Showing papers on "Point (geometry) published in 1973"
TL;DR: Every multivariate observation is visualized as a computer-drawn face that makes it easy for the human mind to grasp many of the essential regularities and irregularities present in the data.
Abstract: A novel method of representing multivariate data is presented. Each point in k-dimensional space, k≤18, is represented by a cartoon of a face whose features, such as length of nose and curvature of mouth, correspond to components of the point. Thus every multivariate observation is visualized as a computer-drawn face. This presentation makes it easy for the human mind to grasp many of the essential regularities and irregularities present in the data. Other graphical representations are described briefly.
1,356 citations
TL;DR: In this paper, the properties of point-to-set maps are studied from an elementary viewpoint oriented toward applications in mathematical programming, and conditions establishing continuity of extremal value functions and properties of maps determined by inequalities are included.
Abstract: Properties of point-to-set maps are studied from an elementary viewpoint oriented toward applications in mathematical programming. A number of different definitions and results are compared and integrated. Conditions establishing continuity of extremal value functions and properties of maps determined by inequalities are included.
391 citations
TL;DR: A novel computer-searchable representation for the three basic pictorial features, contour maps, region coverage, and line structures, is described, which provides a rapid means of searching large files for data associated with geometric position as well as with attribute value.
Abstract: A novel computer-searchable representation for the three basic pictorial features, contour maps, region coverage, and line structures, is described. The representation, which has practical storage requirements, provides a rapid means of searching large files for data associated with geometric position as well as with attribute value. An application of this representation to handling terrain information illustrates its utility. The algebraic properties of the data structure make it computationally easy to determine whether a point lies within a closed boundary; compute the area contained by a closed boundary; generate the closed boundary representing the union or intersection of two closed boundaries; and determine the neighboring boundaries to a point and the minimum distances between them and the point.
108 citations
TL;DR: In this paper, a general system of distributions and the reciprocal transformation is considered and the parameters c,k determine μ,σ and the standardized moments α3,α4. The purpose of this paper is to provide c, k values which cover a wide grid of α 3,α 4.
Abstract: This paper is concerned with a general system of distributions , and the reciprocal transformation . Parameters c,k determine μ,σ and the standardized moments α3,α4. The purpose of this paper is to provide c,k values which cover a wide grid of α3,α4. values, for each c,k matching an α3,α4. point, μ and σ are also provided, The grid of α3,α4 values is sufficiently detailed that interpolation in moat cases appears unnecessary.
102 citations
98 citations
TL;DR: In this article, a dual frequency method interpolates the fringe pattern of any kind of hologram interfermetry down to better than 1 100 of a fringe, independent of intensity variations.
96 citations
43 citations
TL;DR: In this paper, the authors considered elliptic problems in exterior domains polynomially depending on a spectral parameter and derived analytic properties of the resolvent in the neighborhood of the point, which permits, for the corresponding nonstationary problem, a complete asymptotic expansion of solutions as.
Abstract: In this paper elliptic problems in exterior domains polynomially depending on a spectral parameter are considered. These problems are obtained from a mixed problem for hyperbolic equations by substituting for . For such elliptic problems analytic properties of the resolvent are studied in the neighborhood of the point , which permits, for the corresponding nonstationary problem, a complete asymptotic expansion of solutions as .Bibliography: 11 items.
38 citations
TL;DR: In this article, an improved method for calculating shortest paths is presented, and an integer programming application is presented for integer programming with the shortest path algorithm, which is based on integer programming.
Abstract: An improved method for calculating feth shortest paths is presented. We point out an integer programming application.
31 citations
TL;DR: In this article, it was shown that any point of space-time has a neighbourhood U such that the b-boundary of U coincides with U/U, i.e.
Abstract: It is shown that any point of space-time has a neighbourhoodU such that theb-boundaryŪ ofU coincides withŪ/U.
TL;DR: In this article, a special constrained case of a rod theory in which two deformable directors are attached to each point of a curve is introduced, where the curvature is defined as a curve at every point of which is attached a rotation vector.
Abstract: A rod theory, defined as a curve at every point of which is attached a rotation vector, is shown to be a special constrained case of a rod theory in which two deformable directors are attached to each point of a curve.
TL;DR: This paper looks at the maximal-flow-with-gains problem from a new point of view, and finds the maximum output possible for any input, through a two-step parametric solution procedure.
