Naslov
Box dimension and Minkowski content of generalized Euler spirals

Autori
Korkut, Luka ; Vlah, Domagoj ; Žubrinić, Darko ; Županović, Vesna

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Skup
4th Croatian Mathematical Congress June 17 - 20, 2008, Osijek, Croatia

Mjesto i datum
Osijek, Hrvatska, 17.06.2008. - 20.06.2008

Vrsta sudjelovanja
Poster

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Generalized Euler or Cornu spiral; box dimension; Minkowski content; generalized Fresnel integrals

Sažetak
We show that the box dimension of the generalized Euler spirals generated by control functions with $p$-growth at infinity is equal to the box dimension of the $p$-clothoid, $p>1$, also called the generalized Euler or Cornu spiral. This dimension is equal to $d=2p/(2p-1)$. Furthermore, this curve is Minkowski measurable, and we compute its $d$-dimensional Minkowski content. We provide a new, elementary and simple proof of the asymptotic expansion of generalized Fresnel integrals generated by control functions with $p$-growth at infinity. This work is made in collaboration with Luka Korkut, Darko \v Zubrini\' c and Vesna \v Zupanovi\'c. Poster presented by Domagoj Vlah.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA