Showing papers on "Point (geometry) published in 1979"

So What’s The Point?

Abstract: Although much work has been done recently dealing with how people structure the stories they tell, the question of what they tell stories about has remained not only unanswered, but largely unasked. In this paper, I propose that what stories can really be about is, to a very significant extent, culturally constrained: stories, whether fictional or non-fictional, formal and oft-told, or spontaneously generated, can have as their point only culturally salient material generally agreed upon by members of the producer's culture to be self-evidently important and true. Furthermore, the point of a story should not be taken as a fixed formal aspect of the story as originally told, but rather may change in the course of the narration and surrounding conversation as speaker and audience negotiate for what the story will be agreed upon to have been about. In the following paper, we will ask the question, \"What do Americans tell stories about?\", and outline some of the matters which must be dealt with if we are to answer that question in a meaningful manner. A methodology will be presented for abstracting out culturally salient material from oral texts, and a case made that 'negotiating the point of a story' is one aspect of American linguistic behavior. The question \"What do people tell stories about?\" appears to be somewhat pointless if viewed as a special case of the larger question, \"What can people use language to talk about?\", since linguists generally agree that a competent and knowledgeable speaker can discuss any subject in any human language. However, if we see this question about stories as part of the question, \"What is worth

Models of spatial processes : an approach to the study of point, line, and area patterns

Abstract: 1. An Introduction to spatial processes 2. Point patterns: Poisson process model 3. Point patterns: mixed Poisson process models 4. Truly contagious models, disturbed lattices and information theory 5. Line patterns 6. Area patterns: the cell model 7. Area patterns: the Johnson-Mehl model 8. Area patterns: clumping models.

A restart algorithm for computing fixed points without an extra dimension

Abstract: An algorithm to compute a fixed point of an upper semicontinuous point to set mapping using a simplicial subdivision is introduced. The new element of the algorithm is that for a given grid it does not start with a subsimplex but with one (arbitrary) point only; the algorithm will terminate always with a subsimplex. This subsimplex yields an approximation of a fixed point and provides the starting point for a finer grid. Some numerical results suggest that this algorithm converges more rapidly than the known algorithms. Moreover, it is very simple to implement the algorithm on the computer.

Annex 1 The continuities of the point-to-set maps, definitions and equivalences

Abstract: In the theory of set-valued mapping, two kinds of continuity have been developed. For each of them, very closely related definitions have been given using on one hand (Hill (1927), Kuratowsky and Hahn (1932), Bouligand and Blanc (1933)) ordering inclusion properties in terms of limit of sequences of sets and on the other hand (Hahn (1932), Choquet (1948), Berge (1959)) topological properties of the "inverse image". The connexions between these definitions are given in the following. All throughout the paper, we consider a map F from X into ~(Y), the set of subsets of Y, where X, Y are Hausdorff spaces. Particular assumptions (for example, first countability) will be specified when necessary; it is to be noticed that none of the assumptions that are given, can be deleted. The properties are presented without proofs, the majority of the results being stated in the literature (for complete proofs and counter examples see [2]). ~ the family of the neighbourhoods of x ~ X, N' C N will always denote an infinite subset of N, {x.} • a sequence of points in X ({x.}N, an extracted subsequence) [A] ~ " [B] means: (for the meaning of such a specified assumption, see the footnotes to Diagrams 1 and 2). 1. Limits of sets (Hahn and Kuratowski) Let {A.}N be a given sequence of subsets of a topological space Y. limN A. denotes the lower limit of the sequence {A.}N, i.e. the subset of Y (possibly empty) that consists of points x satisfying

Compensation for Viewing Point in the Perception of Pictured Space.

Abstract: : Graphic displays can provide a geometrically accurate representation of space if and only if they are viewed from the correct center of projection. Viewing from other locations results in distortions of the virtual space specified by the display. Despite the ubiquity of such distortions they are seldom noticed; a fact that has lead some to propose that observers can perceptually discount or compensate for these transformations of virtual space. The present report describes the geometric basis of representationality, and provides a specification of the distortions of virtual space in terms of the geometry of linear perspective. The results of several studies are summarized, and it is suggested that pictorial constancy is based on both an active and a passive compensation process. The active process discounts the distortion by an amount equal to that caused by the discrepancy between the actual viewing point and an assumed correct viewing point. The second aspect of constancy appears to be based on familiarity, and on assumptions regarding the nature of the object depicted. (Author)

A Note on a Theorem of Ky Fan

Abstract: Fan ([2, Theorem 2]) has proved the following theorem: Let K be a nonempty compact convex set in a normed linear space X. For any continuous map f from K into X, there exists a point u∈K such that In this note, we prove that the above theorem is true for a continuous condensing map defined on a closed ball in a Banach space. We also prove that it is true for a continuous condensing map defined on a closed convex bounded subset of a Hilbert space.

Linear feedback via polynomial models

Abstract: This paper is an attempt to study state feedback from the module theoretic point of view. It uses the theory of polynomial models to study state feedback in a way which emphasizes both the module theoretic aspects as well as the state space point of view.

