Showing papers on "Point (geometry) published in 1983"

The filling radius of two-point homogeneous spaces

Abstract: is an isometric imbedding, as dist(;c, x') — \\dx — dx,\\ (the triangle inequality). Consider the inclusion homomorphism aε: Hn(X) -* Hn(UεX% where UεX C L^iX) is the ε-neighborhood of X, and the coefficients are in Z 2 . Following M. Gromov [3], we introduce a new metric invariant of X. Definition. The filling radius of X, denoted Fill Rad X, is the infimum of those ε > 0 for which aε([ X]) = 0, where [X] is the fundamental class of X. We prove the following theorems. Theorem 1. The filling radius of the real projectiυe space RP of constant curvature + 1 equals one third of its diameter:

New Results in the Theory of Packing and Covering

Abstract: Let J be a system of sets. If all members of J are contained in a given set C and each point of C belongs to at most one member of J then J is said to be a packing into C. If, on the other hand, each point of C belongs to at least one member of J then we say that J is a covering of C. Packings and coverings have been considered in various spaces and on various combinatorial structures. Here we are interested in problems concerning packings and coverings consisting of convex bodies in spaces of constant curvature, i.e. in Euclidean, spherical and hyperbolic space. Instead of saying that J is a packing into the whole space or J is a covering of the whole space we shall simply use the terms J is a packing and J is a covering.

The point of view: Universal or particular?

Abstract: That there is no "feminine writing" must be said at the outset, and one makes a mistake in using and giving currency to this expression. What is this "feminine" in "feminine writing"? It stands for Woman, thus merging a practice with a myth, the myth of Woman. "Woman" cannot be associated with writing because "Woman" is an imaginary formation and not a concrete reality; it is that old branding by the enemy now flourished like a tattered flag refound and won in battle. "Feminine writing" is the naturalizing metaphor of the brutal political fact of the domination of women, and as such it enlarges the apparatus under which "femininity" presents itself: that is, Difference, Specificity, Female Body/Nature. Through its adjacent position, "writing" is captured by the metaphor in "feminine writing" and as a result fails to appear as work and a production process, since the words "writing" and "feminine" are combined in order to designate a sort of biological production peculiar to " W o m a n , " a secretion natural to "Woman."

Change-configuration climbing chock

Abstract: An artificial chock stone for use by rock climbers to provide a protection point. The chock comprises a pair of slidably engaged wedges which are adjustable between a large dimension and a small dimension upon relative sliding of the wedges, which are biased to a large dimension. The device may be inserted and provide a secure protection point in a narrow, smooth-walled, paralleled-sided crevice and is constructed to provide a point of attachment to which a safety line may be secured.

Optical beam scanner

Abstract: PURPOSE: To decrease the positional fluctuation of a beam on a scanning plane by forming a hologram disk into two-layered constitution in such a manner that the respective layers have diffraction directions of opposite tendencies and that the synthetic sum of the space frequencycies of the two-layered hologram have a max. point at the reconstruction point or near the same. CONSTITUTION: The hologram disk 10 having the two-layered construction is constituted by joining, via a spacer 15, the 1st disk 11 having the hologram 13 of which the interference fringes are made to a monotonic change space frequency by the interference of a spherical wave 17 diverged from one point A on the center line 16 of rotation and a plane wave 18 having the optical axis at the disk plane normal of the incident point of the reconstruction beam and the 2nd disk 12 having the hologram 14 of which the interference fringes are made to the monotonic change space frequency of the interference of the divergent spherical wave 19 diverged from the point (c) on the side outer than the reconstruction point with respect to the axis 16 of rotation and the plane wave 20 having the optical axis at the disk plane normal of the incident point of the reconstruction beam. The incident point of the reconstruction light moves merely near the max. point even if the disk 10 has eccentricity when part of the spherical wave 17 is made incident on the reconstruction point from the point A. COPYRIGHT: (C)1986,JPO&Japio

Image-forming element using both side reflection band of minute width

Abstract: PURPOSE:To facilitate installation to a device and to reduce size by so forming a titled element that no optical axes exist thereby eliminating aberrations and eccentricity and making object distance free. CONSTITUTION:An image-forming element 8 is constituted by disposing plural pieces of both side reflection bands of several mu and several tens mu width in a transparent material 7 in parallel with each other at such micropitches at which the adjacent reflection surfaces face each other. If the imaging element constituted by sandwiching said element 8 with cylindrical lenses 9 in such a way that the generator direction of the cylindrical lenses interrsect orthogonally with the reflection surfaces 2 is so formed that when an object point 3 is put on one side of such element, the element forms an image on the image plane 6 in the position apart twice the distance of the image-forming element point from the object point and in the plane at a right angle thereto the element forms the image on the same plane by the cylindrical lenses 9 as shown in the figure, the light from the object point forms the image at one point on the image plane 5 and therefore the element is usable as an image-forming element for linear scanning.

