## Recursos de colección

#### Project Euclid (Hosted at Cornell University Library) (202.748 recursos)

Bulletin of the Belgian Mathematical Society-Simon Stevin

1. #### A closure operator for clopen topologies

Beer, Gerald; Bloomfield, Colin
A topology $\tau$ on a nonempty set $X$ is called a clopen topology provided each member of $\tau$ is both open and closed. Given a function $f$ from $X$ to $Y$, the operator $E \mapsto f^{-1}(f(E))$ is a closure operator on the power set of $X$ whose fixed points are closed subsets corresponding to a clopen topology on $X$. Conversely, for each clopen topology $\tau$ on $X$, we produce a function $f$ with domain $X$ such that $\tau = \{E \subseteq X : E = f^{-1}(f(E))\}$. We characterize the clopen topologies on $X$ as those that are weak topologies determined...

2. #### Lineability of functionals and renormings

García-Pacheco, F. J.; Puglisi, D.
We prove that every infinite dimensional Banach space can be equivalently renormed so that the set of norm attaining functionals contains an infinite dimensional vector subspace.

3. #### Cycle Index Sum for Non-$k$-Equal Configurations

Grossnickle, Keely; Turchin, Victor
We compute the cycle index sum of the symmetric group action on the homology of the configuration spaces of points in a Euclidean space with the condition that no $k$ of them are equal.

4. #### A characterization of alternatively convex or smooth Banach spaces

In this paper, we give a characterization of alternatively convex or smooth Banach spaces. In fact we prove that every normaloid numerical radius attaining operator on a Banach space $X$ is radialoid if and only if $X$ is alternatively convex or smooth. In addition, we show that every compact normaloid operator on $X$ is radialoid if and only if every rank one normaloid operator on X is radialoid. Finally we present some types of Banach spaces on which the compact normaloid operators are radialoid.

5. #### The $\tau$-precompact Hausdorff Group Reflection of Topological Groups

Hei, Wei; Xiao, Zhiqiang
We give three different descriptions of the $\tau$-precompact Hausdorff group reflection of topological groups. In particular, we describe the $\omega$-narrow Hausdorff reflection of a given topological group. We also prove that the $\tau$-precompact Hausdorff reflection functor preserves perfect surjective homomorphisms, quotient homomorphisms and arbitrary products. As a direct application, we deduce that the compact Hausdorff reflection functor preserves arbitrary products.

6. #### Dynamics of linear operators on non-Archimedean vector spaces

Mukhamedov, Farrukh; Khakimov, Otabek
In the present paper we study dynamics of linear operators defined on topological vector space over non-Archimedean valued fields. We give sufficient and necessary conditions of hypercyclicity (resp. supercyclicity) of linear operators on separable $F$-spaces. It is proven that a linear operator $T$ on topological vector space $X$ is hypercyclic (supercyclic) if it satisfies Hypercyclicity (resp. Supercyclicity) Criterion. We consider backward shifts on $c_0(\bz)$ and $c_0(\bn)$, respectively, and characterize hypercyclicity and supercyclicity of such kinds of shifts. Finally, we study hypercyclicity, supercyclicity of operators $\lambda I+\mu B$, where $I$ is identity and $B$ is backward shift. We note that there...

7. #### Coarse Lipschitz embeddings of James spaces

Netillard, F.
We prove that, for $1< p \neq q < \infty$, there does not exist any coarse Lipschitz embedding between the two James spaces $J_p$ and $J_q$, and that, for $1 < p < q < \infty$ and $1 < r < \infty$ such that $r \notin \{p,q\}$, $J_r$ does not coarse Lipschitz embed into $J_p \oplus J_q$.

8. #### Attached primes and Artinian modules

Pourreza, Naser; A'zami, Jafar
In this paper, we calculate the annihilator of an Artinian module over a complete local ring; moreover, we present a certain generalization of Grothendieck's Non-Vanishing Theorem for local cohomology modules over a local ring which is the homomorphic image of a Gorenstein local ring. Finally, as application of our results, we study the finiteness of local cohomology modules.

9. #### Observations on spaces with property $(DC(\omega_1))$

Xuan, Wei-Feng; Shi, Wei-Xue
A topological space $X$ has property $(DC(\omega_1))$ if it has a dense subspace every uncountable subset of which has a limit point in $X$. In this paper, we make some observations on spaces with property $(DC(\omega_1))$. In particular, we prove that the cardinality of a space $X$ with property $(DC(\omega_1))$ does not exceed $\mathfrak c$ if $X$ satisfies one of the following conditions: (1) $X$ is normal and has a rank $2$-diagonal; (2) $X$ is perfect and has a rank $2$-diagonal; (3) $X$ has a rank $3$-diagonal; (4) $X$ is perfect and has countable tightness. We also prove that if...

