Bulletin of the Belgian Mathematical Society - Simon Stevin Articles (Project Euclid)
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The latest articles from Bulletin of the Belgian Mathematical Society - Simon Stevin on Project Euclid, a site for mathematics and statistics resources.en-usCopyright 2010 Cornell University LibraryEuclid-L@cornell.edu (Project Euclid Team)Thu, 05 Aug 2010 15:41 EDTTue, 07 Jun 2011 09:08 EDThttp://projecteuclid.org/collection/euclid/images/logo_linking_100.gifProject Euclid
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On the Geometry of the Conformal Group in Spacetime
http://projecteuclid.org/euclid.bbms/1274896198
<strong>N. G. Gresnigt</strong>, <strong>P. F. Renaud</strong><p><strong>Source: </strong>Bull. Belg. Math. Soc. Simon Stevin, Volume 17, Number 2, 193--200.</p><p><strong>Abstract:</strong><br/>
The study of the conformal group in $R^{p,q}$ usually involves the conformal compactification of $R^{p,q}$. This allows the transformations to be
represented by linear transformations in $R^{p+1,q+1}$. So, for example, the conformal group of Minkowski space, $R^{1,3}$ leads to its isomorphism
with $SO(2,4)$. This embedding into a higher dimensional space comes at the expense of the geometric properties of the transformations. This is
particularly a problem in $R^{1,3}$ where we might well prefer to keep the geometric nature of the various types of transformations in sight.
In this note, we show that this linearization procedure can be achieved with no loss of geometric insight, if, instead of using this compactification,
we let the conformal transformations act on two copies of the associated Clifford algebra. Although we are mostly concerned with the conformal group
of Minkowski space (where the geometry is clearest), generalization to the general case is straightforward.
</p>projecteuclid.org/euclid.bbms/1274896198_Thu, 05 Aug 2010 15:41 EDTThu, 05 Aug 2010 15:41 EDTFixed point index bounds for self-maps on closed surfaceshttps://projecteuclid.org/euclid.bbms/1515035016<strong>D.L. Gonçalves</strong>, <strong>M.R. Kelly</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 24, Number 4, 673--688.</p><p><strong>Abstract:</strong><br/>
Given a surface with non-positive Euler characteristic and non-empty boundary, and a map which has the least number of fixed points possible within its homotopy class there are known bounds (both upper and lower) regarding the fixed point indices of the map. This paper gives a new proof of this result. In addition, a relative version of the method is developed, which is then used to establish the same index bounds for the case of a closed surface of negative Euler characteristic.
</p>projecteuclid.org/euclid.bbms/1515035016_20180103220342Wed, 03 Jan 2018 22:03 ESTNielsen numbers of iterates and Nielsen type periodic numbers of periodic maps on tori and nilmanifoldshttps://projecteuclid.org/euclid.bbms/1515035017<strong>Philip R. Heath</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 24, Number 4, 689--723.</p><p><strong>Abstract:</strong><br/>
In this paper we compute the Nielsen numbers $N(f^m)$ and the Nielsen type numbers $NP_m(f)$ and $N\Phi_m(f)$ {\it for all $m$}, for periodic maps $f$ on tori and nilmanifolds. For fixed $m$, there are known formulas for these numbers for arbitrary maps on tori and nilmanifolds. However when seeking to determine these numbers for all $m$ for periodic maps, fascinating patterns and shortcuts are revealed. Our method has two main thrusts. Firstly we study $N(f^m)$, $NP_m(f)$ and $N\Phi_m(f)$ on primitives (maps whose linearizations consist of primitive roots of unity), and then secondly we employ fibre techniques to give an inductive approach to the general case adding one primitive at a time. This approach is made possible by the eigen structure of the linearizations of the maps involved.
</p>projecteuclid.org/euclid.bbms/1515035017_20180103220342Wed, 03 Jan 2018 22:03 ESTCommon value pairs and their estimationshttps://projecteuclid.org/euclid.bbms/1515035018<strong>Ying Gu</strong>, <strong>Xuezhi Zhao</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 24, Number 4, 725--739.</p><p><strong>Abstract:</strong><br/>
We shall give a new treatment to intersection points of two maps, named common value pairs. Given two maps $f,g\colon X\to Y$. Instead of considering intersection points on target space $Y$, we focus on the pairs in the domains $X$, the pair $(u,v)$ with $f(u)=g(v)$. The set of all these pairs is exactly the preimage of product $f\times g$ at the diagonal in $Y^2$. We shall apply the idea of Nielsen root theory into such a general case: preimage of a set. Hence, some estimation for common value pairs and therefore for intersection points are obtained.
</p>projecteuclid.org/euclid.bbms/1515035018_20180103220342Wed, 03 Jan 2018 22:03 ESTThe equivalence of two methods: finding representatives of non--empty Nielsen classeshttps://projecteuclid.org/euclid.bbms/1515035019<strong>Evelyn L. Hart</strong>, <strong>Ha T. Vu</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 24, Number 4, 741--745.</p><p><strong>Abstract:</strong><br/>
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 for closed two dimensional CW--complexes, but the step in which they use the Fox calculus, to determine terms in the unreduced Reidemeister trace, produces the Wagner tails and their indices. The equivalence of these steps was stated in [2] without proof. Further developments in this area have caused continued interest in the techniques, and a clarification of the equivalence is needed. Here we provide the proof and an example.
</p>projecteuclid.org/euclid.bbms/1515035019_20180103220342Wed, 03 Jan 2018 22:03 ESTPeriodic points on T-fiber bundles over the circlehttps://projecteuclid.org/euclid.bbms/1515035020<strong>Weslem Liberato Silva</strong>, <strong>Rafael Moreira de Souza</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 24, Number 4, 747--767.</p>projecteuclid.org/euclid.bbms/1515035020_20180103220342Wed, 03 Jan 2018 22:03 ESTParallel Forms, Co-Kähler Manifolds and their Modelshttps://projecteuclid.org/euclid.bbms/1523412047<strong>Giovanni Bazzoni</strong>, <strong>Gregory Lupton</strong>, <strong>John Oprea</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 25, Number 1, 1--11.</p><p><strong>Abstract:</strong><br/>
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.
