Apparent Relative Size in the Judgement of Apparent Distance

Perception ◽  
1983 ◽  
Vol 12 (6) ◽  
pp. 683-700 ◽  
Author(s):  
Denis K Burnham
Keyword(s):  
Linear Function ◽  
Stimulus Pair ◽  
Relative Size ◽  
Apparent Distance ◽  
Relative Area ◽  
The Real ◽  
Comparison Figure ◽  
Series Of Experiments ◽  
Different Shapes ◽  
Real Area

In experiment 1 judgements of the apparent distance of comparison figures (squares or triangles) were obtained under reduction conditions. These comparison figures were either shaped the same as or different from equidistant standard figures, and were half, equal to, or double the area of the standard figures. Apparent distance was found to be a linear function of the relative area of the comparison figure both in same-shape and different-shape stimulus pair conditions. In addition, apparent distance was found to be a function of perceived area, because in different-shape conditions triangles were generally seen to be closer than squares even when the real area of the standard and comparison was equal. The results of experiment 2 and 3 provide some evidence that the effect of different shapes of standard and comparison on apparent distance is due to the observers' perception of the height rather than the area of figures. The series of experiments shows that the traditional transactionalists' explanation of relative size as a cue for distance is inadequate.

Analysis of the Real Area of Contact Between a Polymeric Magnetic Medium and a Rigid Surface

1984 ◽  
Vol 106 (1) ◽  
pp. 26-34 ◽  
Author(s):  
Bharat Bhushan
Keyword(s):  
Complex Modulus ◽  
Critical Value ◽  
Computer Applications ◽  
Hard Material ◽  
Rigid Surface ◽  
Magnetic Medium ◽  
The Real ◽  
Real Area Of Contact ◽  
The Mean ◽  
Real Area

The statistical analysis of the real area of contact proposed by Greenwood and Williamson is revisited. General and simplified equations for the mean asperity real area of contact, number of contacts, total real area of contact, and mean real pressure as a function of apparent pressure for the case of elastic junctions are presented. The critical value of the mean asperity pressure at which plastic flow starts when a polymer contacts a hard material is derived. Based on this, conditions of elastic and plastic junctions for polymers are defined by a “polymer” plasticity index, Ψp which depends on the complex modulus, Poisson’s ratio, yield strength, and surface topography. Calculations show that most dynamic contacts that occur in a computer-magnetic tape are elastic, and the predictions are supported by experimental evidence. Tape wear in computer applications is small and decreases Ψp by less than 10 percent. The theory presented here can also be applied to rigid and floppy disks.

scholarly journals An induced real quaternion spherical ensemble of random matrices

2017 ◽  
Vol 06 (01) ◽  
pp. 1750001
Author(s):  
Anthony Mays ◽  
Anita Ponsaing
Keyword(s):  
Real Line ◽  
Relative Size ◽  
Functional Differentiation ◽  
The Real ◽  
Real Quaternion ◽  
Large Matrix ◽  
Wall Boundary Conditions ◽  
The Matrix ◽  
Soft Wall ◽  
Point Correlation

We study the induced spherical ensemble of non-Hermitian matrices with real quaternion entries (considering each quaternion as a [Formula: see text] complex matrix). We define the ensemble by the matrix probability distribution function that is proportional to [Formula: see text] These matrices can also be constructed via a procedure called ‘inducing’, using a product of a Wishart matrix (with parameters [Formula: see text]) and a rectangular Ginibre matrix of size [Formula: see text]. The inducing procedure imposes a repulsion of eigenvalues from [Formula: see text] and [Formula: see text] in the complex plane with the effect that in the limit of large matrix dimension, they lie in an annulus whose inner and outer radii depend on the relative size of [Formula: see text], [Formula: see text] and [Formula: see text]. By using functional differentiation of a generalized partition function, we make use of skew-orthogonal polynomials to find expressions for the eigenvalue [Formula: see text]-point correlation functions, and in particular the eigenvalue density (given by [Formula: see text]). We find the scaled limits of the density in the bulk (away from the real line) as well as near the inner and outer annular radii, in the four regimes corresponding to large or small values of [Formula: see text] and [Formula: see text]. After a stereographic projection, the density is uniform on a spherical annulus, except for a depletion of eigenvalues on a great circle corresponding to the real axis (as expected for a real quaternion ensemble). We also form a conjecture for the behavior of the density near the real line based on analogous results in the [Formula: see text] and [Formula: see text] ensembles; we support our conjecture with data from Monte Carlo simulations of a large number of matrices drawn from the [Formula: see text] induced spherical ensemble. This ensemble is a quaternionic analog of a model of a one-component charged plasma on a sphere, with soft wall boundary conditions.

