the study of such manifolds.

The radiance obstruction and parallel forms on affine manifolds

Abstract: A manifold M is affine if it is endowed with a distinguished atlas whose coordinate changes are locally affine When they are locally linear M is called radiant The obstruction to radiance is a one-dimensional class CM with coefficients in the flat tangent bundle of M Exterior powers of CM give information on the existence of parallel forms on M, especially parallel volume forms As applications, various kinds of restrictions are found on the holonomy and topology of compact affine manifolds Introduction An affine manifold M is a manifold with a distinguished maximal atlas of charts, all of whose coordinate changes are locally affine On such a manifold there is an intrinsic notion of a parallel tensor: one whose components in any affine chart are constants More generally there is the notion of a polynomial tensor field of given degree In 1962, L Markus conjectured in [Mk] that a compact orientable affine n-dimensional manifold has parallel volume form if and only if it is complete (meaning that its universal covering is affinely isomorphic to Euclidean n-space Rn) The problem of constructing a parallel volume form determines an n-dimensional twisted real cohomology class originally studied by J Smillie [Sm2] In this paper we express this class as the nth exterior power of a twisted one-dimensional real class which we call the radiance obstruction CM By computing CM in various cohomology theories-Cech, singular, de Rham, and others-we are able to exploit CM in several ways to yield more information on the structure of affine manifolds Some of these results will appear in a subsequent paper [GH3] The basic tool used is a formula, proved in ?26, which expresses the cohomology class of a parallel exterior k-form in terms of the k th exterior power of the radiance obstruction, Akcvf MIn ?27 the special case of a parallel volume form on a compact n-dimensional manifold M is examined: the existence of such a form implies that AnCM # 0 In ?28 we show that the affine holonomy group F of such an M cannot preserve a proper affine subspace (In [GH3] this result will be improved by showing that r preserves no proper semialgebraic subset of Rn) In ?210 we show that there tend to be plenty of parallel forms on a compact affine manifold with nilpotent affine holonomy Received by the editors May 26, 1983 1980 Mathematics Subject Classification Primary 57R99, 53C05; Secondary 53C10, 55R25 4c1984 Amencan Mathematical Society 0002-9947/84 $100 + $25 per page

Principal bundles on the affine line

Abstract: We prove that any principal bundle on the affine line over a perfect field with a reductive group as structure group comes from the base field by base change.

Data broadcasting in linearly scheduled array processors

Abstract: A major problem in executing algorithms in array processors is the implementation of broadcasts without unnecessary speed-up factor degradation. We discuss when and how broadcasts can be eliminated or reduced to easily implementable sequences of reduced local broadcasts. Algorithms are modelled as a structured set of indexed computations which operate on variables associated with a referencing or indexing function. The discussion is restricted to variables with linear indexing functions and to algorithms linearly scheduled for execution in array processors. Linear indexing functions are represented as affine matricial functions of the index set of the algorithm. The linear part of such representation is a coefficient matrix denoted the indexing matrix. Linear schedules are defined as linear time-space allocation functions mapping the computations of an algorithm into time and processors. We discuss necessary and sufficient conditions for the occurrence of broadcasts in a linearly scheduled algorithm. Necessary and sufficient conditions and constructive criteria are given for selecting linear schedules for which all broadcasts are eliminated or reduced to sequences of small local broadcasts.

Controllability Properties of Affine Systems

Abstract: This paper deals with transitivity (controllability) of affine families of vector fields on a finite dimensional vector space V. In particular we focus on affine families whose corresponding families of linear fields are transitive on $V - \{ 0\} $, and which in addition have no fixed points in V. We show that such families are necessarily transitive on V, and we also show that they remain transitive under small perturbations. In general, however, affine families need not remain transitive under small perturbations—for example, small affine perturbations of transitive linear systems are not necessarily transitive. Since any affine system $\mathcal{F}$ naturally defines a system $\mathcal{F}_r $ of right-invariant vector fields on the semi-direct product of V with $GL(V)$ we also investigate transitivity properties $\mathcal{F}_r $. Our result is that if $\mathcal{F}$ is an affine family satisfying the preceding conditions then $\mathcal{F}_r $ generates the full Lie algebra on the semi-direct product.

Affine Incentive Schemes for Stochastic Systems with Dynamic Information

Abstract: In this paper we study the derivation of optimal incentive schemes in two-agent stochastic decision problems with a hierarchical decision structure, in a general Hilbert space setting. The agent at the top of the hierarchy is assumed to have access to the value of other agent’s decision variable as well as to some common and private information, and the second agent’s loss function is taken to be strictly convex. In this set-up, it is shown that there exists, under some fairly mild structural restrictions, an optimal incentive policy for the first agent, which is affine in the dynamic information and generally nonlinear in the static (common and private) information. Certain special cases are also discussed and a numerical example is solved.

Real closed spaces

Abstract: ] on M. Then 0 can be reconstructed from se by certain types of ring extensions. The same construction can be done starting from any ring A and any constructible subset K of the real spectrum X(A) of A. In this way one obtains locally ringed spaces which are called affine real closed spaces (real closed since these spaces can be viewed as generalizing real closed fields). A real closed space is a locally ringed space which has an open cover by affine real closed spaces. In particular, to any sa space (M, (9) with an open affine cover M = \JM

Strong infinitesimal linearity, with applications to strong difference and affine connections

Abstract: © Andrée C. Ehresmann et les auteurs, 1984, tous droits réservés. L’accès aux archives de la revue « Cahiers de topologie et géométrie différentielle catégoriques » implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.

