Showing papers on "Point (geometry) published in 1971"

A semi-implicit scheme for grid point atmospheric models of the primitive equations

Abstract: A semi-implicit time integration scheme tested earlier with a spectral model is now adapted to a grid point model of the primitive equations. Predictions prepared by the implicit method compare quite favorably with the forecasts produced by an explicit technique. The implicit model runs about four times faster; and after 5 days of integration, the forecasts differ by less than 20 m.

The evaluation of geometrical effects in four point probe measurements

Abstract: An accurate numerical approach is presented for the evaluation of geometrical effects in four point probe resistivity measurements upon semiconductors. The accuracy of the approach is illustrated by comparing results obtained with correction factors tabulated for probe measurements upon circular and rectangular geometries. Correction factors are presented for measurements with a square probe array upon rectangular specimens. The effect of increasing thickness for specimens of bounded geometry is also investigated. The method allows four point probe measurements to be made not only with an arbitrary probe configuration but also upon thin specimens of an arbitrary geometry.

Clustering in N dimensions by use of a system of forces

Abstract: This paper describes a model and associated computer program for carrying out clustering of elements in a space of a predetermined number of dimensions. In addition to clustering of elements, the model may be used for multi‐dimensional scale analysis and for construction of sociograms. The model takes as input data a set of ‘affinities’ between elements, the inverse of which may be considered as psychological or sociological distances. It then moves elements in a Euclidean n‐space toward the point at which the geometric distance is equal to the given psychological or social ‘distance,’ as if a set of attractive and repulsive forces was acting upon each element from other elements. The second major portion of the paper consists of ten examples, which are analyzed by means of the accompanying computer program.

Data analysis systems: A user's point of view*

Abstract: That the availability of modern high speed computers has dramatically expanded the research possibilities of nearly all sciences is already a commonplace. In the social sciences, this new technology has shifted the accent from data collection to methods of data analysis and to theory building using complex empirical models 1. These changes are an important topic for the sociology of sociology. However, the central concern of this paper is to describe and compare new approaches in the utilization of computing equipment for the social sciences, usually called data analysis systems, facilitating the utilization of these new resources in the day-to-day research process. We will consider the most important data analysis systems for third generation computers, SPSS, DATA-TEXT and OSIRIS 2. These program packages

On Exposed and Farthest Points in Normed Linear Spaces

Abstract: Let S be a nonempty subset of a normed linear space E. A point s0 of S is called a farthest point if for some x ∈ E, . The set of all farthest points of S will be denoted far (S). If S is compact, the continuity of distance from a point x of E implies that far (S) is nonempty.

Tessellations with Pentagons

Abstract: Every triangle can be used to tile or tessellate a plane because the 3 angles add up to 180° and so can be arranged to form a straight line. In a similar way every quadrilateral will tessellate because the 4 angles can be grouped round a point.

Imbedding of zero-dimensional compacta in e^3

Abstract: In this paper, for an arbitrary zero-dimensional compactum in , a pseudoisotopy of the space onto itself is constructed, taking a tame zero-dimensional compactum into ; here each nondegenerate preimage of a point under the mapping is a tame arc.For the zero-dimensional Antoine compactum a pseudoisotopy of onto itself is constructed taking a tame zero-dimensional compactum into it so that the mapping has a countable set of nondegenerate primages of points, but each of these is not a locally connected continuum.Bibliography: 11 items.

Solids in Contact

Abstract: If two spheres touch one another, either externally or internally, the point of contact and the centres of the spheres are in the same straight line.

On Autonomous NOR Sequential Machines

Abstract: This note considers the analysis of autonomous NOR sequential machines from a linear machine point of view. It is shown that, under certain conditions, the techniques developed for linear machines are directly applicable to NOR machines.

Drawing board for preparing perspective drawings

Abstract: 1,241,342 Perspective drawing appliances J H KLOK 16 Aug, 1968 [23 Aug, 1967], No 39422/68 Heading B6P A drawing board for preparing perspective drawings is provided with means whereby a straight edge can be oriented to selected vanishing points, and with perspective scales corresponding to the true width, depth, and height measurements of the object to be drawn, whereby by orienting the straight edge into line with one and the other vanishing points and with appropriate scale markings, and by moving the straight edge parallel to the side edges of the board to register with other scales, point on the drawing corresponding to points on the object can be obtained and the perspective drawing can be completed As shown, a curved opening 22 is provided in the board 20 whereby a T-square with a suitably-curved head can be moved or oriented over the board in known manner so that the drawing edge of the square is always in line with a vanishing point 24 lying outside the board on an horizon line 35 Other vanishing points 25, 36, either one of which may be associated with the point 24, are marked on the board The point 25 is situated beyond the drawing edge of the T-square and is constituted by a pin against which a straight edge can be engaged Scales A, A1, A2 used with the points 24, 36 have markings corresponding to actual height, width and depth dimensions respectively of the object to be drawn but calibrated so that correct lengths of vanishing lines corresponding to the actual dimensions can be obtained Similar scales E, E1, E2 are provided for the points 24, 25 A line EX on the scales E1, E2 corresponds to a line through a viewing point perpendicular to the horizon line 35 By setting the T-square in the opening 22 so that its edge passes through the height scale E at a graduation corresponding eg to the height of the top point on the object in the form of a building with its front corner on the line EX, a line through that graduation and point 24 can be drawn The intersection of that line with line EX is marked and a line drawn between that mark and the vanishing point 25 the required point lying on that line By using the bottom edge of the board as a guide for the T-square and aligning the straight edge of the square with the depth scale E2, the position of the point on the line from point 25 can be determined Similarly the positions of other points can be marked and the drawing completed, the width scale being used for points to the left of the front corner Other scales G, G1, G2 and H, H1, H2 are associated with the points 24, 25 to produce different size drawings, and scales F are provided for interior drawings Additional scales B, C, D are similarly provided for the points 24, 36 Scales 66 68 are associated with a single vanishing point 33 for drawing a perspective view of eg the interior of a room Another vanishing point 34 has associated scales J for making larger size single point perspective drawings

Applications and Methods for the Minimization of Functionals

Abstract: Publisher Summary This chapter discusses the applications and methods for the minimization of functional. Many problems of pure and applied mathematics either arise or can be formulated as variational problems, that is, as problems of locating a minimizing point for some (non-linear) real-valued functional over a certain set. Such a setting is often beneficial from the analytic viewpoint of determining the existence and uniqueness of such points. The chapter focuses on the computational aspects of this approach, that is, the way by which it can be used to compute a solution to the problem by actually minimizing the appropriate functional. The chapter also illustrates that there are immense problems of minimization out of which some typical are discussed here.

Roberts’ Cognate of Space Five-Link RHHHH and HHRHH Mechanisms

Abstract: Using the principle of similarly varying triangles, the existence of the coupler cognate of space five-link RHHHH and HHRHH mechanisms is established for the general case in which the coupler point is arbitrarily located in the plane of one of their coupler links.