Zobrazeno 1 - 10
of 40
pro vyhledávání: '"Abrarov, Sanjar M."'
Publikováno v:
AppliedMath 2024, 4(3), 868-888
In this work, we consider the properties of the two-term Machin-like formula and develop an algorithm for computing digits of $\pi$ by using its rational approximation. In this approximation, both terms are constructed by using a representation of $1
Externí odkaz:
http://arxiv.org/abs/2406.08510
Publikováno v:
Math. Comput. Appl. 2024, 29(2), 17
In this work, we develop a new iterative method for computing the digits of $\pi$ by argument reduction of the tangent function. This method combines a modified version of the iterative formula for $\pi$ with squared convergence that we proposed in a
Externí odkaz:
http://arxiv.org/abs/2312.05413
A generalized series expansion of the arctangent function based on the enhanced midpoint integration
Publikováno v:
AppliedMath 2023, 3(2), 395-405
In this work we derive a generalized series expansion of the acrtangent function by using the enhanced midpoint integration (EMI). Algorithmic implementation of the generalized series expansion utilizes two-step iteration without surd and complex num
Externí odkaz:
http://arxiv.org/abs/2302.01911
Publikováno v:
Mathematics 2022, 10(19), 3451
In this work we develop a new algorithm for the efficient computation of the Voigt/complex error function. In particular, in this approach we propose a two-domain scheme where the number of the interpolation grid-points is dependent on the input para
Externí odkaz:
http://arxiv.org/abs/2209.15378
Publikováno v:
Open Journal of Applied Sciences, 12(8), 2022, pp. 1477-1493
Previously we have proposed a new method of transforming quotients into integer reciprocals in the Machin-like formulas for $\pi$. As a further development, here we show how to generate a multi-term Machin-like formula for $\pi$ with a reduced Lehmer
Externí odkaz:
http://arxiv.org/abs/2202.13787
Publikováno v:
Journal of Integer Sequences, Vol. 25 (2022), Article 22.4.5
We present a new form of the Machin-like formula for $\pi$ that can be generated by using iteration. This form of the Machin-like formula may be promising for computation of the constant $\pi$ due to rapidly increasing integers at each step of the it
Externí odkaz:
http://arxiv.org/abs/2108.07718
Publikováno v:
Mathematics 2021, 9(17), 2162
In our earlier publication we have shown how to compute by iteration a rational number ${u_{2,k}}$ in the two-term Machin-like formula for pi of kind $$\frac{\pi}{4}=2^{k-1}\arctan\left(\frac{1}{u_{1,k}}\right)+\arctan\left(\frac{1}{u_{2,k}}\right),\
Externí odkaz:
http://arxiv.org/abs/2107.01027
Publikováno v:
Natural Science, 14(3), 2022, pp. 133-147
The Radiance Enhancement (RE) method was introduced for efficient detection of clouds from the space. Recently, we have also reported that due to high reflectance of combustion-originated smokes, this approach can also be generalized for detection of
Externí odkaz:
http://arxiv.org/abs/2104.07126
In our earlier publication we introduced the Spectrally Integrated Voigt Function (SIVF) as an alternative to the traditional Voigt function for the HITRAN-based applications [Quine & Abrarov, JQSRT 2013]. It was shown that application of the SIVF en
Externí odkaz:
http://arxiv.org/abs/2105.09891
Publikováno v:
Journal of Environmental Protection, 2021, 12, 717-733
The existing methods for detection of the cloud scenes are applied at relatively small spectral range within shortwave upwelling radiative wavelength flux. We have reported a new method for detection of the cloud scenes based on the Radiance Enhancem
Externí odkaz:
http://arxiv.org/abs/2102.02136