On the equivalence of point configurations due to Euclidean normalizers (Cheshire groups) of space groups

Abstract: The Euclidean normalizers of space groups form the appropriate mathematical tool for several problems treated independently by crystallographers in the past, e.g. the comparison, the classification and the standardized description of crystal structures. Explicit tables are presented that enable the user to handle Euclidean normalizers in an easy way and, especially, to calculate all descriptions of a crystal structure compatible with a chosen space-group setting. The use of the tables is illustrated by different examples, and the role of Euclidean normalizers for crystal-structure determination is discussed.

How to Search in History

Abstract: This paper considers the problem of granting a dynamic data structure the capability of remembering the situation it held at previous times. We present a new scheme for recording a history of h updates over an ordered set S of n objects, which allows fast neighbor computation at any time in the history. This scheme requires O(n + h) space and O(log n log h) query response-time, which saves a factor of log n space over previous structures. Aside from its improved performance, the novelty of our method is to allow the set S to be only partially ordered with respect to queries and the time-measure to be multi-dimensional. The generality of our method makes it useful to a number of problems in three-dimensional geometry. For example, we are able to give fast algorithms for locating a point in a 3d-complex, using linear space, or for finding which of n given points is closest to a query plane. Using a simpler, yet conceptually similar technique, we show that with only O(n2) preprocessing, we can determine in O(log2 n) time which of n given points in E3 is closest to an arbitrary query point.

The Space Charge Computer Program SCHAR

Abstract: The space charge computer program SCHAR uses macrofilaments or macroparticles to model the effects of space charge in ion transport. The program calculates the transport properties of beams of non-relativistic charged particles using two alternative macroparticle formulations. The line mode formulation considers the beam to be composed of a manageable number of infinitely long charged filaments. The paths of these filaments are fixed in time but their positions as a function of distance along the line are determined by a fourth-order Runge-Kutta time step integration. The point mode formulation considers the beam to be composed of a manageable number of charged macroparticles. These macroparticles have the same charge-to-mass ratio as the actual particles. In this mode the space charge effects are modeled solely by the Coulomb repulsion of the macroparticles. In space charge cases, while the calculation steps from SCHAR are identical, the line mode will run by a factor of two or three times faster than the point mode; if beam bunching occurs, however, use of the line mode becomes inappropriate. Both modes are described by SCHAR in a left-handed Cartesian coordinate system. Among the optional methods for spreading out the filaments or particles in phase space are: four-volumemore » distribution, designed for line mode operation; KV distribution, a specialized four-dimensional input assumed also by TRACE; six-volume distribution, meant for point mode but also applicable to line mode operation; and ''observed'' distribution, designed for point mode operation.« less

Using tangential method to detect the singular points and to discriminate the stability condition of a movable mass point on any guide curve rotating about a vertical axis without friction

Abstract: The state plane method has been used to search the singular point and to determine their equilibrium state for a mass point sliding on a guide rail rotating about a vertical axis with friction disregarded. For the same purpose, this paper presents another method which might be briefly named “The Tangential Force Method”. In contrast with the state plane method, the new method is much simpler both in argumentation and calculation, especially when one resorts to the five criteria in section XIII.

Universal parts gripper

Abstract: Universal parts gripper, with which components of different shape and size lying on a storage shelf or similar cavity can be picked up and deposited again at a different point with the execution of spatial movements if required, a telescopically extendible gripper arm being provided which grips under the components with a lower gripping sword and over the components with a holding-down device disposed parallel to this at a variable distance, the holding-down device having a surface geometry that can be automatically adapted to the component surface geometry facing it.

Detecting system for original point of position control machine

Abstract: PURPOSE:To detect a rough original point with a simple constitution by replacing a detector for rough original point with a current detecting circuit of an electric motor. CONSTITUTION:When a detection command for original point is supplied to a control circuit 10 of an electric motor 1 from a central controller, the motor 1 is controlled to the minimum speed. At the same time, a mobile body 5 also starts its right movement at the minimum speed via a drive mechanism 6. Then a dock 3 set to the body 5 has a contact with a stopper 4 of a base 11 with more right movement of the body 5. Thus the load becomes infinite and a large current flows to the motor 1. The variation of said large current is detected by a detection circuit 8 for rough original point. Then the motor 1 is reversed and controlled by a control circuit 10 so that the body 5 is moved left. Then a detection circuit 7 for fine original point detects an original point pulse of an encoder 2 connected to the motor 1. Thus an end signal for detection of original point is delivered from a detection circuit 9 for original point to finish the detection of original point.

