scholarly journals Refined Estimates and Generalizations of Inequalities Related to the Arctangent Function and Shafer’s Inequality

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Branko Malešević ◽  
Marija Rašajski ◽  
Tatjana Lutovac
Keyword(s):  
Shafer’S Inequality ◽  
Arctangent Function

We give some sharper refinements and generalizations of inequalities related to Shafer’s inequality for the arctangent function, stated in Theorems  1, 2,  and  4 in Mortici and Srivastava, 2014, by C. Mortici and H.M. Srivastava.

Estimates for the arctangent function related to Shafer's inequality

2014 ◽  
Vol 136 (2) ◽  
pp. 263-270 ◽  
Author(s):  
Cristinel Mortici ◽  
H. M. Srivastava
Keyword(s):  
Shafer’S Inequality ◽  
Arctangent Function

Full Quadrant Approximations for the Arctangent Function [Tips and Tricks]

2013 ◽  
Vol 30 (1) ◽  
pp. 130-135 ◽  
Author(s):  
Xavier Girones ◽  
Carme Julia ◽  
Domenec Puig
Keyword(s):  
Tips And Tricks ◽  
Arctangent Function

Speed and accuracy improvements in standard algorithm for prismatic gravitational field

2020 ◽  
Vol 222 (3) ◽  
pp. 1898-1908
Author(s):  
Toshio Fukushima
Keyword(s):  
Gravitational Field ◽  
Exact Formula ◽  
New Method ◽  
Gravity Gradient ◽  
Gradient Tensor ◽  
Gravity Gradient Tensor ◽  
Triple Difference ◽  
Transcendental Functions ◽  
Arctangent Function ◽  
Speed And Accuracy

SUMMARY By utilizing the addition theorems of the arctangent function and the logarithm, we developed a new expression of Bessel’s exact formula to compute the prismatic gravitational field using the triple difference of certain analytic functions. The use of the new expression is fast since the number of transcendental functions required is significantly reduced. The numerical experiments show that, in computing the gravitational potential, the gravity vector, and the gravity gradient tensor of a uniform rectangular parallelepiped, the new method runs 2.3, 2.3 and 3.7 times faster than Bessel’s method, respectively. Also, the new method achieves a slight increase in the computing precision. Therefore, the new method can be used in place of Bessel’s method in any situation. The same approach is applicable to the geomagnetic field computation.

Phase Correction of Vibrational Circular Dichroic Features

1988 ◽  
Vol 42 (2) ◽  
pp. 336-341 ◽  
Author(s):  
Colleen A. McCoy ◽  
James A. De Haseth
Keyword(s):  
Phase Error ◽  
Absorption Spectrometry ◽  
Phase Correction ◽  
Phase Curve ◽  
Phase Retardation ◽  
Normal Absorption ◽  
Ft Ir ◽  
Arctangent Function ◽  
Circular Dichroic ◽  
Zero Phase

Several sources of phase-correction-induced spectral anomalies in FT-IR vibrational circular dichroism (VCD) spectra have been investigated. Misidentification of the zero-phase retardation position in dichroic interferograms that exhibit no optical or electronic bias can produce spectral errors. Production of such errors is from the introduction of linear phase error into the phase curve. When the zero-phase retardation position is correctly identified, other spectral anomalies, such as “reflected peaks,” can appear in VCD spectra. These peaks are readily observed in quarterwave plate reference spectra. The anomalies are directly correlated to the arctangent function used to define the phase curve and result only from the nature of the VCD signal. VCD spectra can exhibit negative, as well as positive, peaks; consequently the phase correction must be designed to accommodate negative features. Both Mertz and Forman phase-correction algorithms have been modified to correct the phase of VCD interferograms without error. Such corrections are not necessary, or even desirable, for normal absorption spectrometry.

Error analysis of phase detector based on Clarke transform and arctangent function in polluted grids

2015 ◽  
Vol 127 ◽  
pp. 160-164 ◽  
Author(s):  
Ignacio Carugati ◽  
Carlos M. Orallo ◽  
Sebastian Maestri ◽  
Patricio G. Donato ◽  
Daniel Carrica
Keyword(s):  
Error Analysis ◽  
Phase Detector ◽  
Arctangent Function

scholarly journals The correlation functions of the regular tetrahedron and octahedron

2014 ◽  
Vol 47 (4) ◽  
pp. 1445-1448 ◽  
Author(s):  
Salvino Ciccariello
Keyword(s):  
Correlation Functions ◽  
Rational Functions ◽  
Regular Tetrahedron ◽  
Numerical Determination ◽  
Algebraic Form ◽  
Autocorrelation Functions ◽  
Regular Octahedron ◽  
Size Dispersion ◽  
Arctangent Function

The expressions of the autocorrelation functions (CFs) of the regular tetrahedron and the regular octahedron are reported. They have an algebraic form that involves the arctangent function and rational functions of r and (a + br 2)1/2, a and b being appropriate integers and r a distance. The CF expressions make the numerical determination of the corresponding scattering intensities fast and accurate even in the presence of a size dispersion.

A note on the numerical evaluation of arctangent function

1989 ◽  
Vol 23 (3) ◽  
pp. 8-12 ◽  
Author(s):  
S. Moritsugu ◽  
M. Matsumoto
Keyword(s):  
Numerical Evaluation ◽  
Arctangent Function
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