A ousadia do π ser racional

2020 ◽  
Author(s):  
Sidney Silva
Keyword(s):  
Rational Number ◽  
Pythagorean Theorem ◽  
Regular Polygons ◽  
The Real ◽  
Mathematical Question ◽  
Lower Limits ◽  
Mathematical Constant ◽  
Real Area

Pi (π) is used to represent the most known mathematical constant. By definition, π is the ratio of the circumference of a circle to its diameter. In other words, π is equal to the circumference divided by the diameter (π = c / d). Conversely, the circumference is equal to π times the diameter (c = π . d). No matter how big or small a circle is, pi will always be the same number. The first calculation of π was made by Archimedes of Syracuse (287-212 BC) who approached the area of a circle using the Pythagorean Theorem to find the areas of two regular polygons: the polygon inscribed within the circle and the polygon within which circle was circumscribed. Since the real area of the circle is between the areas of the inscribed and circumscribed polygons, the polygon areas gave the upper and lower limits to the area of the circle. Archimedes knew he had not found the exact value of π, but only an approximation within these limits. In this way, Archimedes showed that π is between 3 1/7 (223/71) and 3 10/71 (22/7). This research demonstrates that the value of π is 3.15 and can be represented by a fraction of integers, a/b, being therefore a Rational Number. It also demonstrates by means of an exercise that π = 3.15 is exact in 100% in the mathematical question.

The Two-Sided Factorization of Ordinary Differential Operators

1980 ◽  
Vol 32 (5) ◽  
pp. 1045-1057 ◽  
Author(s):  
Patrick J. Browne ◽  
Rodney Nillsen
Keyword(s):  
Differential Operator ◽  
Linear Function ◽  
Bilinear Form ◽  
Differential Operators ◽  
Real Numbers ◽  
The Real ◽  
Differentiable Functions ◽  
Ordinary Differential Operators ◽  
Image Position

Throughout this paper we shall use I to denote a given interval, not necessarily bounded, of real numbers and Cn to denote the real valued n times continuously differentiable functions on I and C0 will be abbreviated to C. By a differential operator of order n we shall mean a linear function L:Cn → C of the form1.1where pn(x) ≠ 0 for x ∊ I and pi ∊ Cj 0 ≦ j ≦ n. The function pn is called the leading coefficient of L.It is well known (see, for example, [2, pp. 73-74]) thai a differential operator L of order n uniquely determines both a differential operator L* of order n (the adjoint of L) and a bilinear form [·,·]L (the Lagrange bracket) so that if D denotes differentiation, we have for u, v ∊ Cn,1.2

Perception of Slope and Distance in Photographs and in the Real World

Perception ◽  
1996 ◽  
Vol 25 (1_suppl) ◽  
pp. 33-33 ◽  
Author(s):  
I Davies ◽  
J Howes ◽  
J Huber ◽  
J Nicholls
Keyword(s):  
Individual Differences ◽  
Power Function ◽  
Real World ◽  
Natural World ◽  
Observation Point ◽  
Scale Factor ◽  
Large Individual ◽  
The Real ◽  
Series Of Experiments ◽  
Natural Slopes

We report a series of experiments in which spatial judgments of the real world were compared with equivalent judgments of photographs of the real-world scenes. In experiment 1, subjects judged the angle from the horizontal of natural slopes. Judgments of slope correlated with true slope (r=0.88) but judgments were in general overestimates. Equivalent judgments of slope in photographs again correlated with true slope (r=0.91) but judgments tended to be overestimates for small angles (6°) and underestimates for larger angles (up to 25°). In experiment 2 slope judgments were made under laboratory conditions rather than in the natural world. The slopes, which were viewed monocularly, varied from 5° – 45°, and were either plain, or textured, or included perspective information (a rectangle drawn on the surface) or had both texture and perspective. Judgments were overestimates, but the correlation with true slope was high (r=0.97). Slopes with either texture or perspective were judged more accurately than plain slopes, but combining texture and perspective information conferred no further benefit. Judgment of the angle of the same slopes in photographs produced similar results, but the degree of overestimation (closer to the vertical) was greater than for the real slopes. In experiment 3, subjects either judged the distance of landmarks ranging from 200 m to 5000 m from the observation point, or judged distance to the landmarks in photographs. In both cases subjects' judgments were well described by a power function with exponents close to one. Although there are large individual differences, subjects' judgments of slope and distance are accurate to a scale factor, and photographs yield similar judgments to real scenes.

A Relationship Between Autocorrelation Length and Adhesive Friction Behavior of Rough Surfaces

2005 ◽  
Author(s):  
Yilei Zhang ◽  
Sriram Sundararajan
Keyword(s):  
Rough Surface ◽  
Spatial Information ◽  
Roughness Parameter ◽  
Hertzian Contact ◽  
Root Mean Square Roughness ◽  
Friction Behavior ◽  
The Real ◽  
Real Area Of Contact ◽  
Autocorrelation Length ◽  
Real Area

Autocorrelation Length (ACL) is a surface roughness parameter that provides spatial information of surface topography that is not included in amplitude parameters such as Root Mean Square roughness. This paper presents a statistical relation between ACL and the real area of contact, which is used to study the adhesive friction behavior of a rough surface. The influence of ACL on profile peak distribution is studied based on Whitehouse and Archard’s classical analysis, and their results are extended to compare profiles from different surfaces. With the knowledge of peak distribution, the real area of contact of a rough surface with a flat surface can be calculated using Hertzian contact mechanics. Numerical calculation shows that real area of contact increases with decreasing of ACL under the same normal load. Since adhesive friction force is proportional to real area of contact, this suggests that the adhesive friction behavior of a surface will be inversely proportional to its ACL. Results from microscale friction experiments on polished and etched silicon surfaces are presented to verify the analysis.

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