scholarly journals Identical appended series of points as invariants in the collocal general-colinear fields

2003 ◽  
Vol 2 (5) ◽  
pp. 387-394
Author(s):  
Sonja Krasic
Keyword(s):  
The Other ◽  
Straight Line ◽  
Similar Series ◽  
Vanishing Line ◽  
Identical Series ◽  
Straight Lines ◽  
General Method

In order to bring the collocal collinear fields from the general into the perspective position, it is required to determine the identical appended series of points. Because of the properties depending on the projectivity that is given by the four appended points (straight lines) the appended identical series of the points and types are ranked among the invariants of general-collinear and perspectively-collinear fields. The procedure of determination of appended identical series of points is comprised of the following: in the set of ?1 of perspectively similar series in one field (whose center of perspective is a point on the vanishing line), find those that are identical to all the series in the set ?1 of perspective identical series of points in the other field (whose center of perspective is the point on the infinitely distant straight line). In the procedure, one begins from the appended similar methods obtained by the general method. The procedure is simplified by the introduction of the specially given similar series of points.

Appendix, containing the Investigation of a Formula for the Rectification of any Arch of an Ellipse

1805 ◽  
Vol 5 (2) ◽  
pp. 271-293
Keyword(s):  
Finite Number ◽  
The Other ◽  
Algebraic Equations ◽  
Conic Sections ◽  
Straight Line ◽  
Curve Line ◽  
Straight Lines

It is now generally understood, that by the rectification of a curve line, is meant, not only the method of finding a straight line exactly equal to it, but also the method of expressing it by certain functions of the other lines, whether straight lines or circles, by which the nature of the curve is defined. It is evidently in the latter sense that we must understand the term rectification, when applied to the arches of conic sections, seeing that it has hitherto been found impossible, either to exhibit straight lines equal to them, or to express their relation to their co-ordinates, by algebraic equations, consisting of a finite number of terms.

A New General Method for the Determination of Optical Properties of Amorphous Silicon Films

1990 ◽  
Vol 192 ◽  
Author(s):  
G. Amato ◽  
L. Boarino ◽  
F. Fizzotti ◽  
C. Manfredotti
Keyword(s):  
Thin Films ◽  
Optical Properties ◽  
Amorphous Silicon ◽  
Optical Response ◽  
The Other ◽  
New Method ◽  
Silicon Thin Films ◽  
Physical Insight ◽  
General Method

ABSTRACTWe propose to apply a new method to model the optical response of amorphous silicon thin films. This method presents the advantage of having a good physical insight. On the other hand, although the model has been originally tested on different materials like a-Si, a-Ge and a-GaAs, we show that it is also sensitive to small differences like those that can exist between intrinsic and doped a-Si:H.

THE USE OF CUMULATIVE RESISTANCE IN EARTH-RESISTIVITY SURVEYS

1945 ◽  
Vol 23a (4) ◽  
pp. 57-72 ◽  
Author(s):  
R. Ruedy
Keyword(s):  
Apparent Resistivity ◽  
Middle Layer ◽  
The Other ◽  
Electrode Spacing ◽  
Line Graphs ◽  
Earth Resistivity ◽  
The Earth ◽  
Straight Line ◽  
The Individual

When the soil is assumed to consist of two layers—the upper of resistivity ρ1 and the lower of resistivity ρ2—and cumulative resistances are calculated by adding or integrating the earth-resistivity functions for intervals that are a fraction of the thickness of the upper layer, a practically linear relation is obtained between the cumulative resistance and the electrode spacing until the distance between the electrodes is equal to the thickness of the upper material. Should one of the materials be at least twice as conducting as the other, the extent of the deviation from the linear law enables the determination of the depth of the upper stratum and of the ratio between the resistivities of the two layers. When three layers are present and the middle layer is at least twice as thick as the top stratum, the thicknesses may be deduced from the two departures of the cumulative resistances from the linear law. Since these conclusions are based on the theory of the individual apparent resistivity of stratified ground at various electrode spacings, they have the same range of application as the earth-resistivity curves, but the occurrence of straight line graphs facilitates the plotting and the interpretation of results based on a necessarily limited number of measurements.