</p>projecteuclid.org/euclid.bbms/1523412047_20180410220105Tue, 10 Apr 2018 22:01 EDTGeneralizing nil clean ringshttps://projecteuclid.org/euclid.bbms/1523412048<strong>Peter Danchev</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 25, Number 1, 13--29.</p><p><strong>Abstract:</strong><br/>
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.
</p>projecteuclid.org/euclid.bbms/1523412048_20180410220105Tue, 10 Apr 2018 22:01 EDTSharp height estimate in Lorentz-Minkowski space revisitedhttps://projecteuclid.org/euclid.bbms/1523412050<strong>Eudes L. de Lima</strong>, <strong>Henrique F. de Lima</strong>, <strong>Cícero P. Aquino</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 25, Number 1, 29--38.</p><p><strong>Abstract:</strong><br/>
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 $\mathbb L^{n+1}$.
</p>projecteuclid.org/euclid.bbms/1523412050_20180410220105Tue, 10 Apr 2018 22:01 EDTExistence of multiple nontrivial solutions for a class of quasilinear Schrödinger equations on $\mathbb{R}^{N}$https://projecteuclid.org/euclid.bbms/1523412051<strong>Guofeng Che</strong>, <strong>Haibo Chen</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 25, Number 1, 39--53.</p><p><strong>Abstract:</strong><br/>
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.
</p>projecteuclid.org/euclid.bbms/1523412051_20180410220105Tue, 10 Apr 2018 22:01 EDTObservations on spaces with property $(DC(\omega_1))$https://projecteuclid.org/euclid.bbms/1523412052<strong>Wei-Feng Xuan</strong>, <strong>Wei-Xue Shi</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 25, Number 1, 55--62.</p><p><strong>Abstract:</strong><br/>
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 $X$ is a regular space with a $G_\delta$-diagonal and property $(DC(\omega_1))$ then the cardinality of $X$ is at most $2^\mathfrak c$.
</p>projecteuclid.org/euclid.bbms/1523412052_20180410220105Tue, 10 Apr 2018 22:01 EDTAttached primes and Artinian moduleshttps://projecteuclid.org/euclid.bbms/1523412053<strong>Naser Pourreza</strong>, <strong>Jafar A'zami</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 25, Number 1, 63--70.</p><p><strong>Abstract:</strong><br/>
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.
</p>projecteuclid.org/euclid.bbms/1523412053_20180410220105Tue, 10 Apr 2018 22:01 EDTCoarse Lipschitz embeddings of James spaceshttps://projecteuclid.org/euclid.bbms/1523412054<strong>F. Netillard</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 25, Number 1, 71--84.</p><p><strong>Abstract:</strong><br/>
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 $J_p \oplus J_q$.
</p>projecteuclid.org/euclid.bbms/1523412054_20180410220105Tue, 10 Apr 2018 22:01 EDTDynamics of linear operators on non-Archimedean vector spaceshttps://projecteuclid.org/euclid.bbms/1523412055<strong>Farrukh Mukhamedov</strong>, <strong>Otabek Khakimov</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 25, Number 1, 85--105.</p><p><strong>Abstract:</strong><br/>
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 are essential differences between the non-Archimedean and real cases.
</p>projecteuclid.org/euclid.bbms/1523412055_20180410220105Tue, 10 Apr 2018 22:01 EDTThe $\tau$-precompact Hausdorff Group Reflection of Topological Groupshttps://projecteuclid.org/euclid.bbms/1523412056<strong>Wei Hei</strong>, <strong>Zhiqiang Xiao</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 25, Number 1, 107--120.</p><p><strong>Abstract:</strong><br/>
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.
</p>projecteuclid.org/euclid.bbms/1523412056_20180410220105Tue, 10 Apr 2018 22:01 EDTA characterization of alternatively convex or smooth Banach spaceshttps://projecteuclid.org/euclid.bbms/1523412059<strong>H. Espid</strong>, <strong>R. Alizadeh</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 25, Number 1, 121--127.</p><p><strong>Abstract:</strong><br/>
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.
</p>projecteuclid.org/euclid.bbms/1523412059_20180410220105Tue, 10 Apr 2018 22:01 EDTCycle Index Sum for Non-$k$-Equal Configurationshttps://projecteuclid.org/euclid.bbms/1523412060<strong>Keely Grossnickle</strong>, <strong>Victor Turchin</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 25, Number 1, 129--139.</p><p><strong>Abstract:</strong><br/>
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.
</p>projecteuclid.org/euclid.bbms/1523412060_20180410220105Tue, 10 Apr 2018 22:01 EDTLineability of functionals and renormingshttps://projecteuclid.org/euclid.bbms/1523412061<strong>F. J. García-Pacheco</strong>, <strong>D. Puglisi</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 25, Number 1, 141--147.</p><p><strong>Abstract:</strong><br/>
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.
</p>projecteuclid.org/euclid.bbms/1523412061_20180410220105Tue, 10 Apr 2018 22:01 EDTA closure operator for clopen topologieshttps://projecteuclid.org/euclid.bbms/1523412062<strong>Gerald Beer</strong>, <strong>Colin Bloomfield</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 25, Number 1, 149--159.</p><p><strong>Abstract:</strong><br/>
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 by a surjective function with values in some discrete topological space. Paralleling this result, we show that a topology admits a clopen base if and only if it is a weak topology determined by a family of functions with values in discrete spaces.
