scholarly journals Local Linear Scale Factors in Map Projections of an Ellipsoid

Geographies ◽  
2021 ◽  
Vol 1 (3) ◽  
pp. 238-250
Author(s):  
Miljenko Lapaine
Keyword(s):  
Extreme Values ◽  
Scale Factor ◽  
Linear Scale ◽  
Map Projections ◽  
Scale Factors ◽  
Local Linear ◽  
Ellipsoidal Surface ◽  
Point To Point ◽  
Definition Of ◽  
Factor C

The main problem in cartography is that it is not possible to map/project/transform a spherical or ellipsoidal surface into a plane without distortions. The distortions of areas, angles, and/or distances are immanent to all maps. It is known that scale changes from point to point, and at certain points, the scale usually depends on the direction. The local linear scale factor c is one of the most important indicators of distortion distribution in the theory of map projections. It is not possible to find out the values of the local linear scale factor c in directions of coordinate axes x and y immediately from the definition of c. To solve this problem, in this paper, we derive new formulae for the calculation of c for a rotational ellipsoid. In addition, we derive the formula for computing c in any direction defined by dx and dy. We also considered the position and magnitude of the extreme values of c and derived new formulae for a rotational ellipsoid.

Perceptual-Motor Attributes of Mental Retardates: A Factor Analytic Study

1971 ◽  
Vol 33 (3) ◽  
pp. 927-934 ◽  
Author(s):  
Renate L. Neeman
Keyword(s):  
Survey Methodology ◽  
Arm Movement ◽  
Mentally Retarded ◽  
Total Sample ◽  
Developmental Factor ◽  
Similar Factor ◽  
Mentally Retarded Children ◽  
Item Scores ◽  
Definition Of ◽  
Factor C

19 items of the Purdue Perceptual-motor Survey were administered to 99 mentally retarded children and young adults of mean IQ 52.3. Factor analyses of the item scores of the total sample, and of a subgroup of 66 non-mongoloid Ss, led to the definition of 7 factors: A, postural dimensionality; B, shoulder-arm movement factor; C, laterality; D, ocular control; E, intelligence; F, developmental factor; and G, possibly cultural sex bias factor. Similar factor structures emerged for the total sample, and for the non-mongoloid subgroup, with the exception of Factor E, intelligence. The results generally agree with previous correlational analyses of comparable samples and tend to support the construct validity of the Purdue Perceptual-motor Survey methodology as applied to the mentally retarded.

Legibility Study of Selected Scale Characteristics for Moving-Tape Instruments

1965 ◽  
Vol 7 (6) ◽  
pp. 545-555 ◽  
Author(s):  
Barbara J. Kelso
Keyword(s):  
Air Force ◽  
Reaction Times ◽  
Scale Factor ◽  
Verbal Response ◽  
Scale Factors ◽  
Scale Characteristics ◽  
The Mean ◽  
Standard Deviations ◽  
Vertical Scales ◽  
Speed And Accuracy

A legibility study was performed to investigate the effects of scale factors, graduation marks, orientation of scales, and reading conditions on the speed and accuracy of reading moving-tape instruments. Each of 150 Air Force Officers made 150 self-paced readings from slides of hand drawn tape instruments. Error was expressed as the magnitude of deviation of a subjects' verbal response from the set scale value. An analysis of variance was performed on the mean error scores, standard deviations of error, mean reaction times, and standard deviations of reaction times. The results clearly favored the 1 7/8 inch scale factor over the 1 3/8 inch and the 2 3/8 scale factor. The use of 9 graduation marks was superior to either 0, 1, 3, or 4 graduation marks. Reading conditions had little effect on performance. Horizontal scales were read more rapidly but no more accurately than vertical scales.

Issues of organizing computations in multicomputersystems with the software-controlled failure- and fault-tolerance. Part 1

2021 ◽  
Author(s):  
I.V. Asharina
Keyword(s):  
Fault Tolerance ◽  
Critical Level ◽  
Fault Tolerant ◽  
Communication Channels ◽  
State Standards ◽  
Modern Concept ◽  
Multiple Faults ◽  
Point To Point ◽  
Definition Of ◽  
Test Diagnostics

This three-part paper analyzes existing approaches and methods of organizing failure- and fault-tolerant computing in distributed multicomputer systems (DMCS), identifies and provides rationale for a list of issues to be solved. We present the concept of fault tolerance proposed by A. Avizienis, explicate its dissimilarity from the modern concept and the reason for its inapplicability with regard to modern distributed multicomputer systems. We justify the necessity to refine the definition of fault tolerance approved by the State Standards, as well as the necessity to specify three input parameters to be taken into account in the DMCS design methods: permitted fault models, permitted multiplicity of faults, permitted fault sequence capabilities. We formulate the questions that must be answered in order to design a truly reliable, fault-tolerant system and consider the application areas of the failure- and fault-tolerant control systems for complex network and distributed objects. System, functional, and test diagnostics serve as the basis for building unattended failure- and fault-tolerant systems. The concept of self-managed degradation (with the DMCS eventually proceeding to a safe shutdown at a critical level of degradation) is a means to increase the DMCS active life. We consider the issues related to the diagnosis of multiple faults and present the main differences in ensuring fault tolerance between systems with broadcast communication channels and systems with point-to-point communication channels. The first part of the work mainly deals with the analysis of existing approaches and methods of organizing failure- and fault-tolerant computing in DMCS and the definition of the concept of fault-tolerance.

