scholarly journals Analytical studies on the Sunyaev–Zeldovich effect in the cluster of galaxies for three Lorentz frames – II. Single integral formula

2014 ◽  
Vol 441 (4) ◽  
pp. 3018-3027 ◽  
Author(s):  
Satoshi Nozawa ◽  
Yasuharu Kohyama
2021 ◽  
Vol 9 (1) ◽  
pp. 17-23
Author(s):  
Ayyidatul Imaniyah ◽  
Keto Susanto ◽  
Andika Setyo Budi Lestari

Integral can be used to determine several quantities, one of them is to determine the length of a curve in the plane. It can be applied to prove the circumference formula of a circle. This research aims to explain how to prove the circumference formula of a circle using a single integral expressed in both cartesian and polar coordinates. The method used in this research is a study of literature. The result of this research shows that proving the circumference of a circle can be done by determining the implicit derivative of the circle equation. Then, the circle equation and its implicit derivative are substituted into the integral formula for determining the length of the curve in both cartesian and polar coordinates so that the circumference formula of a circle is obtained.


1982 ◽  
Vol 43 (2) ◽  
pp. 189-195 ◽  
Author(s):  
Claude Esling ◽  
Jacques Muller ◽  
Hans-Joachim Bunge
Keyword(s):  

Author(s):  
B. P. Khozyainov

The article carries out the experimental and analytical studies of three-blade wind power installation and gives the technique for measurements of angular rate of wind turbine rotation depending on the wind speeds, the rotating moment and its power. We have made the comparison of the calculation results according to the formulas offered with the indicators of the wind turbine tests executed in natural conditions. The tests were carried out at wind speeds from 0.709 m/s to 6.427 m/s. The wind power efficiency (WPE) for ideal traditional installation is known to be 0.45. According to the analytical calculations, wind power efficiency of the wind turbine with 3-bladed and 6 wind guide screens at wind speedsfrom 0.709 to 6.427 is equal to 0.317, and in the range of speed from 0.709 to 4.5 m/s – 0.351, but the experimental coefficient is much higher. The analysis of WPE variations shows that the work with the wind guide screens at insignificant average air flow velocity during the set period of time appears to be more effective, than the work without them. If the air flow velocity increases, the wind power efficiency gradually decreases. Such a good fit between experimental data and analytical calculations is confirmed by comparison of F-test design criterion with its tabular values. In the design of wind turbines, it allows determining the wind turbine power, setting the geometrical parameters and mass of all details for their efficient performance.


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