</p>projecteuclid.org/euclid.bbms/1523412062_20180410220105Tue, 10 Apr 2018 22:01 EDTNielsen-Reidemeister indices for multivalued mapshttps://projecteuclid.org/euclid.bbms/1530065006<strong>A. Przestacki</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 25, Number 2, 161--170.</p><p><strong>Abstract:</strong><br/>
In 2011 Kenessey and Wengenroth gave a full description of closed range composition operators $C_\psi:C^{\infty}(\mathbb{R}^d)\toC^{\infty}(\mathbb{R})$, $F\mapsto F\circ\psi$, corresponding to smooth injective symbols $\psi:\mathbb{R}\to\mathbb{R}^d$. In 2012 Przestacki gave a sufficient condition for the range of $C_\psi$ to be closed in case if $\psi:\mathbb{R}\to\mathbb{R}$ is a smooth not necessarily injective symbol. Using their ideas we give a sufficient condition ensuring that the range of $C_\psi$ is closed when $\psi:\mathbb{R}\to\mathbb{R}^d$ is a smooth not necessarily injective function.
</p>projecteuclid.org/euclid.bbms/1530065006_20180626220337Tue, 26 Jun 2018 22:03 EDTJohnson pseudo-contractibility of various classes of Banach algebrashttps://projecteuclid.org/euclid.bbms/1530065007<strong>A. Sahami</strong>, <strong>A. Pourabbas</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 25, Number 2, 171--182.</p><p><strong>Abstract:</strong><br/>
The notion of Johnson pseudo-contractibility for Banach algebras is introduced. We investigate this notion for Banach algebras defined on locally compact groups. For a compact metric space $X$ and $\alpha>0$, we show that the Lipschitz algebra $Lip_{\alpha}(X)$ is Johnson pseudo-contractible if and only if $X$ is finite. We give some examples to distinguish our new notion with the classical ones.
</p>projecteuclid.org/euclid.bbms/1530065007_20180626220337Tue, 26 Jun 2018 22:03 EDTLaplacian solitons on nilpotent Lie groupshttps://projecteuclid.org/euclid.bbms/1530065008<strong>Marina Nicolini</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 25, Number 2, 183--196.</p><p><strong>Abstract:</strong><br/>
We investigate the existence of closed $G_2$-structures which are solitons for the Laplacian flow on nilpotent Lie groups. We obtain that seven of the twelve Lie algebras admitting a closed $G_2$-structure do admit a Laplacian soliton. Moreover, one of them admits a continuous family of Laplacian solitons which are pairwise non-homothetic and the Laplacian flow evolution on four of the Lie groups is not diagonal.
</p>projecteuclid.org/euclid.bbms/1530065008_20180626220337Tue, 26 Jun 2018 22:03 EDTOn $(t-1)$-colored paths in $t$-colored complete graphshttps://projecteuclid.org/euclid.bbms/1530065009<strong>Amir Khamseh</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 25, Number 2, 197--207.</p><p><strong>Abstract:</strong><br/>
Given $t$ distinct colors, we order the $t$ subsets of $t-1$ colors in some arbitrary manner. Let $G_1, G_2, \ldots , G_t$ be graphs. The $(t-1)$-chromatic Ramsey number, denoted by $r_{t-1}^t(G_1, G_2, \ldots, G_t)$, is defined to be the least number $n$ such that if the edges of the complete graph $K_n$ are colored in any fashion with $t$ colors, then for some $i$ the subgraph whose edges are colored with the $i$th subset of colors contains a $G_i$. In this paper, we find the value of $r_4^5(G_1, \ldots, G_5)$ when each $G_i$ is a path.
</p>projecteuclid.org/euclid.bbms/1530065009_20180626220337Tue, 26 Jun 2018 22:03 EDTDisk-cyclic and codisk-cyclic weighted pseudo-shiftshttps://projecteuclid.org/euclid.bbms/1530065010<strong>Ya Wang</strong>, <strong>Hong-Gang Zeng</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 25, Number 2, 209--224.</p><p><strong>Abstract:</strong><br/>
In this paper, we characterize disk-cyclic and codisk-cyclic weighted pseudo-shifts on Banach sequence spaces, and consider the bilateral operator weighted shifts on $\ell^2(\mathbb{Z,\mathcal{K}})$ as a special case. Moreover, we present a counter-example to show that a result in [Y. X. Liang and Z. H. Zhou], Disk-cyclicity and Codisk-cyclicity of certain shift operators, Operators and Matrices, \textbf{9}(2015), 831--846] is not correct.
</p>projecteuclid.org/euclid.bbms/1530065010_20180626220337Tue, 26 Jun 2018 22:03 EDTValue distribution and uniqueness results of L-functions concerning certain linear differential polynomialshttps://projecteuclid.org/euclid.bbms/1530065011<strong>Fang Liu</strong>, <strong>Xiao-Min Li</strong>, <strong>Hong-Xun Yi</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 25, Number 2, 225--240.</p><p><strong>Abstract:</strong><br/>
In this paper, we study a uniqueness question of meromorphic functions concerning certain linear differential polynomials that share a nonzero finite value with the same of L-functions. The results in this paper extend the corresponding results from Li[6] and Li & Li[7].
</p>projecteuclid.org/euclid.bbms/1530065011_20180626220337Tue, 26 Jun 2018 22:03 EDTOn Weierstrass' monsters in the disc algebrahttps://projecteuclid.org/euclid.bbms/1530065012<strong>L. Bernal-González</strong>, <strong>J. López-Salazar</strong>, <strong>J.B. Seoane-Sepúlveda</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 25, Number 2, 241--262.</p><p><strong>Abstract:</strong><br/>
Let $\Omega$ be a Jordan domain in the complex plane whose boundary is piecewise analytic, and let $A(\Omega )$ be the algebra of all holomorphic functions on $\Omega$ that are continuous up to the boundary. We prove the existence of dense linear subspaces and of infinitely generated subalgebras in $A(\Omega )$ all of whose nonzero members are, in a strong sense, not differentiable at almost any point of the boundary. We also obtain infinite-dimensional closed subspaces consisting of functions that are not differentiable at any point of a dense subset of the boundary. In the case of the unit disc, those dense linear subspaces can be found with their functions being nowhere differentiable in the unit circle.
