On the beta distribution, the nonlinear Fourier transform and a combinatorial problem

Saksida, Pavle (avtor)

The paper describes some probabilistic and combinatorial aspects of the nonlinear Fourier transform associated with the AKNS-ZS problems. We show that the volumes of a family of polytopes that appear in a power expansion of the nonlinear Fourier transform are distributed according to the beta probability distribution. We establish this result by studying an Euler-type discretization of the nonlinear Fourier transform. This approach leads to the combinatorial problem of finding the number of alternating ordered partitions of an integer into a fixed number of distinct parts. We find the explicit formula for these numbers and show that they are essentially distributed according to a novel discretization of the beta distribution for a suitable choice of the shape parameters. We also find the generating functions of the numbers of alternating sums. These functions are expressed in terms of the our discrete nonlinear Fourier transform.

• Jezik: Angleški jezik
• Ključne besede: beta distribution, nonlinear Fourier transform, discretization
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: FMF - Fakulteta za matematiko in fiziko
• Status publikacije: Objavljeno
• Različica publikacije: Objavljena publikacija
• Datum objave: 01.01.2024
• Leto izida: 2024
• Št. strani: 20 str.
• Številčenje: Vol. 24, no. 1, article no. P1.08
• PID: 20.500.12556/RUL-154482
• UDK: 517.95:519.1
• ISSN pri članku: 1855-3966
• DOI: 10.26493/1855-3974.2976.f76
• COBISS.SI-ID: 165700867
• Datum objave v RUL: 16.02.2024

Gradivo je del revije

• Naslov: Ars mathematica contemporanea
• Založnik: Društvo matematikov, fizikov in astronomov, Društvo matematikov, fizikov in astronomov, Univerza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologije
• ISSN: 1855-3966
• COBISS.SI-ID: 239049984

Licence

• Licenca: CC BY 4.0, Creative Commons Priznanje avtorstva 4.0 Mednarodna
• Povezava: http://creativecommons.org/licenses/by/4.0/deed.sl
• Opis: To je standardna licenca Creative Commons, ki daje uporabnikom največ možnosti za nadaljnjo uporabo dela, pri čemer morajo navesti avtorja.

Sekundarni jezik

• Jezik: Slovenski jezik
• Ključne besede: distribucija beta, nelinearna Fourierova transformacija, diskretizacija

Projekti

• Financer: ARRS - Agencija za raziskovalno dejavnost Republike Slovenije
• Program financ.: Javna agencija za znanstvenoraziskovalno in inovacijsko dejavnost Republike Slovenije
• Številka projekta: P1- 0291
• Naslov: Analiza in geometrija