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Naslov:On a continuation of quaternionic and octonionic logarithm along curves and the winding number
Avtorji:ID Gentili, Graziano (Avtor)
ID Prezelj, Jasna (Avtor)
ID Vlacci, Fabio (Avtor)
Datoteke:URL URL - Izvorni URL, za dostop obiščite https://www.sciencedirect.com/science/article/pii/S0022247X24001410
 
.pdf PDF - Predstavitvena datoteka, prenos (720,93 KB)
MD5: 67E62C9CA46C7537CC66F52581457EAB
 
Jezik:Angleški jezik
Tipologija:1.01 - Izvirni znanstveni članek
Organizacija:Logo IMFM - Inštitut za matematiko, fiziko in mehaniko
Povzetek:This paper deals with the problem of finding a continuous extension of the hypercomplex (quaternionic or octonionic) logarithm along (quaternionic or octonionic) paths which avoid the origin. The main difficulty depends upon this fact: while a branch of the complex logarithm can be defined in a small open neighbourhood of a strictly negative real point, no continuous branch of the hypercomplex logarithm can be defined in any open set which contains a strictly negative real point. To overcome this difficulty, we use the logarithmic manifold: in general, the existence of a lift of a path to this manifold is not guaranteed and, indeed, the problem of lifting a path to the logarithmic manifold is completely equivalent to the problem of finding a continuation of the hypercomplex logarithm along this path. The second part of the paper scrutinizes the existence of a notion of winding number (with respect to the origin) for hypercomplex loops that avoid the origin, even though it is known that the definition of winding number for such loops is not natural in Rn when n is greater than 2. The surprise is that, in the hypercomplex setting, the new definition of winding number introduced in this paper can be given and has full meaning for a large class of hypercomplex loops (untwisted loops with companion that avoid the origin). Finally an original but rather natural notion of homotopy for these hypercomplex loops (the c-homotopy) is presented and it is proved to be suitable to comply with the intrinsic geometrical meaning of the winding number for this class of loops, namely, two such hypercomplex loops are c-homotopic if, and only if, they have the same winding number.
Ključne besede:hypercomplex logarithm, continuation of the hypercomplex logarithm along paths, winding number
Status publikacije:Objavljeno
Verzija publikacije:Objavljena publikacija
Datum objave:01.08.2024
Leto izida:2024
Št. strani:25 str.
Številčenje:Vol. 536, iss. 1, [article no.] 128219
PID:20.500.12556/DiRROS-18310 Novo okno
UDK:517.5
ISSN pri članku:0022-247X
DOI:10.1016/j.jmaa.2024.128219 Novo okno
COBISS.SI-ID:187512579 Novo okno
Datum objave v DiRROS:04.03.2024
Število ogledov:708
Število prenosov:318
Metapodatki:XML DC-XML DC-RDF
:
GENTILI, Graziano, PREZELJ, Jasna in VLACCI, Fabio, 2024, On a continuation of quaternionic and octonionic logarithm along curves and the winding number. Journal of mathematical analysis and applications [na spletu]. 2024. Vol. 536, no. 1,  128219. [Dostopano 4 april 2025]. DOI 10.1016/j.jmaa.2024.128219. Pridobljeno s: https://dirros.openscience.si/IzpisGradiva.php?lang=slv&id=18310
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Gradivo je del revije

Naslov:Journal of mathematical analysis and applications
Skrajšan naslov:J. math. anal. appl.
Založnik:Elsevier
ISSN:0022-247X
COBISS.SI-ID:3081231 Novo okno

Gradivo je financirano iz projekta

Financer:ARIS - Javna agencija za znanstvenoraziskovalno in inovacijsko dejavnost Republike Slovenije
Program financ.:Javna agencija za znanstvenoraziskovalno in inovacijsko dejavnost Republike Slovenije
Številka projekta:P1-0291-2022
Naslov:Analiza in geometrija
Financer:ARIS - Javna agencija za znanstvenoraziskovalno in inovacijsko dejavnost Republike Slovenije
Program financ.:Javna agencija za znanstvenoraziskovalno in inovacijsko dejavnost Republike Slovenije
Številka projekta:N1-0237-2022
Naslov:Holomorfne parcialne diferencialne relacije
Financer:ARIS - Javna agencija za znanstvenoraziskovalno in inovacijsko dejavnost Republike Slovenije
Program financ.:Javna agencija za znanstvenoraziskovalno in inovacijsko dejavnost Republike Slovenije
Številka projekta:J1-3005-2021
Naslov:Kompleksna in geometrijska analiza
Financer:Drugi - Drug financer ali več financerjev
Program financ.:GNSAGA
Številka projekta:INdaM
Naslov:Hypercomplex function theory and applications
Financer:Drugi - Drug financer ali več financerjev
Program financ.:MIUR, Italy
Številka projekta:FOE 2014
Naslov:Splines for accUrate NumeRics: adaptIve models for Simulation Environments

Licence

Licenca:CC BY 4.0, Creative Commons Priznanje avtorstva 4.0 Mednarodna
Povezava:http://creativecommons.org/licenses/by/4.0/deed.sl
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