</p>projecteuclid.org/euclid.bbms/1530065012_20180626220337Tue, 26 Jun 2018 22:03 EDTSplitting Madsen-Tillmann spectra I. Twisted transfer mapshttps://projecteuclid.org/euclid.bbms/1530065013<strong>Takuji Kashiwabara</strong>, <strong>Hadi Zare</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 25, Number 2, 263--304.</p><p><strong>Abstract:</strong><br/>
We record various properties of twisted Becker-Gottlieb transfer maps and study their multiplicative properties analogous to Becker-Gottlieb transfer. We show these twisted transfer maps factor through Becker-Schultz-Mann-Miller-Miller transfer; some of these might be well known. We apply this to show that $BSO(2n+1)_+$ splits off $MTO(2n)$, which after localisation away from $2$, refines to a homotopy equivalence $MTO(2n)\simeq BO(2n)_+$ as well as $MTO(2n+1)\simeq *$ for all $n\geqslant0$. This reduces the study of $MTO(n)$ to the $2$-localized case. At the prime $2$ our splitting allows us to identify some algebraically independent classes in mod $2$ cohomology of $\Omega^\infty MTO(2n)$. We also show that $BG_+$ splits off $MTK$ for some pairs $(G,K)$ at appropriate set of primes $p$, and investigate the consequences for characteristic classes, including algebraic independence and non-divisibility of some universally defined characteristic classes, generalizing results of Ebert and Randal-Williams.
</p>projecteuclid.org/euclid.bbms/1530065013_20180626220337Tue, 26 Jun 2018 22:03 EDTRicci solitons in almost $f$-cosymplectic manifoldshttps://projecteuclid.org/euclid.bbms/1530065014<strong>Xiaomin Chen</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 25, Number 2, 305--319.</p><p><strong>Abstract:</strong><br/>
In this article we study an almost $f$-cosymplectic manifold admitting a Ricci soliton. We first prove that there do not exist Ricci solitons on an almost cosymplectic $(\kappa,\mu)$-manifold. Further, we consider an almost $f$-cosymplectic manifold admitting a Ricci soliton whose potential vector field is the Reeb vector field and show that a three dimensional almost $f$-cosymplectic is a cosymplectic manifold. Finally we classify a three dimensional $\eta$-Einstein almost $f$-cosymplectic manifold admitting a Ricci soliton..
</p>projecteuclid.org/euclid.bbms/1530065014_20180626220337Tue, 26 Jun 2018 22:03 EDTInverse map and equicontinuity of power maps in locally convex algebrashttps://projecteuclid.org/euclid.bbms/1536631230<strong>A. El Kinani</strong>, <strong>R. Choukri</strong>, <strong>A. Oudades</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 25, Number 3, 321--329.</p><p><strong>Abstract:</strong><br/>
We show that the inverse map $x\longmapsto x^{-1}$ is continuous in any unitary non commutative locally convex algebra in which the sequence of power maps $\left( x\longmapsto x^{n}\right) _{n}$ is equicontinuous at zero. As a consequence, we obtain that the inverse map is continuous in any unitary $B_{0}$-algebra not necessarily commutative in which entire functions operate.
</p>projecteuclid.org/euclid.bbms/1536631230_20180910220053Mon, 10 Sep 2018 22:00 EDTCommon Fixed Points Results of Multivalued Perov type Contractions on Cone Metric Spaces with a Directed Graphhttps://projecteuclid.org/euclid.bbms/1536631231<strong>Mujahid Abbas</strong>, <strong>Talat Nazir</strong>, <strong>Vladimir Rakočević</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 25, Number 3, 331--354.</p><p><strong>Abstract:</strong><br/>
In this paper, we establish the existence of common fixed points of multivalued Perov type contraction mappings on cone metric space endowed with a graph. An example is presented to support the results proved herein. Our results unify, generalize and complement various known comparable results in the literature.
</p>projecteuclid.org/euclid.bbms/1536631231_20180910220053Mon, 10 Sep 2018 22:00 EDTSplit extension classifiers in the category of cocommutative Hopf algebrashttps://projecteuclid.org/euclid.bbms/1536631232<strong>Marino Gran</strong>, <strong>Gabriel Kadjo</strong>, <strong>Joost Vercruysse</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 25, Number 3, 355--382.</p><p><strong>Abstract:</strong><br/>
We describe the split extension classifiers in the semi-abelian category of cocommutative Hopf algebras over an algebraically closed field of characteristic zero. The categorical notions of centralizer and of center in the category of cocommutative Hopf algebras is then explored. We show that the categorical notion of center coincides with the one that is considered in the theory of general Hopf algebras.
</p>projecteuclid.org/euclid.bbms/1536631232_20180910220053Mon, 10 Sep 2018 22:00 EDTOn totally singular generalized quadratic formshttps://projecteuclid.org/euclid.bbms/1536631233<strong>A.-H. Nokhodkar</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 25, Number 3, 383--392.</p><p><strong>Abstract:</strong><br/>
The algebra of similitudes of totally singular generalized quadratic forms in characteristic two is investigated. It is shown that this algebra satisfies certain functorial properties. An application of this study to central simple algebras with orthogonal involutions is also given.
</p>projecteuclid.org/euclid.bbms/1536631233_20180910220053Mon, 10 Sep 2018 22:00 EDTPointwise amenability for dual Banach algebrashttps://projecteuclid.org/euclid.bbms/1536631234<strong>Mannane Shakeri</strong>, <strong>Amin Mahmoodi</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 25, Number 3, 393--401.</p><p><strong>Abstract:</strong><br/>
We shall develop two notions of pointwise amenability, namely pointwise Connes amenability and pointwise $w^*$-approximate Connes amenability, for dual Banach algebras which take the $w^*$-topology into account. We shall study these concepts for the Banach sequence algebras $\ell^1(\omega)$ and the weighted semigroup algebras $ \ell^{1}(\mathbb{N}_{\wedge},\omega)$. For a weight $\omega$ on a discrete semigroup $S$, we shall investigate pointwise amenability/Connes amenability of $\ell^1(S,\omega)$ in terms of diagonals.