Abstract: This paper looks at the maximal-flow-with-gains problem from a new point of view. We with to discover the maximum output possible for any input. This approach leads naturally to a two-step parametric solution procedure: The first step finds the maximum output for zero input, and resolves all difficulties with flow-generating loops; the second determines how the maximum output increases as input is increased.
TL;DR: In this article, an analysis of the straight lip conical grinding method for drill point sharpening is presented, and it is shown that the standard drill specification is such that a variety of grinding cones may be used to satisfy the specified drill geometry.
TL;DR: In this article, a natural metric, d, on the space of infinitely differentiable real valued functions defined on an open subset U of the real numbers, R, is defined, and the elements of C∞, which are analytic near at least one point of U comprise a first category subset of C ∞,.
Abstract: We define a natural metric, d, on the space, C∞, , of infinitely differentiable real valued functions defined on an open subset U of the real numbers, R, and show that C∞, is complete with respect to this metric. Then we show that the elements of C∞, which are analytic near at least one point of U comprise a first category subset of C∞, .
Patent•
05 Dec 1973
TL;DR: In this article, a tubular section converging towards a connecting point is connected to a support element by means of sleeves held on studs which extend from the support element, and mutually engaging annular stops prevent removal of the sleeves from the studs.
Abstract: Frame elements such as tubular sections converging towards a connecting point are connected to a support element by means of sleeves held on studs which extend from the support element, and mutually engaging annular stops prevent removal of the sleeves from the studs. The respective sections are threaded into the sleeves.
Patent•
26 Apr 1973
TL;DR: In this article, a submerged arc welding machine is described, where a welding head is pivoted to a frame of the machine so as to be rockable across the seam of a workpiece being welded.
Abstract: A submerged-arc welding machine comprises a welding head pivoted to a frame of the machine so as to be rockable across the seam of a workpiece being welded, and a vertically movable oscillation mechanism provided with an eccentric cam engaging the welding head for causing the welding head to rock across the seam as the cam rotates Further included is an oscillation amplitude adjusting device for moving the oscillation mechanism as well as the cam vertically, whereby the axis of rotation of the cam is adjustable relative to that point on the frame about which the welding head pivots to adjust the amplitude of the rockable movement of the welding head
TL;DR: An attempt is made to obtain a further criterion to arrive at a solution to the conical grinding method for a given drill specification, from a study of the drill point geometry for a variety of grinding cones.
TL;DR: In this article, it was shown that the following two conditions are independent: (1) every line of P is incident with at least one point of B and (2) every point of P points are incident with B points.
Abstract: LetP be an infinite projective plane and letB be a subplane ofP. An example is given which shows that the following two conditions are independent: (1) Every line ofP is incident with at least one point ofB. (2) Every point ofP is incident with at least one line ofB.
TL;DR: A two-step strategy for optimizing design systems is presented in the form of two algorithms based on the strategy known as restriction to optimize the system once feasible, which has proved remarkably effective on three relatively simple examples.
Abstract: Structured design systems are systems which may be represented by generally nonlinear equality and inequality constraints, each of which contains few of the variables in the system. Assuming the existence of an automatic capabity to derive and modify as needed effective solution procedures for sets of structured equality constraints, a two-step strategy for optimizing design systems is presented in the form of two algorithms. An earlier paper presented an algorithm for locating a first feasible point, and this paper presents a companion algorithm based on the strategy known as restriction to optimize the system once feasible.
This companion algorithm divides the set of inequality constraints into three sets: the set of those currently being held as equality constraints, the set currently released but being used as search coordinates, and the set of all remaining constraints which are not currently part of the problem. Solution procedures are modified as inequality constraints and are moved from one set to another. Added constraints in the set being held tend to aid the optimization process by reducing the dimension of search space for what is usually a marginal added burden in solving an enlarged set of (structured) equations.
The strategy has proved remarkably effective on three relatively simple examples, including a nonlinear 31 constraint, 10 variable alkylation problem.
Patent•
23 Jul 1973
TL;DR: In this article, a system for displaying on a standard television monitor a horizontal line along a scan line or a vertical line orthogonal to the scan line, where coded digital signals from a memory define the location of the starting point of the line and also identify the line as either a horizontal or vertical line.