scholarly journals City Shape and the Fractality of Street Patterns

2012 ◽  
Vol 31 (2) ◽  
pp. 29-37 ◽  
Author(s):  
Nahid Mohajeri ◽  
Paul Longley ◽  
Michael Batty
Keyword(s):  
Fractal Dimension ◽  
Power Laws ◽  
Step Length ◽  
The Other ◽  
Main Street ◽  
Straight Line ◽  
Line Slope ◽  
Straight Lines ◽  
The City ◽  
Street Segments

City Shape and the Fractality of Street Patterns This paper discusses, first, the concepts of fractals and power laws in relation to the street patterns of the city of Dundee, East Scotland and, second, the results of the measurement of 6,004 street segments in the city. The trends of the street segments are presented through rose diagrams and show that there are two main street trends in the city: one is parallel with the coast, the other is roughly perpendicular to the coast. It is clear that the coastline largely regulates the street trend, because both the main street trends change along the city so as to be nearly coast-perpendicular and coast-parallel everywhere. The lengths of the street segments follow power laws. When presented on log-log plots, however, the result is not a single straight line but two straight lines. At the break in line slope, the fractal dimension changes from 0.88 to 2.20. The change occurs at the step length of about 100 m, indicating that the short streets belong to a population that is different from that of the longer streets.

scholarly journals Detour Extra Straight Lines in the Euclidean Plane

2020 ◽  
pp. 237-249
Author(s):  
I. Szalay ◽  
B. Szalay
Keyword(s):  
Euclidean Plane ◽  
Euclidean Geometry ◽  
The Other ◽  
Real Numbers ◽  
Other Hand ◽  
Straight Line ◽  
Axiom Systems ◽  
Straight Lines

Using the theory of exploded numbers by the axiom-systems of real numbers and Euclidean geometry, we explode the Euclidean plane. Exploding the Euclidean straight lines we get super straight lines. The extra straight line is the window phenomenon of super straight line. In general, the extra straight lines are curves in Euclidean sense, but they have more similar properties to Euclidean straight lines. On the other hand, with respect of parallelism we find a surprising property: there are detour straight lines.

scholarly journals III.—On the Extension of Brouncker's Method to the Comparison of Several Magnitudes.

1870 ◽  
Vol 26 (1) ◽  
pp. 59-67
Author(s):  
Edward Sang
Keyword(s):  
The Other ◽  
Exact Science ◽  
Straight Line ◽  
The One ◽  
Definition Of ◽  
Straight Lines

The discovery of those numbers which shall, either truly or approximately, represent the ratio of two magnitudes, necessarily attracted the attention of the earliest cultivators of exact science. The definition of the equality of ratios given in Euclid's compilation clearly exposes the nature of the process used in his time. This process consisted in repeating each of the two magnitudes until some multiple of the one agreed perfectly or nearly with a multiple of the other; the numbers of the repetitions, taken in inverse order, represented the ratio. Thus, if the proposed magnitudes were two straight lines, Euclid would have opened two pairs of compasses, one to each distance, and, beginning at some point in an indefinite straight line, he would step the two distances along, bringing up that which lagged behind, until he obtained an exact or a close coincidence.

Kinematical Analysis of Slope Stability Using Triangular Slices Method

2008 ◽  
Vol 33-37 ◽  
pp. 1115-1122
Author(s):  
Yong Jian Zhu
Keyword(s):  
Limit Analysis ◽  
Failure Criterion ◽  
Failure Criteria ◽  
Soil Mass ◽  
Nonlinear Failure Criterion ◽  
Analysis Theory ◽  
Straight Line ◽  
Straight Lines ◽  
Limit Analysis Method

Conventional stability analysis of slopes is established on vertical slices with a linear Mohr-Coulomb (MC) failure criterion. In this paper, the soil mass of slopes is assumed to follow linear and nonlinear failure criteria. A new procedure is proposed for determination of stability factors of slopes using triangular slices within the framework of limit analysis method under plane strain condition. The potential sliding mass is divided into a series of triangular slices, rather than vertical slices as usual. Using a generalized tangential technique, the nonlinear failure criterion is simplified as a set of straight lines according to the linear MC failure criterion. The straight line is tangential to the curve of the nonlinear failure criterion. With a linear MC failure criterion, solutions to stability factors are determined by limit analysis theory, which agree well with the published solutions. With triangular slices method, a study is carried out to investigate the influences of nonlinear parameter on stability of the soil slope.