</p>projecteuclid.org/euclid.bbms/1536631234_20180910220053Mon, 10 Sep 2018 22:00 EDTReal hypersurfaces with Killing type structure Jacobi operators in $\mathbb{C}P^2$ and $\mathbb{C}H^2$https://projecteuclid.org/euclid.bbms/1536631235<strong>Yaning Wang</strong>, <strong>Wenjie Wang</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 25, Number 3, 403--414.</p><p><strong>Abstract:</strong><br/>
In this paper, we prove that if the structure Jacobi operator of a $3$-dimen\-sional real hypersurface in a nonflat complex plane is of Killing type, then the hypersurface is either a tube of radius $\frac{\pi}{4}$ over a holomorphic curve in $\mathbb{C}P^2$ or a Hopf hypersurface with vanishing Hopf principal curvature in $\mathbb{C}H^2$. This extends the corresponding results in [6].
</p>projecteuclid.org/euclid.bbms/1536631235_20180910220053Mon, 10 Sep 2018 22:00 EDTOn well-posedness, regularity and ill-posedness for the nonlinear fourth-order Schrödinger equationhttps://projecteuclid.org/euclid.bbms/1536631236<strong>Van Duong Dinh</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 25, Number 3, 415--437.</p><p><strong>Abstract:</strong><br/>
We prove the local well-posedness for the nonlinear fourth-order Schrödinger equation (NL4S) in Sobolev spaces. We also study the regularity of local solutions in the sub-critical case. A direct consequence of this regularity is the global well-posedness above mass and energy spaces under some assumptions. Finally, we show the ill-posedness for (NL4S) in some cases of the super-critical range.
</p>projecteuclid.org/euclid.bbms/1536631236_20180910220053Mon, 10 Sep 2018 22:00 EDTPolish factorizations, cosmic spaces and domain representabilityhttps://projecteuclid.org/euclid.bbms/1536631237<strong>Jila Niknejad</strong>, <strong>Vladimir V. Tkachuk</strong>, <strong>Lynne Yengulalp</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 25, Number 3, 439--452.</p><p><strong>Abstract:</strong><br/>
We say that a space $X$ is {\it cofinally Polish} if for every continuous onto map $f:X\to M$ of $X$ onto a separable metrizable space $M$, there exists a Polish space $P$ and continuous onto maps $g:X\to P$ and $h:P\to M$ such that $f=h\circ g$. We study general properties of cofinally Polish spaces and compare the property of being cofinally Polish with subcompactness and domain representability. It is established, among other things, that a space with a countable network is cofinally Polish if and only if it is domain representable. We also show that any $G_\delta$-subset of an Eberlein compact space must be subcompact thus giving an answer to an open problem published in 2013.
</p>projecteuclid.org/euclid.bbms/1536631237_20180910220053Mon, 10 Sep 2018 22:00 EDTExistence and asymptotically stable solution of a Hammerstein type integral equation in a Hölder spacehttps://projecteuclid.org/euclid.bbms/1536631238<strong>Somayeh Saiedinezhad</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 25, Number 3, 453--465.</p><p><strong>Abstract:</strong><br/>
The following nonlinear quadratic integral equation of Hammerstein type is studied. $$x(t)=p(t)+x(t)\int_0^{q(t)} H(t,\tau,x(\tau)){\rm d}\tau.$$ The methodology relies on the measure of noncompactness in the space of functions with tempered increments, namely the space of $\alpha$-Hölder continuous functions. The results follow from the Darbo fixed point theorem. Some examples are included to show the applicability of the main results.
</p>projecteuclid.org/euclid.bbms/1536631238_20180910220053Mon, 10 Sep 2018 22:00 EDTOn injectivity of the ring of real-valued continuous functions on a framehttps://projecteuclid.org/euclid.bbms/1536631239<strong>Ali Akbar Estaji</strong>, <strong>Mostafa Abedi</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 25, Number 3, 467--480.</p><p><strong>Abstract:</strong><br/>
We give characterizations of $P$-frames and extremally disconnected $P$-frames based on ring-theoretic features of the ring of continuous real- valued functions on a frame $L$, i.e. $\mathcal RL$. It is shown that $L$ is a $P$-frame if and only if $\mathcal RL$ is an $\aleph_0$-self-injective ring. Consequently for pseudocompact frames if $\mathcal RL$ is $\aleph_0$-self-injective, then $L$ is finite. We also prove that $L$ is an extremally disconnected $P$-frame iff $\mathcal{R}L$ is a self-injective ring iff $\mathcal{R}L$ is a Baer regular ring iff $\mathcal{R}L$ is a continuous regular ring iff $\mathcal{R}L$ is a complete regular ring.
</p>projecteuclid.org/euclid.bbms/1536631239_20180910220053Mon, 10 Sep 2018 22:00 EDTNew criteria for $p$-nilpotency of finite groupshttps://projecteuclid.org/euclid.bbms/1546570904<strong>Xinjian Zhang</strong>, <strong>Long Miao</strong>, <strong>Jia Zhang</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 25, Number 4, 481--493.</p><p><strong>Abstract:</strong><br/>
A subgroup $H$ of a group $G$ is said to be weakly $s$-supplementedly embedded in $G$ if there exists a subgroup $T$ of $G$ such that $G=HT$ and $H\cap T\leq H_{se}\leq H$, where $H_{se}$ is an S-permutably embedded subgroup of $G$. In this paper, we investigate the structure of $G$ under the assumption that some subgroups of prime-power order are weakly S-supplementedly embedded in $G$, and some new criteria for $p$-nilpotency are obtained.