Cancellation over affine varieties

Abstract: It is proved that if X is a smooth affine curve over a field F of characteristic ≠l, then the group SK1(X)/l SK1(X) is isomorphic to a subgroup of the etale cohomology group H et 3 (X,Μ e Ф2 ) and if F is algebraically closed, then SK1(X) is a uniquely divisible group. The following cancellation theorem is obtained from results about SK1 for curves: If X is a normal affine variety of dimension n over a field F, and if char F > n and C.d.e(F)⩽1 for any prime l>/n then any stably trivial vector bundle of rank n over X is trivial.

Ebenen mit Kongruenz

Abstract: Euclidean planes are characterized as affine planes with a congruence relation on the set of the pairs of points. Furthermore we study the consequences of the congruence axioms for other incidence structures e.g. finite or half ordered ones, and discuss the question when the 3-reflection theorem is valid.

Homogeneous spaces with integrable g-invariant hamiltonian flows

Abstract: Examples are constructed of homogeneous spaces M with semisimple groups of motions G for which all G-invariant Hamiltonian systems on T*M are integrable. Particular examples of such include affine symmetric spaces. Bibliography: 11 titles.

On the projective invariance of shaky structures in euclidean space

Abstract: Let there be given a spatial or plane system of rigid rods having freely movable connections at their endpoints, the knots of the system. Such a framework is called shaky if there exists a nonisometric infinitesimal deformation of its knots which preserves the lengths of the rods. In this paper it is shown that shakiness is preserved under affine and projective transformations The method of proof gives an easy interpretation of this invariance property and leads to the construction of new shaky frameworks in space from plane ones. Furthermore it shows that there is no theoretical reason to restrict the investigations to low-dimensional ambient spaces.

Affine Domains of Finite Gelfand‐Kirillov Dimension which are Right, but not Left, Noetherian

Abstract: Examples of noncommutative domains which are right, but not left, noetherian have long been known, the standard one being a skew polynomial ring of the form F\\t;

Quantum gravity in the Eddington purely affine picture

Abstract: It was shown by Kijowski and Tulczjew that pure gravity with a cosmological constant can be obtained by a covariant Legendre transformation of a purely affine Lagrangian "in the manner of Eddington" constructed from a symmetric linear connection. In this paper I prove by explicit calculations that the Eddington Lagrangian is equivalent, in the sense which gives the same field equations, to a polynomial effective Lagrangian which turns out to be power-counting renormalizable. Then a formal proof of the unitarity of this theory is stated in the Kugo-Ojima formalism on the basis of the existence of two local Becchi-Rouet-Stora symmetries. These supertransformations are related to the algebra of the diffeomorphisms of the space-time, as well as to that of the volume-preserving space-time transformations which are not fixed by the gauge fixing used for the diffeomorphism group itself. Furthermore, I find that in the purely affine picture quantum gravity exhibits an infrared freedom. Since now the self-coupling constant is given by the cosmological constant, such a property could explain the observed almost zero value of the cosmological term at very large distances, i.e., to very low energies.

On the étale cohomology of hensel rings

Abstract: We prove that if (A,a) is an Eensel couple and G is an affine, smooth commutative group scheme over A, then for all r ≥ 1.

State-space equivalence of an affine non-linear system with outputs to a minimal linear system

Abstract: This paper studies the state-space equivalence of affine non-linear control systems with outputs to linear systems with outputs. Necessary and sufficient conditions are derived for performing a local diffeomorphism on the state space such that in these new coordinates the complete system becomes a minimal linear one.

Extended dual affine planes

Abstract: We study a class of diagram geometries, achieve a characterization of extended dual affine planes, and embed extended dual affine planes in extended projective planes. The geometries studied are rank 3 diagram geometries such that the residue of a point is a dual net, and the residue of a plane is linear; the dual of such a geometry has partitions on lines and planes which are reminiscent of parallelism of lines and planes of an affine 3-space. Examples of these geometries (some in dual form) include extended dual affine planes, Laguerre planes, 3-nets, and orthogonal arrays of strength 3. Theorem: Any such finite geometry satisfying Buekenhout's intersection property, and such that any two points are coplanar, is an extended dual affine plane (and has order 2, 4, or 10). Theorem: This geometry may be embedded in an extended projective plane of the same order.

On the Representative Domain

Abstract: Professor Stefan Bergman [1] introduced the idea of Reprasentantenbereich of a bounded domain Open image in new window in ℂn. However the strict definition of a representative domain is not very clear as noted in [2]. It seems that he called the image f( Open image in new window ) of the mapping f:

(k, 1) Exponential Transformation Models

Abstract: An investigation is presented of the class of exponential transformation models, for which the affine transformation group acting on the parameter space is one-dimensional. Such a group is characterized by a fixed matrix, and this is used to express the derivatives of the log-likelihood function. It is discussed how different algebraic properties of such matrices give rise to different statistical models. In the case where the minimal canonical statistic is of dimension two it is shown that the maximum likelihood estimate of the group parameter exists uniquely and that it is the unique solution to the likelihood equation, provided the group is noncompact. Furthermore, in this case a complete list is developed of all the possible types of conditional distribution given the maximal invariant affine ancillary.