A comparative study of several general convergence conditions for algorithms modeled by point-to-set maps

Abstract: A general structure is established that allows the comparison of various conditions that are sufficient for convergence of algorithms that can be modeled as the recursive application of a point-to-set map. This structure is used to compare several earlier sufficient conditions as well as three new sets of sufficient conditions. One of the new sets of conditions is shown to be the most general in that all other sets of conditions imply this new set. This new set of conditions is also extended to the case where the point-to-set map can change from iteration to iteration.

Feedback controlled geometry registration system for radiographs

Abstract: A system for reproducibly aiming an X-ray source array to provide substantial registration of exposure geometry through an organ or a portion of tissue from one examination to the next. The system derives functions or signals based on computer controlled X-ray source point geometries to create multiple images produced from known positions via a detector array which feeds this information to a computer image storage system and which provides for comparison of the detected signals with reference signals originally stored in a memory; the comparison yields correction signals which act to shift the X-ray raster toward restoration of the original effective geometry. Thus, the X-ray sources are coupled to the detector array through a feedback loop circuit including a computer which, by sequentially activating each X-ray point source and noting the resulting functions generated by the detector array, can compare the results with the stored functions and revise the working geometry to simulate that of the original geometry from which the stored reference functions were obtained. The computer also activates a visual display device providing a crude X-ray scan through the tissue of interest, which can be used to create low resolution tomograms of the irradiated structures.

An efficient approach for computing the geometrical optics field reflected from a numerically specified surface

Abstract: In the conventional geometrical optical analysis of smooth surfaces it is customary, to search for a specular point on the surface of the scatterer for each given combination of source and observation points. In many situations only a numerical description of the surface is available rather than an analytical expression which lends itself more readily to a determination of the specular point. The numerically prescribed form for the surface may be locally interpolated each time a specular point is to be calculated. An alternative approach is investigated that circumvents the step of deriving the specular point and obtains the scattered field in a more direct manner. Basically, the method begins by computing the reflected rays off the surface at the points where their coordinates, as well as the partial derivatives (or equivalently, the direction of the normal), are numerically specified. Next, a cluster of three adjacent rays are chosen to define a "mean ray" and the divergence factor associated with this mean ray. Finally, the amplitude, phase, and vector direction of the reflected field at a given observation point are derived by associating this point with the nearest mean ray and determining its position relative to such a ray.

Bounds on the Optimal Location to the Weber Problem Under Conditions of Uncertainty

Abstract: Optimal and Heuristic bounds are given for the optimal location to the Weber problem when the locations of demand points are not deterministic but may be within given circles. Rectilinear, Euclidean and square Euclidean types of distance measure are discussed. The exact shape of all possible optimal points is given in the rectilinear and square Euclidean cases. A heuristic method for the computation of the region of possible optimal points is developed in the case of Euclidean distance problem. The maximal distance between a possible optimal point and the deterministic solution is also computed heuristically.

On the Precision of a Euclidean Structure.

Abstract: This paper is concerned with the development of a measure of the precision of a multidimensional euclidean structure. The measure is a precision index for each point in the structure, assuming that all the other points are precisely located. The measure is defined and two numerical methods are presented for its calculation. A small Monte Carlo study of the measure's behavior is performed and findings discussed.

Asymptotic properties of sequences iteratively generated by point-to-set maps

Abstract: In this paper, we examine the relationships between the fixed point set of a point-to-set map A(·), and the asymptotic properties of the sequences which may be iteratively generated by using the map A(·) Let L be the set of all limit points, and Q be the set of all cluster points of all sequences which may be iteratively generated by A(·) The consequences of various assumptions on the map A(·) and the sequences generated by A(·) on lower-bounds and upper-bounds for L and Q are discussed

Extensions of Zangwill’s theorem

Abstract: The validity of Zangwill’s general algorithm for finding a point of a subset of a set is given here with weakened hypotheses. In particular the closedness of the point-to-set map used in the algorithm is not needed.

Multi-element writing instrument

Abstract: A multi-element writing instrument is disclosed for use in computer-operated plotters or similar graphics systems. Successive applications of a linear force applied along the axis of the instrument are converted to rotary motion which is employed to select successive elongate writing elements normally positioned at a uniform radial spacing from the axis of the writing instrument. Each selected element is displaced in a substantially axial direction a distance sufficient to extend the writing point of the element through the exit opening of the instrument.

On infinitesimal isometric deformations

Abstract: We consider an analytic n-dimensional submanifold M of the Euclidean space EN, where N = n(n + 1)/2, and we prove the existence of analytic, nontrivial, infinitesimal isometric deformations, in a neighborhood of any point of M, which admits a nonasymptotic tangent hyperplane.

An isoperimetric problem with lattice point constraints

Abstract: The isoperimetric problem in the Euclidean plane is completely solved for bounded, convex sets which are symmetric about the origin, and which contain no non-zero point of the integral lattice.