Chemorheological Treatment of Crosslinked EPDM

1971 ◽  
Vol 44 (5) ◽  
pp. 1334-1340 ◽  
Author(s):  
Kenkichi Murakami ◽  
Saburo Tamura
Keyword(s):  
Stress Relaxation ◽  
Main Chain ◽  
Relaxation Curve ◽  
Oxidative Cleavage ◽  
The Other ◽  
Carbon Bond ◽  
Carbon Carbon Bond ◽  
Straight Line ◽  
Interchange Reaction ◽  
Straight Lines

Abstract Stress relaxation mechanisms were investigated on three types of (EPDM) ethylene-propylene terpolymers in air at 109° C. These polymers differ only by the structure of the crosslinkage in which there is a carbon-carbon bond, a polysulfide linkage −Sx⁁− or a monosulfide linkage (—S—). All the stress relaxation of peroxide-cured EPDM polymer was not due to the oxygen-induced cleavage of the main chain but to a physical flow. In the case of sulfur-cured EPDM polymer, the relaxation curve is divided into three straight lines when the procedure X is used and log f(t)/f(0( is plotted linearly with time. It was concluded that this graph was in agreement with an interchange reaction of the polysulfide linkage by an oxidative cleavage of the monosulfide linkage. On the other hand, a TT-cured EPDM polymer gave a plot with a straight line. This stress relaxation could be explained by an oxidative cleavage of the monosulfide linkage.

scholarly journals Limit Cycles of Planar Piecewise Differential Systems with Linear Hamiltonian Saddles

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1128
Author(s):  
Jaume Llibre ◽  
Claudia Valls
Keyword(s):  
Limit Cycle ◽  
Differential System ◽  
Limit Cycles ◽  
The Other ◽  
Differential Systems ◽  
Other Hand ◽  
Straight Line ◽  
Line Of Discontinuity ◽  
Straight Lines

We provide the maximum number of limit cycles for continuous and discontinuous planar piecewise differential systems formed by linear Hamiltonian saddles and separated either by one or two parallel straight lines. We show that when these piecewise differential systems are either continuous or discontinuous and are separated by one straight line, or are continuous and are separated by two parallel straight lines, they do not have limit cycles. On the other hand, when these systems are discontinuous and separated by two parallel straight lines, we prove that the maximum number of limit cycles that they can have is one and that this maximum is reached by providing an example of such a system with one limit cycle. When the line of discontinuity of the piecewise differential system is formed by one straight line, the symmetry of the problem allows to take this straight line without loss of generality as the line x=0. Similarly, when the line of discontinuity of the piecewise differential system is formed by two parallel straight lines due to the symmetry of the problem, we can assume without loss of generality that these two straight lines are x=±1.

Determination of the lattice translation across {110} APBs in GaAs

1988 ◽  
Vol 46 ◽  
pp. 600-601
Author(s):  
D.R. Rasmussen ◽  
N.-H. Cho ◽  
C.B. Carter
Keyword(s):  
Grain Boundaries ◽  
Lower Energy ◽  
Antiphase Boundary ◽  
The Other ◽  
Boundary Structure ◽  
Interface Plane ◽  
Inversion Symmetry ◽  
High Angle ◽  
Equilibrium Distance

Domains in GaAs can exist which are related to one another by the inversion symmetry, i.e., the sites of gallium and arsenic in one domain are interchanged in the other domain. The boundary between these two different domains is known as an antiphase boundary [1], In the terminology used to describe grain boundaries, the grains on either side of this boundary can be regarded as being Σ=1-related. For the {110} interface plane, in particular, there are equal numbers of GaGa and As-As anti-site bonds across the interface. The equilibrium distance between two atoms of the same kind crossing the boundary is expected to be different from the length of normal GaAs bonds in the bulk. Therefore, the relative position of each grain on either side of an APB may be translated such that the boundary can have a lower energy situation. This translation does not affect the perfect Σ=1 coincidence site relationship. Such a lattice translation is expected for all high-angle grain boundaries as a way of relaxation of the boundary structure.

Sign in / Sign up

Export Citation Format

Share Document