</p>projecteuclid.org/euclid.bbms/1546570904_20190103220159Thu, 03 Jan 2019 22:01 ESTSporadic finite simple groups and block designshttps://projecteuclid.org/euclid.bbms/1546570905<strong>Xiaohong Zhang</strong>, <strong>Shenglin Zhou</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 25, Number 4, 495--506.</p><p><strong>Abstract:</strong><br/>
The purpose of this paper is to classify all pairs $(\mathcal{D}, G)$, where $\mathcal{D}$ is a non-trivial $2$-$(v, k, \lambda)$ design with $\lambda\leq10$, and $G\leq \mathrm{Aut}(\mathcal{D})$ acts transitively on the set of blocks of $\mathcal{D}$ and primitively on the set of points of $\mathcal{D}$ with sporadic socle. We prove that there are exactly 15 such pairs $(\mathcal{D}, G)$.
</p>projecteuclid.org/euclid.bbms/1546570905_20190103220159Thu, 03 Jan 2019 22:01 ESTNorm growth for the Busemann cocyclehttps://projecteuclid.org/euclid.bbms/1546570906<strong>Thibaut Dumont</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 25, Number 4, 507--526.</p><p><strong>Abstract:</strong><br/>
Using explicit methods, we provide an upper bound to the norm of the Busemann cocycle of a locally finite regular tree $X$, emphasizing the symmetries of the cocycle. The latter takes value into a submodule of square summable functions on the edges of $X$, which corresponds to the Steinberg representation for rank one groups acting on their Bruhat-Tits tree. The norm of the Busemann cocycle is asymptotically linear with respect to square root of the distance between any two vertices. Independently, Gournay and Jolissaint [10] proved an exact formula for harmonic 1-cocycles covering the present case.
</p>projecteuclid.org/euclid.bbms/1546570906_20190103220159Thu, 03 Jan 2019 22:01 ESTStarlikeness of a generalized Bessel functionhttps://projecteuclid.org/euclid.bbms/1546570907<strong>Rosihan M. Ali</strong>, <strong>See Keong Lee</strong>, <strong>Saiful R. Mondal</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 25, Number 4, 527--540.</p><p><strong>Abstract:</strong><br/>
This paper investigates three functions $\mathtt{f}_{a, \nu}$, $\mathtt{g}_{a, \nu}$ and $\mathtt{h}_{a, \nu}$ in the class $\mathcal{A}$ consisting of analytic functions $f$ in the unit disk satisfying $f(0)=f'(0)-1=0$. Here $a \in \{1, 2, 3, \ldots\},$ and $\nu$ is real. Each function is related to the generalized Bessel function. The radius of starlikeness of positive order is obtained for each of the three functions. Further, the best range on $\nu$ is determined for a fixed $a$ to ensure the functions $\mathtt{f}_{a, \nu}$ and $\mathtt{g}_{a, \nu}$ are starlike of positive order in the entire unit disk. When $a=1,$ the results obtained reduced to earlier known results.
</p>projecteuclid.org/euclid.bbms/1546570907_20190103220159Thu, 03 Jan 2019 22:01 ESTA note on the Vestfrid theoremhttps://projecteuclid.org/euclid.bbms/1546570908<strong>Yu Zhou</strong>, <strong>Zihou Zhang</strong>, <strong>Chunyan Liu</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 25, Number 4, 541--544.</p><p><strong>Abstract:</strong><br/>
Let $X$ be a real Banach space, $T$ be a compact metrizable space, $C(T)$ be the real-valued continuous functions space, and $f:X\rightarrow C(T)$ be a standard $\varepsilon$-isometric embedding. Then for any $\lambda>6$ there is an isometric embedding $h: X\rightarrow C(T)$ such that $\|f(u)-h(u)\|\leq\lambda\varepsilon$ for all $u\in X$.
</p>projecteuclid.org/euclid.bbms/1546570908_20190103220159Thu, 03 Jan 2019 22:01 ESTRegular methods of summability and the weak $\sigma$-Fatou property in abstract Banach lattices of integrable functionshttps://projecteuclid.org/euclid.bbms/1546570909<strong>E. Jiménez Fernández</strong>, <strong>M. A. Juan</strong>, <strong>E. A. Sánchez Pérez</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 25, Number 4, 545--553.</p><p><strong>Abstract:</strong><br/>
Consider an abstract Banach lattice. Under some mild assumptions, it can be identified with a Banach ideal of integrable functions with respect to a (non necessarily $\sigma$-finite) vector measure on a $\delta$-ring. Extending some nowadays well-known results for the Koml\'os property involving Cesaro sums, we prove that the weak $\sigma$-Fatou property for a Banach lattice of integrable functions $E$ is equivalent to the existence for each norm bounded sequence $(f_n)$ in $E$ of a regular method of summability $D$ such that the sequence $(f_n^D)$ converges.
</p>projecteuclid.org/euclid.bbms/1546570909_20190103220159Thu, 03 Jan 2019 22:01 ESTA new characterization of differences of weighted composition operators on weighted type spaceshttps://projecteuclid.org/euclid.bbms/1546570910<strong>Lixu Zhang</strong>, <strong>Yanhua Zhang</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 25, Number 4, 555--563.</p><p><strong>Abstract:</strong><br/>
A new characterization for the boundedness, compactness and essential norm for the differences of weighted composition operators on weighted type spaces is given in this paper.
</p>projecteuclid.org/euclid.bbms/1546570910_20190103220159Thu, 03 Jan 2019 22:01 ESTTwo-numbers and their applications - A surveyhttps://projecteuclid.org/euclid.bbms/1546570911<strong>Bang-Yen Chen</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 25, Number 4, 565--596.</p><p><strong>Abstract:</strong><br/>
The notion of two-numbers of connected Riemannian manifolds was introduced about 35 years ago in [Un invariant geometrique riemannien, C. R. Acad. Sci. Paris Math. 295 (1982), 389--391] by B.-Y. Chen and T. Nagano. Later, two-numbers have been studied by a number of mathematicians and it was then proved that two-numbers related closely with several important areas in mathematics. The main purpose of this article is to survey on two-numbers and their applications. At the end of this survey, we present several open problems and conjectures on two-numbers.