A spatial smoothing formulation for location systems

Abstract: Two extensions of the classic passive location problem are considered. The first examines the ranging ability of passive receivers. The second presents alternative ways of describing the geometric content in positioning problems. The implications of the different approaches on the structure and performance of the location receiver are discussed. Because range determination by passive means is missing, the classical formulation of passive location may be viewed as a local geometry demodulation problem. With the explicit consideration of range, passive location becomes a global problem. At stake is what may be gained by processing the small but valuable amount of information carried by the wavefront curvature of the signals. Relevant questions relate to the design of passive receivers that aptly demodulate the range and the remaining quantities defining the geometry. There are passive applications where models exhibiting a high degree of (geometric) regularity are viable from a practical point of view. These occur, for example, when one can assume that the array sensors are collinear and that the moving target follows a deterministic linear path. In these models, the geometry is completely determined by a finite set of (unknown) parameters (e.g., range, bearing, speed, etc.). Accordingly, it is said that the regular models use an integral or ensemble approach for the description of the geometry. In many other problems, the geometry is more adequately described by statistical processes. Examples arise when the source follows a disturbed path, or when, due to towing, the array shape deforms, acquiring a not-completely-known shape. The paper models these constraints via a set of stochastic differential equations. The resulting representation is termed a differential description. It is emphasized that the differential approach is not only applied to the time content (relative dynamics), but also to the spatial dimension (array shape). The technique dualizes the space and time aspects of the problem. It provides a more flexible framework than the previous one. More general motions and array shapes than the traditional collinear ones can be considered by the analysis, e.g., irregular line arrays or arrays where the sensors are located at positions with a certain degree of randomness. Each approach fits a different design framework. The ensemble description is associated with the maximum likelihood technique. The differential representation uses recursive estimation methods (as provided by the Kalman-Bucy filtering theory). The paper discusses the main aspects of the structure of the resulting receivers and the associated measures of error performance. A second advantage of the differential model is immediately apparent The recursiveness of the differential receiver reduces its computational load. The speed-up obtained is fully appreciated in tracking applications, where the observations are sequentially updated. Finally, it is interesting to note that the time/space duality provided by the differential approach exhibits a remarkable distinction: the location recursive receiver behaves in time as a filter, while it behaves in space as a smoother.

Correcting apparatus for abrasion amount of grinder grinding stone

Abstract: PURPOSE:To permit the working point of a grindstone to be held stone in accordance with the detection of the abrasion amount by installing an abrasion-amount detector and the grindstone onto a special proportional link installed at the top edge of a supporting arm and setting the ratio of transfer amount of the detection point and the working point due to the swing of the link to a specific value. CONSTITUTION:The ratio between the distance l3 between a detection point A and the point A'' of a supporting pin 59 and the distance l4 between the point A' of a pin 63 and the point A'' is set to 3:1, and the ratio between the distance l1 between the working point B of a grindstone G1 and the point B'' of a supporting shaft 56 and the distance l2 between the poing B' of a supporting pin 64 and th point B'' is set to 3:2. When a shaking link 60 swings in the alpha direction, and the point A' shifts by DELTAz, also the point B' shifts towards an object W by the equal amount, and the point A shifts in the same direction by DELTAz X 3 in accordance with the ratio of link. While, as the point B' shifts also the point B shifts by DELTAz X 3/2 towards the object W, having the point B'' as center. Therefore, the point A shifts towards the object W by twice the amount with respect to the point B in accordance with the unit amount of frequent appearance of a connecting rod 52. Therefore, the working point B is held always at a constant position with respect to an arm 15, so far as an abrasion-amount detecting element 68 catches the detection point A between light receiving elements.

Teaching method of robot

Abstract: PURPOSE:To improve remarkably the working performance of teaching by replacing the relation between a face formed by the 1st representative point and the tool attitude equally to the relation between a face formed by the 2nd representative point and said attitude so as to form a teaching data with a simple teaching work. CONSTITUTION:A work of the same shape as a work for which a robot should work is set to the robot, and the position coordinate of the 2nd work point corresponding to the 1st work point is calculated by the relative position between the face formed by the 1st representative point and the face formed by the three 2nd representative points. The teaching data is generated at the same time by making an angle between the two 1st representative points among the 1st representative points and the axial line of the working tool or teaching tool at the position of the 1st working point equal to an angle between the working tool or the teaching tool axis line at the position of the 2nd working point and the two 2nd representative points and operating and calculating the result into a robot wrist angle at the 2nd working point.