Typical dimension of the graph of certain functions

1995 ◽  
Vol 119 (4) ◽  
pp. 303-320 ◽  
Author(s):  
J�rg Schmeling ◽  
Reinhard Winkler
Keyword(s):  
Typical Dimension

scholarly journals Possible Mechanisms of Single and Multiple Star Formation

1958 ◽  
Vol 8 ◽  
pp. 1017-1019
Author(s):  
G. J. Odgers ◽  
R. W. Stewart
Keyword(s):  
Star Formation ◽  
Dimensional Analysis ◽  
Gravitational Collapse ◽  
Gravitational Constant ◽  
Characteristic Velocity ◽  
Multiple Star ◽  
Typical Dimension ◽  
Jeans Criterion ◽  
Image Position

If we suppose that at least some stars are the result of the gravitational collapse of HI clouds, it seems necessary to consider Jeans' criterion. This can be derived by a number of arguments, but for our purpose it is sufficient to consider it a result of dimensional analysis, and we get where G is the gravitational constant, M is a typical dimension, and V is a characteristic velocity comprising all velocities interior to the region of gas being considered.

The generation of internal waves by vibrating elliptic cylinders. Part 2. Approximate viscous solution

1997 ◽  
Vol 351 ◽  
pp. 119-138 ◽  
Author(s):  
D. G. HURLEY ◽  
G. KEADY
Keyword(s):  
Approximate Solution ◽  
Circular Cylinder ◽  
Flow Field ◽  
Cross Section ◽  
Similarity Solution ◽  
Internal Gravity Waves ◽  
Approximate Theory ◽  
Viscous Effects ◽  
Typical Dimension ◽  
Viscous Solution

An approximate theory is given for the generation of internal gravity waves in a viscous Boussinesq fluid by the rectilinear vibrations of an elliptic cylinder. A parameter λ which is proportional to the square of the ratio of the thickness of the oscillatory boundary layer that surrounds the cylinder to a typical dimension of its cross-section is introduced. When λ[Lt ]1 (or equivalently when the Reynolds number R[Gt ]1), the viscous boundary condition at the surface of the cylinder may to first order in λ be replaced by the inviscid one. A viscous solution is proposed for the case λ[Lt ]1 in which the Fourier representation of the stream function found in Part 1 (Hurley 1997) is modified by including in the integrands a factor to account for viscous dissipation. In the limit λ→0 the proposed solution becomes the inviscid one at each point in the flow field.For ease of presentation the case of a circular cylinder of radius a is considered first and we take a to be the typical dimension of its cross-section in the definition of λ above. The accuracy of the proposed approximate solution is investigated both analytically and numerically and it is concluded that it is accurate throughout the flow field if λ is sufficiently small, except in a small region near where the characteristics touch the cylinder where viscous effects dominate.Computations indicate that the velocity on the centreline on a typical beam of waves, at a distance s along the beam from the centre of the cylinder, agrees, within about 1%, with the (constant) inviscid values provided λs/a is less than about 10−3. This result is interpreted as indicating that those viscous effects which originate from the characteristics that touch the cylinder (places where the inviscid velocity is singular) reach the centreline of the beam when λs/a is about 10−3. For larger values of s, viscous effects are significant throughout the beam and the velocity profile of the beam changes until it attains, within about 1% when λs/a is about 2, the value given by the similarity solution obtained by Thomas & Stevenson (1972). For larger values of λs/a, their similarity solution applies.In an important paper Makarov et al. (1990) give an approximate solution for the circular cylinder that is very similar to ours. However, it does not reduce to the inviscid one when the viscosity is taken to be zero.Finally it is shown that our results for a circular cylinder apply, after small modifications, to all elliptical cylinders.

A STUDY OF YBa2Cu3O9−δ TYPE SUPERCONDUCTING SINGLE CRYSTALS

1987 ◽  
Vol 01 (04) ◽  
pp. 167-169
Author(s):  
H.X. LU ◽  
J. WU ◽  
X.Y. ZHANG ◽  
X.K. GAO ◽  
X.J. LI ◽  
...  
Keyword(s):  
Single Crystals ◽  
Typical Dimension

Single crystals of Y-Ba-Cu-O type superconductors having the typical dimension 0.5 to 1 mm in the plane of the plate have been prepared. The analysis of composition show that they correspond to YBa2Cu3O9−δ. Laue photographs, which prove the samples to be single crystals, show some diffraction spots instead of rings. The measurement of susceptibility and other measurements have been performed.