</p>projecteuclid.org/euclid.bbms/1546570911_20190103220159Thu, 03 Jan 2019 22:01 ESTSuper-biderivations and super-commuting maps on the topological $N=2$ superconformal algebrahttps://projecteuclid.org/euclid.bbms/1546570912<strong>Lili Chi</strong>, <strong>Jiancai Sun</strong>, <strong>Hengyun Yang</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 25, Number 4, 597--609.</p><p><strong>Abstract:</strong><br/>
Let $\mathcal{T}$ be the well-known topological $N=2$ superconformal algebra. In this paper, we prove that every super-skewsymmetric super-biderivation of $\mathcal{T}$ is inner. Based on the result of super-biderivations, we show that all the linear super-commuting maps on $\mathcal{T}$ which have the form $\psi(x)=\lambda x+f(x)c$ are not standard.
</p>projecteuclid.org/euclid.bbms/1546570912_20190103220159Thu, 03 Jan 2019 22:01 ESTPeriodic orbits of the three dimensional logarithm galactic potentialhttps://projecteuclid.org/euclid.bbms/1546570913<strong>Daniel Paşca</strong>, <strong>Bogdan Mircea Tătaru</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 25, Number 4, 611--627.</p><p><strong>Abstract:</strong><br/>
We apply the averaging theory of first order to study analytically families of periodic orbits for a three dimensional logarithmic galactic potential $H=\dfrac12 (p_x^2+p_y^2+p_z^2) + \dfrac{ v_0^2}{2} \ln(x^2 - \lambda x^3 + \alpha y^2+b z^2 + c_b^2)$, that is relevant in the study of elliptic galactic dynamics. We first introduce a scale transformation in the coordinates and momenta with a parameter $\varepsilon$ and we find, using averaging theory of first order in $\varepsilon$, the existence up to three periodic orbits if $\alpha,\beta$ are irrational, and one periodic orbit if either $\alpha$ is irrational and $\beta$ is rational, or $\beta$ is irrational and $\alpha$ is rational, for $\varepsilon$ sufficiently small.
</p>projecteuclid.org/euclid.bbms/1546570913_20190103220159Thu, 03 Jan 2019 22:01 ESTCompactness of the automorphism group of a topological parallelism on real projective 3-space: The disconnected casehttps://projecteuclid.org/euclid.bbms/1546570914<strong>Rainer Löwen</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 25, Number 4, 629--640.</p><p><strong>Abstract:</strong><br/>
We prove that the automorphism group of a topological parallelism on real projective 3-space is compact. This settles a conjecture stated in [1], where it was proved that at least the connected component of the identity is compact.
</p>projecteuclid.org/euclid.bbms/1546570914_20190103220159Thu, 03 Jan 2019 22:01 ESTAlmost $\eta$-Ricci solitons in $(LCS)_n$-manifoldshttps://projecteuclid.org/euclid.bbms/1547780426<strong>Adara M. Blaga</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 25, Number 5, 641--653.</p><p><strong>Abstract:</strong><br/>
We consider almost $\eta$-Ricci solitons in $(LCS)_n$-manifolds satisfying certain curvature conditions. We provide a lower and an upper bound for the norm of the Ricci curvature in the gradient case, derive a Bochner-type formula for an almost $\eta$-Ricci soliton and state some consequences of it on an $(LCS)_n$-manifold.
</p>projecteuclid.org/euclid.bbms/1547780426_20190117220049Thu, 17 Jan 2019 22:00 ESTOn the generic triangle group and the free metabelian group of rank 2https://projecteuclid.org/euclid.bbms/1547780427<strong>Stefano Isola</strong>, <strong>Riccardo Piergallini</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 25, Number 5, 653--676.</p><p><strong>Abstract:</strong><br/>
We introduce the concept of a generic Euclidean triangle $\tau$ and study the group $G_\tau$ generated by the reflection across the edges of $\tau$. In particular, we prove that the subgroup $T_\tau$ of all translations in $G_\tau$ is free abelian of infinite rank, while the index 2 subgroup $H_\tau$ of all orientation preserving transformations in $G_\tau$ is free metabelian of rank 2, with $T_\tau$ as the commutator subgroup. As a consequence, the group $G_\tau$ cannot be finitely presented and we provide explicit minimal infinite presentations of both $H_\tau$ and $G_\tau$. This answers in the affirmative the problem of the existence of a minimal presentation for the free metabelian group of rank 2. Moreover, we discuss some examples of non-trivial relations in $T_\tau$ holding for given non-generic triangles $\tau$.
</p>projecteuclid.org/euclid.bbms/1547780427_20190117220049Thu, 17 Jan 2019 22:00 ESTStrong topological transitivity of some classes of operatorshttps://projecteuclid.org/euclid.bbms/1547780428<strong>Mohammad Ansari</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 25, Number 5, 677--685.</p><p><strong>Abstract:</strong><br/>
In this paper, we investigate the strong topological transitivity of some well-known classes of topologically transitive operators. Also, topological largeness of the set of all strongly topologically transitive operators on a second countable Baire locally convex space is investigated.
