Spherical Bessel transform via exponential sum approximation of spherical Bessel function

Hankel transform (or Fourier-Bessel transform) is a fundamental tool in many areas of mathematics and engineering, including analysis, partial differential equations, probability, analytic number theory, data analysis, etc. In this article, we prove an analog of Titchmarsh's theorem for the Hankel transform of functions satisfying the Hankel-Lipschitz condition.

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An exponential sum involving Fourier coefficients of eigenforms for $$SL(2,\pmb {{\mathbb {Z}}})$$

The Ramanujan Journal ◽

10.1007/s11139-020-00255-0 ◽

2020 ◽

Author(s):

Ratnadeep Acharya ◽

Saurabh Kumar Singh

Keyword(s):

Fourier Coefficients ◽

Exponential Sum

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The Power Losses in Cable Lines Supplying Nonlinear Loads

Energies ◽

10.3390/en14051374 ◽

2021 ◽

Vol 14 (5) ◽

pp. 1374

Author(s):

Bartosz Rozegnał ◽

Paweł Albrechtowicz ◽

Dominik Mamcarz ◽

Monika Rerak ◽

Maciej Skaza

Keyword(s):

Bessel Function ◽

Cross Section ◽

Power Loss ◽

Sine Wave ◽

Active Power ◽

New Method ◽

Power Losses ◽

Nonlinear Loads ◽

Current Harmonics ◽

Cable Lines

This paper presents the skin effect impact on the active power losses in the sheathless single-core cables/wires supplying nonlinear loads. There are significant conductor losses when the current has a distorted waveform (e.g., the current supplying diode rectifiers). The authors present a new method for active power loss calculation. The obtained results have been compared to the IEC-60287-1-1:2006 + A1:2014 standard method and the method based on the Bessel function. For all methods, the active power loss results were convergent for small-cable cross-section areas. The proposed method gives smaller power loss values for these cable sizes than the IEC and Bessel function methods. For cable cross-section areas greater than 185 mm2, the obtained results were better than those for the other methods. There were also analyses of extra power losses for distorted currents compared to an ideal 50 Hz sine wave for all methods. The new method is based on the current penetration depth factor calculated for every considered current harmonics, which allows us to calculate the precise equivalent resistance for any cable size. This research is part of our work on a cable thermal analysis method that has been developed.

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