Concerning the numerical constant 0.16...

1981 ◽  
Vol 70 (5) ◽  
pp. 1530-1531
Author(s):  
Benjamin Bernfeld
Keyword(s):  
Numerical Constant

scholarly journals On a Simple Method for Calculating Laminar Boundary Layers

1954 ◽  
Vol 5 (1) ◽  
pp. 25-38 ◽  
Author(s):  
K. E. G. Wieghardt
Keyword(s):  
Boundary Layers ◽  
Parametric Method ◽  
Symmetric Flow ◽  
Numerical Constant ◽  
Simple Method ◽  
Plane Flow ◽  
Laminar Boundary Layers ◽  
Energy Equations

SummaryA simple one parametric method, due to A. Walz and based on the momentum and energy equations, for calculating approximately laminar boundary layers is extended to cover axi-symmetric flow as well as plane flow. The necessary computing work is reduced a little.Another known method which requires still less computing work is also extended for axi-symmetric flow and, with the amendment of a numerical constant, proves adequate for practical purposes.

scholarly journals Vertex Corrections in Gauge Theories for Two-dimensional Condensed Matter Systems

1998 ◽  
Vol 12 (16n17) ◽  
pp. 1673-1692 ◽  
Author(s):  
Peter Kopietz
Keyword(s):  
Gauge Field ◽  
Condensed Matter ◽  
Finite Energy ◽  
Energy Scale ◽  
Gauge Fields ◽  
Logarithmic Correction ◽  
Two Dimensional ◽  
Numerical Constant ◽  
Self Energy ◽  
Vertex Corrections

We calculate the self-energy of two-dimensional fermions that are coupled to transverse gauge fields, taking two-loop corrections into account. Given a bare gauge field propagator that diverges for small momentum transfers q as 1/qη, 1<η≤ 2, the fermionic self-energy without vertex corrections vanishes for small frequencies ω as Σ(ω)∝ ωγ with γ=2/(1+η)<1. We show that inclusion of the leading radiative correction to the fermion-gauge field vertex leads to Σ(ω)∝ωγ [1-aη ln (ω0/ω)], where aη is a positive numerical constant and ω0 is some finite energy scale. The negative logarithmic correction is consistent with the scenario that higher order vertex corrections push the exponent γ to larger values.

Maximal inequalities of Kahane–Khintchine's type in Orlicz spaces

1994 ◽  
Vol 115 (1) ◽  
pp. 175-190 ◽  
Author(s):  
Goran Peškir
Keyword(s):  
Invariance Principle ◽  
Orlicz Spaces ◽  
Orlicz Norm ◽  
Numerical Constant ◽  
Maximal Inequalities ◽  
Sharp Estimates ◽  
Bernoulli Sequence ◽  
Image Position ◽  
Donsker’S Invariance Principle

AbstractSeveral maximal inequalities of Kahane–Khintchine's type in certain Orlicz spaces are proved. The method relies upon Lévy's inequality and the technique established in [14] which is obtained by Haagerup–Young–Stechkin's best possible constants in the classical Khintchine inequalities. Moreover by using Donsker's invariance principle it is shown that the numerical constant in the inequality deduced by the method presented is nearly optimal: If is a Bernoulli sequence, and ‖ · ‖ψ denotes the Orlicz norm induced by the function then the following inequality is satisfied:for all a1,…, an and all n ≥ 1, and the best possible numerical constant which can take the place of lies in the interval ]. Sharp estimates of this type are also deduced for some other maximal inequalities in Orlicz spaces discovered in this paper.

scholarly journals The thermal conductivity of air

1919 ◽  
Vol 95 (668) ◽  
pp. 190-210 ◽  
Keyword(s):  
Thermal Conductivity ◽  
Specific Heat ◽  
Reasonable Agreement ◽  
Numerical Constant ◽  
Molecular Collision ◽  
Absolute Value ◽  
Absolute Determination ◽  
Methods Of Determination ◽  
And Performance

The thermal conductivity, k , of a gas is connected with its specific heat, C v , and its viscosity, η ; by the relation k = fη C v . The numerical constant, f , in this relation can be deduced theoretically, and various values, which are given later, from 1·25 to 2·5 have been obtained according to the law of force assumed to act in a molecular collision. Which of these laws of force holds is determined when k , η , and C v are accurately known for a number of gases. A large number of determinations of both the viscosity and specific heat of each of the more simply constituted gases have been made that are in reasonable agreement with one another, but, compared with these, the independent values of the thermal conductivities are fewer, in poorer agreement, and the methods of determination are more open to criticism both in conception and performance. Eucken has determined relative to air the conductivity of a number of gases; the accuracy of his experiments made a new absolute determination of k for air desirable. The investigation to be described was an attempt to supply an absolute value of the thermal conductivity of air by a method which would not be open to the objections which can be brought against all the methods previously used, excepting that of one observer. Heat in general is carried through a gas by conduction, radiation, and convection. In all past determinations of the thermal conductivity of gases, except those of Todd, the flow of heat by convection was present to an uncertain amount; in the experiments to be described it was absent.

Crystal growth and nucleation in two large diabase dikes

1970 ◽  
Vol 7 (2) ◽  
pp. 366-375 ◽  
Author(s):  
N. H. Gray
Keyword(s):  
Crystal Growth ◽  
Nucleation Rate ◽  
Unit Volume ◽  
Single Phase ◽  
Bulk Composition ◽  
Numerical Constant ◽  
N Value ◽  
Olivine Tholeiite

The total number of nuclei, Z, of a single phase formed in a unit volume of a crystallizing magma at the distance y from the contact of a semi-infinite intrusion is[Formula: see text]where n is a numerical constant determined by growth controlling process during the nucleation period and the value of m in the expression assumed for the nucleation rate, J[Formula: see text]The observed variation of Z for clinopyroxene and plagioclase from the contact towards the center of two large dikes appears to follow this relation. In the 106 m wide Kigaviarluk olivine tholeiite dike the value of n is significantly greater for the clinopyroxene (−2.2) than the plagioclase (−0.84). In the 60 m Grenville dike, a quartz tholeiite, the n value (−1.5) is the same for both minerals. The growth-controlling mechanisms of plagioclase and clinopyroxene appears to be sensitive to the bulk composition of the magma from which it is crystallizing.

A note on functions regular and bounded in the unit circle and small at a set of points near the circumference of the circle

1939 ◽  
Vol 35 (3) ◽  
pp. 382-388 ◽  
Author(s):  
B. J. Maitland
Keyword(s):  
Unit Circle ◽  
Numerical Constant ◽  
Image Position ◽  
Set Of Points

The following theorem was proved by Milloux:Theorem A. Suppose that f (z) is regular and that | f(z) | < 1 in the unit circle. Suppose also that the set of points in the circle | z | ≤ r′ < 1 at whichcannot be enclosed in circles, the sum of whose radii is equal to 2eh−1. Thenwhere K is a numerical constant.

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