10. #### Existence of multiple nontrivial solutions for a class of quasilinear Schrödinger equations on $\mathbb{R}^{N}$

Che, Guofeng; Chen, Haibo
This paper is concerned with the following fourth-order elliptic equations $$\triangle^{2}u-\Delta u+V(x)u-\frac{\kappa}{2}\Delta(u^{2})u=f(x,u),\rm \mbox{ \ \ }in~\mathbb{R}^{N},$$ where $N\leq6$, $\kappa\geq0$. Under some appropriate assumptions on $V(x)$ and $f(x, u)$, we prove the existence and multiplicity of solutions for the above equations via variational methods. Recent results from the literature are extended.

11. #### Sharp height estimate in Lorentz-Minkowski space revisited

de Lima, Eudes L.; de Lima, Henrique F.; Aquino, Cícero P.
In this paper, we deal with compact (necessarily with nonempty boundary) generalized linear Weingarten spacelike hypersurfaces immersed into the Lorentz-Minkowski space $\mathbb L^{n+1}$, which means that there exists a linear relation involving some of the corresponding higher order mean curvatures. In this setting, we obtain a sharp height estimate concerning such a hypersurfaces whose boundary is contained in a spacelike hyperplane of $\mathbb L^{n+1}$. Furthermore, we apply our estimate to describe the nature of the end of a complete generalized linear Weingarten spacelike hypersurface in $\mathbb L^{n+1}$.

12. #### Generalizing nil clean rings

Danchev, Peter
We introduce the class of {\it unipotently nil clean} rings as these rings $R$ in which for every $a\in R$ there exist an idempotent $e$ and a nilpotent $q$ such that $a-e-1-q\in (1-e)Ra$. Each unipotently nil clean ring is weakly nil clean as well as each nil clean ring is unipotently nil clean. Our results obtained here considerably extend those from [8] and [7], respectively.

13. #### Parallel Forms, Co-Kähler Manifolds and their Models

Bazzoni, Giovanni; Lupton, Gregory; Oprea, John
We show how certain topological properties of co-Kähler manifolds derive from those of the Kähler manifolds which construct them. In particular, we show that the existence of parallel forms on a co-Kähler manifold reduces the computation of cohomology from the de Rham complex to certain amenable sub-cdga's defined by geometrically natural operators derived from the co-Kähler structure. This provides a simpler proof of the formality of the foliation minimal model in this context.

14. #### Periodic points on T-fiber bundles over the circle

Silva, Weslem Liberato; de Souza, Rafael Moreira

15. #### Periodic points on T-fiber bundles over the circle

Silva, Weslem Liberato; de Souza, Rafael Moreira

16. #### Periodic points on T-fiber bundles over the circle

Silva, Weslem Liberato; de Souza, Rafael Moreira

17. #### Periodic points on T-fiber bundles over the circle

Silva, Weslem Liberato; de Souza, Rafael Moreira

18. #### The equivalence of two methods: finding representatives of non--empty Nielsen classes

Hart, Evelyn L.; Vu, Ha T.
Let $f:X\to X$ be a self--map with $X$ a wedge of circles or a compact surface with boundary, so that the fundamental group of $X$ is finitely generated and free. In [3], Wagner presents an algorithm for extracting information from the homomorphism induced by $f$ on the fundamental group. This information involves the fixed point index of $f$ and the Nielsen classes of fixed points of $f$. The step in which the representatives of Nielsen classes, Wagner tails, are calculated is equivalent to a step in the method presented by Fadell and Husseini in [1]. The Fadell--Husseini method was designed...

19. #### The equivalence of two methods: finding representatives of non--empty Nielsen classes

Hart, Evelyn L.; Vu, Ha T.
Let $f:X\to X$ be a self--map with $X$ a wedge of circles or a compact surface with boundary, so that the fundamental group of $X$ is finitely generated and free. In [3], Wagner presents an algorithm for extracting information from the homomorphism induced by $f$ on the fundamental group. This information involves the fixed point index of $f$ and the Nielsen classes of fixed points of $f$. The step in which the representatives of Nielsen classes, Wagner tails, are calculated is equivalent to a step in the method presented by Fadell and Husseini in [1]. The Fadell--Husseini method was designed...

20. #### The equivalence of two methods: finding representatives of non--empty Nielsen classes

Hart, Evelyn L.; Vu, Ha T.
Let $f:X\to X$ be a self--map with $X$ a wedge of circles or a compact surface with boundary, so that the fundamental group of $X$ is finitely generated and free. In [3], Wagner presents an algorithm for extracting information from the homomorphism induced by $f$ on the fundamental group. This information involves the fixed point index of $f$ and the Nielsen classes of fixed points of $f$. The step in which the representatives of Nielsen classes, Wagner tails, are calculated is equivalent to a step in the method presented by Fadell and Husseini in [1]. The Fadell--Husseini method was designed...

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