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Volume 56

2019 Next

Publication date: 17.12.2019

Licence: CC BY-NC-ND  licence icon

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Editor-in-Chief Sławomir Kołodziej

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Zahra Barqsouz, Seadat Ollah Faramarzi

Universitatis Iagellonicae Acta Mathematica, Volume 56, 2019, pp. 7-14

https://doi.org/10.4467/20843828AM.19.001.12109

We show some results about local homology modules when they are in a Serre subcategory of the category of R-modules. For an ideal of R, we also define the concept of the condition Ca on a Serre category, which seems dual to the condition Ca in Melkersson [1]. As a main result we show that for an Artinian R-module M and any Serre subcategory S of the category of R-modules and a non-negative integer s, HomR(R/a,Has (M))  S if Hai (M S for all s.

2010 Mathematics Subject Classification. 13D45, 13M10; 13E15.

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Armen Edigarian

Universitatis Iagellonicae Acta Mathematica, Volume 56, 2019, pp. 15-21

https://doi.org/10.4467/20843828AM.19.002.12110

M. A. Selby [8-10] and, independently, N. Sibony [11] proved that on the complex plane c-completeness is equivalent to c-finitely compactness. Their proofs are quite similar and are based on [4]. We give more refined equivalent conditions and, along the way, simplify the proofs.

2010 Mathematics Subject Classification. 30H05, 30H50.

The author was supported in part by the Polish National Science Centre (NCN) grant no. 2015/17/B/ST1/00996.
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Amele Taïeb, Zoubir Dahmani

Universitatis Iagellonicae Acta Mathematica, Volume 56, 2019, pp. 23-40

https://doi.org/10.4467/20843828AM.19.003.12111

In this paper, we study several fractional variational problems with functionals that contain n unknown functions with their higher order Caputo derivatives and RiemannLiouville integrals. We prove generalized fractional EulerLagrange equations. We also study an isoperimetric problem with multiple constraints, and we find the optimality conditions. Some examples are provided to illustrate the applications of the results.

2000 Mathematics Subject Classification. 49K10, 26A33, 26B20.

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