scholarly journals Integral Means and Arc length of Starlike Log-harmonic Mappings

2011 ◽  
Vol 2011 ◽  
pp. 1-7
Author(s):  
Z. Abdulhadi ◽  
Y. Abu Muhanna
Keyword(s):  
Upper Bound ◽  
Harmonic Mappings ◽  
Arc Length ◽  
Integral Means

We use star functions to determine the integral means for starlike log-harmonic mappings. Moreover, we include the upper bound for the arc length of starlike log-harmonic mappings.

THE MODULUS OF THE IMAGE ANNULI UNDER UNIVALENT HARMONIC MAPPINGS AND A CONJECTURE OF NITSCHE

2001 ◽  
Vol 64 (2) ◽  
pp. 369-384 ◽  
Author(s):  
ABDALLAH LYZZAIK
Keyword(s):  
Upper Bound ◽  
Harmonic Mapping ◽  
Ring Domain ◽  
Harmonic Mappings ◽  
Univalent Harmonic Mappings

The object of the paper is to show that if f is a univalent, harmonic mapping of the annulus A(r, 1) = {z : r < [mid ]z[mid ] < 1} onto the annulus A(R, 1), and if s is the length of the segment of the Grötzsch ring domain associated with A(r, 1), then R < s. This gives the first, quantitative upper bound of R, which relates to a question of J. C. C. Nitsche that he raised in 1962. The question of whether this bound is sharp remains open.

The visual perception of arc length on a real surface

1997 ◽  
Author(s):  
J. Farley Norman ◽  
Joseph S. Lappin ◽  
Hideko F. Norman
Keyword(s):  
Visual Perception ◽  
Real Surface ◽  
Arc Length

Dimensions of plane and solid angles and their units in the International System of Units (SI)

2020 ◽  
pp. 26-32
Author(s):  
M. I. Kalinin ◽  
L. K. Isaev ◽  
F. V. Bulygin
Keyword(s):  
Solid Angle ◽  
International System ◽  
International Committee ◽  
Plane Angle ◽  
Arc Length ◽  
Weights And Measures ◽  
International System Of Units ◽  
System Of Units ◽  
In Series ◽  
Solid Angles

The situation that has developed in the International System of Units (SI) as a result of adopting the recommendation of the International Committee of Weights and Measures (CIPM) in 1980, which proposed to consider plane and solid angles as dimensionless derived quantities, is analyzed. It is shown that the basis for such a solution was a misunderstanding of the mathematical formula relating the arc length of a circle with its radius and corresponding central angle, as well as of the expansions of trigonometric functions in series. From the analysis presented in the article, it follows that a plane angle does not depend on any of the SI quantities and should be assigned to the base quantities, and its unit, the radian, should be added to the base SI units. A solid angle, in this case, turns out to be a derived quantity of a plane angle. Its unit, the steradian, is a coherent derived unit equal to the square radian.

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