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 Annales Universitatis Mariae Curie-Sklodowska, sectio A – MathematicaNumber of Followers: 1     Open Access journal ISSN (Print) 0365-1029 - ISSN (Online) 2083-7402 Published by Wydawnictwo UMCS  [25 journals]
• On the necessary condition for Baum-Katz type theorem for non-identically
distributed and negatively dependent random fields

• Authors: Zbigniew Łagodowski
First page: 1
Abstract: Let  $$\{ X_{\bf n}, {\bf n}\in \mathbb{N}^d \}$$ be a random field of negatively dependent  random variables.  The complete  convergence results for negatively dependent  random fields  are refined. To obtain the main theorem several lemmas  for convergence of families indexed by $$\mathbb{N}^d$$   have been proved. Auxiliary lemmas have wider application to study  the random walks on the lattice.
PubDate: 2018-12-22
DOI: 10.17951/a.2018.72.2.1
Issue No: Vol. 72, No. 2 (2018)

• The density Turan problem for 3-uniform linear hypertrees. An efficient
testing algorithm

• Authors: Halina Bielak, Kamil Powroźnik
First page: 9
Abstract: Let $$\mathcal{T}=(V,\mathcal{E})$$ be a  3-uniform linear hypertree. We consider a blow-up hypergraph $$\mathcal{B}[\mathcal{T}]$$. We are interested in the following problem. We have to decide whether there exists a blow-up hypergraph $$\mathcal{B}[\mathcal{T}]$$ of the hypertree $$\mathcal{T}$$, with hyperedge densities satisfying some conditions, such that the hypertree $$\mathcal{T}$$ does not appear in a blow-up hypergraph as a transversal. We present an efficient algorithm to decide whether a given set of hyperedge densities ensures the existence of a 3-uniform linear hypertree $$\mathcal{T}$$ in a blow-up hypergraph $$\mathcal{B}[\mathcal{T}]$$.
PubDate: 2018-12-22
DOI: 10.17951/a.2018.72.2.9
Issue No: Vol. 72, No. 2 (2018)

• On a two-parameter generalization of Jacobsthal numbers and its graph
interpretation

• Authors: Dorota Bród
First page: 21
Abstract: In this paper we introduce a two-parameter generalization of the classical Jacobsthal numbers ((s,p)-Jacobsthal numbers). We present some properties of the presented sequence, among others Binet’s formula, Cassini’s identity, the generating function. Moreover, we give a graph interpretation of (s,p)-Jacobsthal numbers, related to independence in graphs.
PubDate: 2018-12-22
DOI: 10.17951/a.2018.72.2.21
Issue No: Vol. 72, No. 2 (2018)

• On the Courant bracket on couples of vector fields and $$p$$-forms

• Authors: Miroslav Doupovec, Jan Kurek, Włodzimierz Mikulski
First page: 29
Abstract: If $$m\geq p+1\geq 2$$ (or $$m=p\geq 3$$), all  natural bilinear  operators $$A$$ transforming pairs of couples of vector fields and $$p$$-forms on $$m$$-manifolds $$M$$ into couples of vector fields and $$p$$-forms on $$M$$ are described. It is observed that  any natural skew-symmetric bilinear operator $$A$$ as above coincides with the generalized Courant bracket up to three (two, respectively) real constants.
PubDate: 2018-12-22
DOI: 10.17951/a.2018.72.2.29
Issue No: Vol. 72, No. 2 (2018)

• On the existence of connections with a prescribed skew-symmetric Ricci
tensor

• Authors: Jan Kurek, Włodzimierz Mikulski
First page: 37
Abstract: We study the so-called inverse problem. Namely, given a prescribed skew-symmetric Ricci tensor we find (locally) a respective linear connection.
PubDate: 2018-12-22
DOI: 10.17951/a.2018.72.2.37
Issue No: Vol. 72, No. 2 (2018)

• On $$\ell_1$$-preduals distant by 1

• Authors: Łukasz Piasecki
First page: 41
Abstract: For every predual $$X$$ of $$\ell_1$$ such that the standard basis in $$\ell_1$$ is weak$$^*$$ convergent, we give explicit models of all Banach spaces $$Y$$ for which the Banach-Mazur distance $$d(X,Y)=1$$. As a by-product of our considerations, we obtain some new results in metric fixed point theory. First, we show that the space $$\ell_1$$, with a predual $$X$$ as above, has the stable weak$$^*$$ fixed point property if and only if it has almost stable weak$$^*$$ fixed point property, i.e. the dual $$Y^*$$ of every Banach space $$Y$$ has the weak$$^*$$ fixed point property (briefly, $$\sigma(Y^*,Y)$$-FPP) whenever $$d(X,Y)=1$$. Then, we construct a predual $$X$$ of $$\ell_1$$ for which $$\ell_1$$ lacks the stable $$\sigma(\ell_1,X)$$-FPP but it has almost stable $$\sigma(\ell_1,X)$$-FPP, which in turn is a strictly stronger property than the $$\sigma(\ell_1,X)$$-FPP. Finally, in the general setting of preduals of $$\ell_1$$, we give a sufficient condition for almost stable weak$$^*$$ fixed point property in $$\ell_1$$ and we prove that for a wide class of spaces this condition is also necessary.
PubDate: 2018-12-22
DOI: 10.17951/a.2018.72.2.41
Issue No: Vol. 72, No. 2 (2018)

• Products of Toeplitz and Hankel operators on the Bergman space in the
polydisk

• Authors: Paweł Sobolewski
First page: 57
Abstract: In this paper we obtain a condition for analytic square integrable functions $$f,g$$ which guarantees the boundedness of products of the Toeplitz operators $$T_fT_{\bar g}$$ densely defined on the Bergman space in the polydisk. An analogous condition for the products of the Hankel operators $$H_fH^*_g$$ is also given.
PubDate: 2018-12-22
DOI: 10.17951/a.2018.72.2.57
Issue No: Vol. 72, No. 2 (2018)

• Generalized trend constants of Lipschitz mappings

• Authors: Mariusz Szczepanik
First page: 71
Abstract: In 2015, Goebel and Bolibok defined the initial trend coefficient of a mapping and the class of initially nonexpansive mappings. They proved that the fixed point property for nonexpansive mappings implies the fixed point property for initially nonexpansive mappings. We generalize the above concepts and prove an analogous fixed point theorem. We also study the initial trend coefficient more deeply.
PubDate: 2018-12-22
DOI: 10.17951/a.2018.72.2.71
Issue No: Vol. 72, No. 2 (2018)

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