Showing papers on "Pencil (mathematics) published in 1986"

Finite projective spaces of three dimensions

Abstract: This self-contained and highly detailed study considers projective spaces of three dimensions over a finite field It is the second and core volume of a three-volume treatise on finite projective spaces, the first volume being Projective Geometrics Over Finite Fields (OUP, 1979) The present work restricts itself to three dimensions, and considers both topics which are analogous of geometry over the complex numbers and topics that arise out of the modern theory of incidence structures The book also examines properties of four and five dimensions, fundamental applications to translation planes, simple groups, and coding theory

Projective geometry of elliptic curves

Abstract: © Société mathématique de France, 1986, tous droits réservés. L’accès aux archives de la collection « Astérisque » (http://smf4.emath.fr/ Publications/Asterisque/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/conditions). 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.

The pencil ( sE–A ) and controllability-observability for generalized linear systems: a geometric approach

Abstract: In the first part of the paper we study the pencil $(sE - A)$ by using some geometric concepts given by Bernhard [SIAM J. Control Optim., 20 (1982), pp. 612–6331 and some new ones which are introduced here. Such concepts are then used to obtain an alternative characterization for the finite and infinite-zero structure of the pencil and to construct a polynomial basis for ker $(sE - A)$. Necessary and sufficient conditions for the rows or/and the columns of the pencil to be linearly independent over the ring of the polynomials are also given. The main geometric properties of a regular pencil are presented, including the identification of the subspace in which the impulsive response of the autonomous generalized linear system $E\dot x = Ax$ takes place. In the second part we consider the generalized linear system $E\dot x = Ax + Bu;y = Cx$ and we give necessary and sufficient conditions for the infinite-zeros of the regular pencil $(sE - A)$ to be controllable and observable.

A Generalized Approach to Direction Finding

Abstract: Assuming d sources and m sensors, a generalized formulation is proposed for the direction of arrival estimation problem. It is shown that several different techniques are special cases of the generalized approach. The techniques differ depending upon the manner in which either 1) the measured data is processed or 2) the angular information is extracted from the resulting equations. In the generalized formulation a matrix pencil M - ?N is constructed. In general, the rank of the matrix pencil is d. However, for particular values of ?, the rank is decreased by 1. The values of ? for which this happens contain the information needed to estimate the angles of arrival. The pencil theorem establishes the relationship between these values of ? and some functional form f(? i ) generated by the operators applied to the measurements.

Projective manifolds whose topology is strongly reflected in their hyperplane sections

Abstract: Let ℒk be the class of complex algebraic k-folds X ⊂ ℙn such that Hi(X, ℚ) ≅ Hi(H, ℚ) for i≤k−1, H a general hyperplane section. Topological characterizations of -k and several other classes of projective manifolds are given. Moreover, classes ℒ2, ℒ3, ℒ5 are completely described and a partial description of ℒ4 is given. A key role is played by projective bundles.

On hyperbolic embedding of complements of divisors and the limiting behavior of the kobayashi-royden metric

Abstract: In the following three cases criteria are found for complements of divisors in compact complex manifolds to be hyperbolically embedded in the sense of Kobayashi: for divisors with normal crossings, for arbitrary divisors in complex surfaces, and for unions of hyperplanes in projective space. A criterion is given for two-dimensional polynomial polyhedra to be hyperbolically embedded, and Iitaka's conjecture about conditions for hyperbolicity of the complement of a set of projective lines is confirmed. Upper semicontinuity is proved for the Kobayashi-Royden pseudometrics and Kobayashi-Eisenman pseudovolumes of a family of complex manifolds containing degenerate fibers, and conditions are given under which the hyperbolic length (volume) on the smooth part of a degenerate fiber is the limit of the hyperbolic length (volume) on the nonsingular fibers.Bibliography: 28 titles.

Simultaneous estimation of state variables and parameters for multivariable linear systems with singular pencil models

Abstract: A new algorithm is presented for the simultaneous estimation of the state variables, system parameters, and noise parameters of linear multivariable systems using a canonical singular pencil model. The proposed algorithm is computationally efficient and is easy to implement. Convergence analysis and simulation results are also given.

On the projectivity of B-ovals

Abstract: In this paper, a method of coordinatizing a B-oval is introduced which gives rise to a ternary ring structure called anoval ternary ring (or OTR). By examining these OTR's, we can deduce sufficient conditions for a B-oval to be projective. The connections between OTR's and the Hall ternary rings, which arise from the coordinatization of a projective plane, are also examined.

Method for baking wooden board with reagents for making pencils

Abstract: This invention may be used in the baking process in pencil making. Paraffin and rosin are placed in a steel open vessel in a ratio of 3:2. After molten by heat the pencil wooden boards are put into it, heated to 180-220 deg.C and then taken out. This method can be used not only to treat common pencil boards, such as linden, but also to treat any wooden boards used for making pencils, especially those from masson pine timber of less than 30 years of age. This method extends the resource of pencil timber and the baked boards are soft, smooth and easy to cut on sharpening the pencil

On bundles of collineations and null-systems of projective spaces

Abstract: The idea of the invariants of bundles of collineations and null-systems of projective spaces is introduced. The process of recovering the bundles from the invariants is described. Bibliography: 8 titles.

Subpopulation differences in equating computerized adaptive and paper-and-pencil versions of the asvab

Abstract: Abstract : Computerized adaptive test (CAT) and paper-and-pencil (PP) ASVAB scores are equated in several subpopulations to determine if racial minorities, females, nonhigh school graduates, or those lacking experience using computers would be at a disadvantage if CAT rather that PP scores were used for selection. Equating is generally independent of population group. To maintain continuity of enlistment standards, scores on the CAT and the PP version of the test must be interchangeable, and the proportion of examinees who qualify for enlistment should be the same for both versions of the test. If CAT scores do not equate to PP scores in a similar manner for males and females, for example, then one of these subpopulations could be at a disadvantage.

Pascalian Configurations in Projective Planes

Abstract: Publisher Summary If Ω is a projective oval of a projective plane π and if P (Ω) be the figure formed by all of the secants or tangents to omega, which are pascalian lines with respect to omega, then the figures P (Ω) are called “Ω-pascalian configurations” of π. The problem of determining the configuration P (Ω) have been introduced, and by using these configurations, it is possible to produce an interesting classification for the projective ovals. If P (Ω) is a Ω-pascalian configuration of one of the four known projective plane of order 4: Desargues, Hughes, and two Hall planes, then P (Ω) coincides with one of the specific sets outlined in the chapter. Such sets are defined as all the tangents and all the secants, the empty set, and all the tangents and all the secants through a unique point. There are projective ovals having non-exterior pascalian lines in non-desarguesian planes, but in this setting, the problem is very far from being resolved. At present, two other Ω-pascalian configurations have been found.

A Free Extension Process Yielding a Projective Geometry

Abstract: Summary Presented is a free extension process, mainly based on the configuration of Veblen and yielding a projective geometry.

A general approach to reducing a regular linear pencil to a pencil of quasitriangular form

Abstract: A general approach to constructing the algorithms for solving a spectral problem for a regular pencil A − λB of matrices by reducing it to a pencil of quasitriangular form with diagonal boxes which have eigenvalues equal in absolute value to that of the initial pencil is discussed A theoretical justification of the approach proposed, and examples of constructing algorithms are given