scholarly journals Consensus under general convexity

2007 ◽  
Author(s):  
S. Emre Tuna ◽  
Rodolphe Sepulchre
Keyword(s):  
General Convexity

scholarly journals Evidence for a general convexity assumption in 6-month-old infants.

2013 ◽  
Vol 13 (9) ◽  
pp. 736-736
Author(s):  
J. Mathison ◽  
S. Corrow ◽  
V. Adamson ◽  
C. Granrud ◽  
A. Yonas
Keyword(s):  
Convexity Assumption ◽  
General Convexity

Six-Month-Old Infants' Perception of the Hollow Face Illusion: Evidence for a General Convexity Bias

Perception ◽  
10.1068/p7689 ◽  
2014 ◽  
Vol 43 (11) ◽  
pp. 1177-1190 ◽  
Author(s):  
Sherryse L Corrow ◽  
Jordan Mathison ◽  
Carl E Granrud ◽  
Albert Yonas
Keyword(s):  
Visual System ◽  
Binocular Viewing ◽  
Viewing Condition ◽  
Binocular Condition ◽  
General Convexity ◽  
As If

Corrow, Granrud, Mathison, and Yonas (2011, Perception, 40, 1376–1383) found evidence that 6-month-old infants perceive the hollow face illusion. In the present study we asked whether 6-month-old infants perceive illusory depth reversal for a nonface object and whether infants' perception of the hollow face illusion is affected by mask orientation inversion. In experiment 1 infants viewed a concave bowl, and their reaches were recorded under monocular and binocular viewing conditions. Infants reached to the bowl as if it were convex significantly more often in the monocular than in the binocular viewing condition. These results suggest that infants perceive illusory depth reversal with a nonface stimulus and that the infant visual system has a bias to perceive objects as convex. Infants in experiment 2 viewed a concave face-like mask in upright and inverted orientations. Infants reached to the display as if it were convex more in the monocular than in the binocular condition; however, mask orientation had no effect on reaching. Previous findings that adults' perception of the hollow face illusion is affected by mask orientation inversion have been interpreted as evidence of stored-knowledge influences on perception. However, we found no evidence of such influences in infants, suggesting that their perception of this illusion may not be affected by stored knowledge, and that perceived depth reversal is not face-specific in infants.

scholarly journals Pebbles, natural and artificial, Their shape under various conditions of abrasion

1944 ◽  
Vol 182 (991) ◽  
pp. 321-335 ◽  
Keyword(s):  
Sheet Glass ◽  
Cylindrical Vessel ◽  
Polished Surface ◽  
Abrasive Material ◽  
Equatorial Diameter ◽  
Oblate Spheroids ◽  
The One ◽  
General Convexity ◽  
The Given ◽  
Made In

This paper may be regarded as the sequel to an earlier one (Rayleigh 1942) and deals with the formation of artificial pebbles under controlled conditions, and their comparison with the pebbles found in nature. As before, symmetrical pebbles having an approximate figure of revolution are chiefly considered. A series of marble pebbles, made experimentally by attrition of rectangular blocks by fragments of hard steel, is shown in comparison with natural pebbles. The series ranges from cylinders with rounded ends, to an approximately spherical figure, and then on to oblate forms ending in a disk with rounded edges. These are closely matched by a series of natural flint pebbles collected from the glacial gravel. Prolate or oblate spheroids, differing widely from the sphere, are not obtained in experiments of this kind, nor are they found in the gravel formation. An alternative way of making pebbles in the laboratory is by ‘pothole’ action. The experimental pothole is a cylindrical vessel containing water with a paddle revolving coaxially with it. The paddle maintains a vortex, which carries the stone round. Either the bottom or the wall of the vessel may be made of abrasive material. When the bottom is abrasive, the pebbles are of such a shape that they lie inside a spheroid of the same polar and equatorial diameter in contrast to the previous case, where they lie outside. When the sides are abrasive, the form tends to the spherical. This effect appears to depend on the well-known tendency of an elongated body to set itself athwart the stream; thus the end tends to rub against the abrasive wall. Spherical pebbles of considerable perfection can be made in this way. As regards concave pebbles, the discussion in the former paper is withdrawn. A new method of experiment is used, depending on the pitting of a small square of sheet glass, revolved in a box with the abrasive. If many broken flints are used, each comparable in size with the glass, the latter is chiefly pitted in the middle, tending to form a concavity. If a single flint only is used, the pittings on the polished surface are uniformly distributed, and there is no tendency to form a concavity. It would seem, therefore, that concavity is produced by the edges being more protected than the middle, the protection being given by pebbles other than the one which is making the wound at the given moment. This action is apart from the rounding of the edges, which ultimately spreads, invading the concavity and producing a general convexity as in ordinary pebbles.

scholarly journals Multidimensional general convexity for stochastic processes and associated with Hermite-Hadamard type integral inequalities

2019 ◽  
Vol 23 (Suppl. 6) ◽  
pp. 1971-1979 ◽  
Author(s):  
Nurgul Okur
Keyword(s):  
Stochastic Processes ◽  
Integral Inequalities ◽  
Type Integral ◽  
General Convex ◽  
General Convexity ◽  
Convex Stochastic Processes

In this study, we idetified multidimensional general convex stochastic processes. Concordantly, we obtained some important results related stochastic processes. Moreover, we derived some Hermite-Hadamard type integral inequalities for these stochastic processes.

scholarly journals Duality for a non-differentiable programming problem

1997 ◽  
Vol 55 (1) ◽  
pp. 29-44 ◽  
Author(s):  
J. Zhang ◽  
B. Mond
Keyword(s):  
Programming Problem ◽  
Second Order ◽  
Duality Theorems ◽  
General Convexity

A generalised dual to a non-differentiable programming problem is given and duality established under general convexity and invexity conditions. A second order dual is also given and duality theorems proved under generalised second order invexity condition.

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