The Effects of Counterfactual Attacks on the Morality and Leadership of Different Professionals

2018 ◽  
Vol 49 (3) ◽  
pp. 154-167 ◽  
Author(s):  
Mauro Bertolotti ◽  
Patrizia Catellani
Keyword(s):  
Past Research ◽  
Social Judgments ◽  
Personality Dimensions ◽  
Typical Dimension ◽  
Professional Category

Abstract. Past research has offered contrasting results regarding the effects of attacks on social judgments. In three experiments, we investigated the effects of counterfactual (“If only…”) and non-counterfactual attacks on the morality versus leadership of politicians versus entrepreneurs. First, participants rated morality as the most desirable, but least typical dimension of politicians, and leadership as the most desirable and most typical dimension of entrepreneurs (Study 1). Then, counterfactual attacks led to poorer evaluation of the attacked target and better evaluation of the attacking source as compared to non-counterfactual attacks, especially when counterfactuals were focused on the most desirable dimension for the professional category of the attacked target (Study 2). Similar results emerged when the typicality of the attacked dimension was manipulated (Study 3). Discussion focuses on the higher success of attacks on desirable personality dimensions and of counterfactual attacks as compared to other attacks.

Representational Value, Meaningfulness, and Pronunciability in Serial Learning

1965 ◽  
Vol 16 (3) ◽  
pp. 997-1000 ◽  
Author(s):  
Pietro Badia ◽  
B. G. Rosenberg ◽  
Jonas Langer
Keyword(s):  
Serial Learning ◽  
Verbal Learning ◽  
Two Dimensions ◽  
Differential Effects ◽  
Typical Dimension ◽  
Learning Conditions ◽  
Serial Task ◽  
Relationship Of ◽  
The Relationship

60 Ss were randomly assigned to 1 of 4 verbal learning conditions involving a serial task. The differential effects on learning of stimuli representing referent dimensions (representational value) were contrasted with the more typical dimension of meaningfulness (association value). The relationship of pronunciability to those two dimensions was also evaluated. While data suggest that association value and, to some extent, representational value contribute to the variance, the possibility that pronunciability is basic to both these dimensions could no: be ruled out.

Diffraction by a spherical cap

1963 ◽  
Vol 59 (1) ◽  
pp. 197-209 ◽  
Author(s):  
D. P. Thomas
Keyword(s):  
Wave Equation ◽  
Steady State ◽  
Systematic Approach ◽  
Low Frequency ◽  
Higher Order ◽  
Wave Number ◽  
Systematic Method ◽  
Spherical Cap ◽  
Typical Dimension ◽  
Higher Order Terms

1. It was first observed by Rayleigh(17) in 1897 that low-frequency approximations to the solutions of the steady-state wave equation could be obtained from the solutions of the corresponding static problems. Rayleigh determined only the first term in the expansion of the solution in powers of the product of the wave number and a typical dimension. Many recent investigations have been concerned with deriving a systematic method of calculating the higher-order terms in the above expansion. Most of the problems which have been solved in this manner have been concerned with scattering by a disk or by a strip: the first systematic approach to these problems was that of Bouwkamp ((3), p. 71).

A STUDY OF YBa2Cu3O9−δ TYPE SUPERCONDUCTING SINGLE CRYSTALS

1987 ◽  
Vol 01 (02) ◽  
pp. 327-330 ◽  
Author(s):  
H.X. Lu ◽  
J. Wu ◽  
X.Y. Zhang ◽  
X.K. Gao ◽  
X.J. Li ◽  
...  
Keyword(s):  
Single Crystals ◽  
Typical Dimension

Single crystals of Y-Ba-Cu-O type superconductors having the typical dimension 0.5 to 1 mm in the plane of the plate have been prepared. The analysis of compositions show that they correspond to YBa2Cu3O9−δ . Laue photographs, which prove the samples to be single crystals, show some diffraction spots instead of rings. The measurement of susceptibility and other measurements have been performed.

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