Abstract: A system for displaying on a standard television monitor a horizontal line along a scan line or a vertical line orthogonal to the scan line wherein coded digital signals from a memory define the location of the starting point of the line and also identify the line as either a horizontal or a vertical line. For horizontal line drawing, circuit means are provided to respond to the starting point identification to gate the beam on and to the horizontal line identification to maintain the beam gated on along a scan line until the end of the line. For vertical line drawing, the beam is gated on at the starting point and a recirculating shift register stores the starting point identification to gate the beam on at the corresponding positions in successive scan lines.
TL;DR: In this article, a stochastic theory is proposed which takes into account changes in the transfer probability at a carding point upon collection by a worker and redeposition on the cylinder.
Abstract: A stochastic theory is proposed which takes into account changes in the transfer probability at a carding point upon collection by a worker and redeposition on the cylinder. This theory reduces to an earlier work of Monfort, if such changes are ignored. The theory explains quantitatively the observed nature of fiber movement in roller-top cards. This new approach is then coupled with the work of Baturin to successfully predict the behavior at different speed conditions. The present theory "fits" the observed speed effects over a two- to three-fold range of worker velocities, while the older theory yields a systematic deviation between the observed and calculated collection probabilities. Indices are formulated which describe blending, mixing and equalizing as it occurs in the carding process. These formulations, based in part upon previous literature, are modified in the light of the new theory developed in this paper.
Patent•
02 Oct 1973
TL;DR: In this paper, a yarn is caused to travel at a velocity w 1 under a constant tension sufficient to straighten but insufficient to stretch the yarn, and a second constant tension is applied to the yarn at the point of application of this tension, the second tension being small enough to allow any crimp in the yarn to be re-formed.
Abstract: Yarn is caused to travel at a velocity w1 under a constant tension sufficient to straighten but insufficient to stretch the yarn. Downstream of the point of application of this tension, a second constant tension is applied to the yarn, the second tension being small enough to allow any crimp in the yarn to be re-formed. The velocity w2 of the yarn traveling past the point of application of the second constant tension is continuously measured, and the crimp along the length of the yarn is continuously evaluated by means of the relationship Crimp (%) = [(w1 - w2)100./w1 ] If desired, measurement of latent crimp may be obtained according to this invention by developing the crimp (e.g., by the application of steam or boiling water to the yarn) between the two points where tension is applied to the yarn.
TL;DR: In this article, a necessary condition is given for a real-valued function f to attain a maximum at a point b subject to the condition $x \in S, where S is given as an intersection of a finite number of sets in an n-dimensional Euclidean space.
Abstract: In this paper a necessary condition is given for a real-valued function f to attain a maximum at a point b subject to the condition $x \in S$, where S is given as an intersection of a finite number of sets in an n-dimensional Euclidean space. It is shown that well-known necessary conditions in mathematical programming, like the Lagrange multipliers theorem and results of F. John, Mangasarian and Fromovitz, are immediate consequences of this general condition. The result is also used to derive a general necessary condition for discrete-time optimal control problems, which contains the results of Halkin (discrete maximum principle), Jordan and Polak, and Canon, Cullum and Polak as special cases. As a final application of the necessary condition a simple proof of the Pontryagin maximum principle for continuous-time control problems is given.
01 Jan 1973
TL;DR: In this paper, a bounded domain in Euclidean space R m and a point in this space is represented as a real function, and the closure of the set A is defined by the symbol A ⊂ B.
Abstract: We shall denote by Ω a bounded domain in Euclidean space R m , and by x = (x1, ⋯, x m ) a point in this space. All functions considered in Chapter I are assumed real unless otherwise specified. As usual, the symbol A ⊂ B means that the set A is contained in B, and Ā denotes the closure of the set A.
TL;DR: In this article, it was shown that if Ai converges in the Hausdorff metric to the unit sphere in En, then S(A) is the Steiner point of the set A.
Abstract: To each convex compact A in Euclidian space En there corresponds a point S (A) from En such that 1) S(x) = x for x ∈ En, 2) S(A + B) = S(A) + S(B), 3) S (Ai) →θ, if Ai converges in the Hausdorff metric to the unit sphere in En, then S(A) is the Steiner point of the set A. The theorem improves certain earlier results on characterizations of the Steiner point.
Journal Article•