Studies on the zeros of Bessel functions and methods for their computation: 3. Some new works on monotonicity, convexity, and other properties

Kerimov, M. K.

doi:10.1134/s0965542516120125

Cited by 3 publications

(2 citation statements)

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“…The Fourier representation is thus "complete" only in one-dimension, in transmission lines and as far field plane wave approximations. The convexity of zeroes [10] implies wavelengths decreasing with distance, and a distance dependence in interference patterns amplified by the present solutions.…”

Section: Introductionmentioning

confidence: 61%

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Parametric separation of variables and the complete propagation law

Guruprasad¹

2022

Preprint

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Solving partial differential equations by separation of variables is historically thought to require equating the parts to a constant. Shown, with robust observational support, is that equating to a function of time yields a dimension of novel solutions to the wave equation. They transform known solutions in time, represent Doppler with acceleration, and correct wave idealizations that wrongly constrained fundamental physics, as well as communication and spectrum use. This is a draft version meant to time-stamp & share for comments mainly the following: <ul> <li>discovery of incompleteness of Fourier's method and the full separation of variables for the wave equation (Section 2, Appendices A, B);</li> <li>discovery of Green's function wave solutions with intrinsic phase acceleration and expansion (Section 3);</li> <li>first explanation of the range data lags in the flyby anomalies (Sections 4, 5 and Appendix C);</li> <li>elegant proof of redundancy of quantization postulate (improving over arXiv:1602.04136, Appendix D); and</li> <li>possible redundancy of speed of light postulate over variable measuring rods and clocks (Section 7 conclusion).</li> </ul> An equivalence principle between true acceleration in Doppler and uplink transmitter frequency ramp appears already implied by the similarity of the anomalies with ramping (NEAR) and without (Rosetta 2005). Experimental verification is being planned, to be performed in a proposed prototype of an acceleration spectrum receiver under funding review.

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Section: Introductionmentioning

confidence: 61%

“…Next, as defined by the zeroes of spherical and cylindrical harmonics, respectively, the wavelengths in atomic and antenna radiation patterns, even ripples on a pond, are periodic only at infinity [10]. The Fourier representation is thus "complete" only in one-dimension, in transmission lines and as far field plane wave approximations.…”

Section: Introductionmentioning

confidence: 99%