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Periodic solutions of second-order differential inclusions systems with p-Laplacian

  • Paşca, Daniel
Some existence results are obtained for periodic solutions of nonautonomous second-order differential inclusions systems with p-Laplacian
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The orthogonal subcategory problem in homotopy theory

  • Casacuberta i Vergés, Carles
  • Chorny, Boris
It is known that, in a locally presentable category, localization exists with respect to every set of morphisms, while the statement that localization with respect to every (possibly proper) class of morphisms exists in locally presentable categories is equivalent to a large-cardinal axiom from set theory. One proves similarly, on one hand, that homotopy localization exists with respect to sets of maps in every cofibrantly generated, left proper, simplicial model category M whose underlying category is locally presentable. On the other hand, as we show in this article, the existence of localization with respect to possibly proper classes of maps in a model category M satisfying the above assumptions is implied by a large-cardinal axiom called Vopënka's principle, although we do not know if the reverse implication holds. We also show that, under the same assumptions on M, every endofunctor of M that is idempotent up to homotopy is equivalent to localization with respect to some class S of maps, and if Vopënka's principle holds then S can be chosen to be a set. There are examples showing that the latter need not be true if M is not cofibrantly generated. The above assumptions on M are satisfied by simplicial sets and symmetric spectra over simplicial sets, among many other model categories.
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Global eriodicity and complete integrability of discrete dynamical systems

  • Cima, Anna
  • Gasull i Embid, Armengol
  • Mañosa, Víctor
Vegeu el resum a l'inici del document del fitxer adjunt
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Embedding theorems of funcitional classes, III

  • Simonov, Boris V.
  • Tikhonov, Sergey Yu.
In this paper we obtain the necessary and sufficient conditions for embedding results of different function classes. The main result is a criterion for embedding theorems for the so-called generalized Weyl-Nikol'skii class and the generalized Lipschitz class. To define the Weyl-Nikol'skii class, we use the concept of a (λ,β)-derivative, which is a generalization of the derivative in the sense of Weyl. As corollaries, we give estimates of norms and moduli of smoothness of transformed Fourier series.
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The unbounded dead-end depth propertie is not a group invariant

  • Riley, Tim
  • Warshall, Andrew D.
Vegeu el resum a l'inici del document del fitxer adjunt
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Examples of retracts in a free group that are not the fixed subgroup of any group of automorphisms

  • Ciobanu, Laura
  • Dicks, Warren
Let F be a free group of rank at least three. We show that some retracts of F previously studied by Martino-Ventura are not equal to the fixed subgroup of any group of automorphisms of F. This shows that, in F, there exist subgroups that are equal to the fixed subgroup of some set of endomorphisms but are not equal to the fixed subgroup of any set of automorphisms. Moreover, we determine the Galois monoids of these retracts, where, by the Galois monoid of a subgroup H of F, we mean the monoid consisting of all endomorphisms of F that fix H.
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On the set of subrings wich are directed unions of Artinian subrings

  • Karim, Darioush
  • Zarzuela, Santiago
The paper contributes to the investigation of zero-dimensional rings which can be written as a directed union of Artinian subrings. We give conditions on DU(R) in order to be nonempty.
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Periodic orbits of the planar collision restricted 3-body problem

  • Llibre i Saló, Jaume
  • Paşca, Daniel
Using the continuation method we prove that the circular and the elliptic symmetric periodic orbits of the planar rotating Kepler problem can be continued into periodic orbits of the planar collision restricted 3–body problem. Additionally, we also continue to this restricted problem the so called “comets orbits”.
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