How close is our ΛCDM physical universe to de Sitter spacetime dS4?

2020 ◽  
Vol 29 (14) ◽  
pp. 2043032
Author(s):  
Arthur E. Fischer
Keyword(s):  
Error Function ◽  
Main Idea ◽  
Scale Factor ◽  
Fine Tuning ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
Physical Universe ◽  
Scale Factors ◽  
Sitter Spacetime ◽  
Physical Formula

We introduce a methodology for quantitatively measuring at all times in its evolution how close our physical spatially flat [Formula: see text] CDM universe with cosmological constant [Formula: see text] is to the de Sitter spacetime [Formula: see text] with de Sitter radius [Formula: see text]. The main idea in this study is to align the respective scale factors [Formula: see text] and [Formula: see text] of these two spacetimes, where de Sitter spacetime is taken with respect to a spatially flat foliation. This goal is accomplished by fine-tuning an adjustable parameter [Formula: see text] that arises naturally in the de Sitter scale factor by requiring that these scale factors be future-asymptotically convergent. Once this parameter is adjusted and the scale factors are aligned, we define a relative error function [Formula: see text] that computes as a function of time [Formula: see text] how close the scale factors of these two spacetimes are to one another. Our results quantify how close our physical [Formula: see text]CDM universe is to its corresponding de Sitter spacetime as both spacetimes converge as they expand. As an example of our results, we show that at the present time [Formula: see text][Formula: see text]Gy, to an accuracy of [Formula: see text], and at [Formula: see text][Formula: see text]Gy, to an accuracy of [Formula: see text], we can use de Sitter spacetime to model our own [Formula: see text]CDM universe. Our results also show by statistical analysis that with a confidence level of 68.3%, for [Formula: see text][Formula: see text]Gy, the scale factor [Formula: see text] of our [Formula: see text] universe and the scale factor [Formula: see text] of the corresponding de Sitter spacetime are indistinguishable to within the accuracy of current cosmological measurements.

Generalized ghost pilgrim dark energy in F(T,TG) cosmology

2016 ◽  
Vol 31 (25) ◽  
pp. 1650148 ◽  
Author(s):  
M. Sharif ◽  
Kanwal Nazir
Keyword(s):  
Dark Energy ◽  
Scale Factor ◽  
The Other ◽  
Frw Universe ◽  
Eos Parameter ◽  
Pilgrim Dark Energy ◽  
Pde Model ◽  
Scale Factors ◽  
Two Phases ◽  
Friedmann Robertson Walker

This paper is devoted to study the generalized ghost pilgrim dark energy (PDE) model in [Formula: see text] gravity with flat Friedmann–Robertson–Walker (FRW) universe. In this scenario, we reconstruct [Formula: see text] models and evaluate the corresponding equation of state (EoS) parameter for different choices of the scale factors. We assume power-law scale factor, scale factor for unification of two phases, intermediate and bouncing scale factor. We study the behavior of reconstructed models and EoS parameters graphically. It is found that all the reconstructed models show decreasing behavior for PDE parameter [Formula: see text]. On the other hand, the EoS parameter indicates transition from dust-like matter to phantom era for all choices of the scale factor except intermediate for which this is less than [Formula: see text]. We conclude that all the results are in agreement with PDE phenomenon.

Centrifuge modelling of ice and brittle materials

1991 ◽  
Vol 28 (6) ◽  
pp. 896-898 ◽  
Author(s):  
Andrew Palmer
Keyword(s):  
Crack Length ◽  
Key Words ◽  
Material Property ◽  
Brittle Materials ◽  
Scale Factor ◽  
The Other ◽  
Field Observations ◽  
Linear Scale ◽  
Centrifuge Modelling ◽  
Scaling Rule

Centrifuge modelling of a system that deforms by repeated fracture is analysed. If the governing crack length during repeated fracture is a material property, classical centrifuge modelling continues to apply. If, on the other hand, the cracks and ice fragments scale with the system as a whole, a different scaling rule follows: the acceleration imposed in the centrifuge should be the 3/2 power of the linear scale factor. Though at first sight surprising, this rule is consistent with field observations. Key words: ice, centrifuge modelling, fracture.

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