</p>projecteuclid.org/euclid.bbms/1547780428_20190117220049Thu, 17 Jan 2019 22:00 ESTInvariant $\varphi$-means for abstract Segal algebras related to locally compact groupshttps://projecteuclid.org/euclid.bbms/1547780429<strong>Hossein Javanshiri</strong>, <strong>Mehdi Nemati</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 25, Number 5, 687--698.</p><p><strong>Abstract:</strong><br/>
In this paper, for a locally compact group ${\mathcal G}$ we characterize character amenability and character contractibility of abstract Segal algebras with respect to the group algebra $L^1({\mathcal G})$ and the generalized Fourier algebra $A_p({\mathcal G})$. As a main result we prove that ${\mathcal G}$ is discrete and amenable if and only if some class of abstract Segal algebras in $L^1({\mathcal G})$ is character amenable. We also prove a similar result for abstract Segal algebras in $A_p({\mathcal G})$ and $C_0({\mathcal G})$. Finally, under some conditions we investigate when a commutative, semisimple, Tauberian Banach algebra is an ideal in its second dual space.
</p>projecteuclid.org/euclid.bbms/1547780429_20190117220049Thu, 17 Jan 2019 22:00 ESTCounting Unlabeled Bipartite Graphs Using Polya's Theoremhttps://projecteuclid.org/euclid.bbms/1547780430<strong>Abdullah Atmaca</strong>, <strong>A. Yavuz Oruç</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 25, Number 5, 699--715.</p><p><strong>Abstract:</strong><br/>
This paper solves a problem that was stated by M. A. Harrison in 1973. The problem has remained open since then, and it is concerned with counting equivalence classes of $n\times r$ binary matrices under row and column permutations. Let $I$ and $O$ denote two sets of vertices, where $I\cap O =\emptyset$, $|I| = n$, $|O| = r$, and $B_u(n,r)$ denote the set of unlabeled graphs whose edges connect vertices in $I$ and $O$. Harrison established that the number of equivalence classes of $n\times r$ binary matrices is equal to the number of unlabeled graphs in $B_u(n,r).$ He also computed the number of such matrices (hence such graphs) for small values of $n$ and $r$ without providing an asymptotic formula for $|B_u(n,r)|.$ Here, such an asymptotic formula is provided by proving the following two-sided inequality using Polya's Counting Theorem. \begin{equation} \displaystyle \frac{\binom{r+2^{n}-1}{r}}{n!} \le |B_u(n,r)| \le 2\frac{\binom{r+2^{n}-1}{r}}{n!}, n< r. \end{equation}
</p>projecteuclid.org/euclid.bbms/1547780430_20190117220049Thu, 17 Jan 2019 22:00 ESTThe Helmholtz decomposition in weighted $L^p$ spaces in coneshttps://projecteuclid.org/euclid.bbms/1547780431<strong>Serge Nicaise</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 25, Number 5, 717--728.</p><p><strong>Abstract:</strong><br/>
In this paper we prove the Helmholtz decomposition in conical domains of $\mathbb{R}^3$ in weighted $L^p_\beta$ spaces under a spectral condition on $\beta,p$. The basic elements are the transformation of the original problem into a problem set in cylindrical domains and the combination of a priori bounds from [5] with the vector-valued multiplier theorem [29].
</p>projecteuclid.org/euclid.bbms/1547780431_20190117220049Thu, 17 Jan 2019 22:00 ESTFunction Spaces and Nonsymmetric Norm Preserving Mapshttps://projecteuclid.org/euclid.bbms/1547780432<strong>Hadis Pazandeh</strong>, <strong>Fereshteh Sady</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 25, Number 5, 729--740.</p><p><strong>Abstract:</strong><br/>
Let $X,Y$ be compact Hausdorff spaces and $A,B$ be either closed subspaces of $C(X)$ and $C(Y)$, respectively, containing constants or positive cones of such subspaces. In this paper we study surjections $T:A \longrightarrow B$ satisfying the norm condition $\|T(f) T(g) -1 \|_Y=\|fg-1\|_X$ for all $f,g \in A$, where $\|\cdot\|_X$ and $\|\cdot\|_Y$ denote the supremum norms. We show that under a mild condition on the strong boundary points of $A$ and $B$ (and the assumption $T(i)=i T(1)$ in the subspace case), the map $T$ is a weighted composition operator on the set of strong boundary points of $B$. This result is an improvement of the known results for uniform algebra case to closed linear subspaces and their positive cones.
</p>projecteuclid.org/euclid.bbms/1547780432_20190117220049Thu, 17 Jan 2019 22:00 ESTHigher Order Hochschild (Co)homology of Noncommutative Algebrashttps://projecteuclid.org/euclid.bbms/1547780433<strong>Bruce R. Corrigan-Salter</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 25, Number 5, 741--754.</p><p><strong>Abstract:</strong><br/>
Hochschild (co)homology and Pirashvili's higher order Hochschild (co)homology are useful tools for a variety of applications including deformations of algebras. When working with higher order Hochschild (co)homology, we can consider the (co)homology of any commutative algebra with symmetric coefficient bimodules, however traditional Hochschild (co)homology is defined for any associative algebra with not necessarily symmetric coefficient bimodules. In the present paper, we generalize higher order Hochschild (co)homology to work with associative algebras which need not be commutative and in particular, show that simplicial sets admit such a generalization if and only if they are one dimensional.
</p>projecteuclid.org/euclid.bbms/1547780433_20190117220049Thu, 17 Jan 2019 22:00 ESTA potpourri of algebraic properties of the ring of periodic distributionshttps://projecteuclid.org/euclid.bbms/1547780434<strong>Amol Sasane</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 25, Number 5, 755--776.</p><p><strong>Abstract:</strong><br/>
The set of periodic distributions, with usual addition and convolution, forms a ring, which is isomorphic, via taking a Fourier series expansion, to the ring $\mathcal{S}'(\mathbb{Z}^d)$ of sequences of at most polynomial growth with termwise operations. In this article, we establish several algebraic properties of these rings.
</p>projecteuclid.org/euclid.bbms/1547780434_20190117220049Thu, 17 Jan 2019 22:00 ESTOn the multiplication by a polynomial of bounded continued fraction over a finite fieldhttps://projecteuclid.org/euclid.bbms/1547780435<strong>Khalil Ayadi</strong>, <strong>Awatef Azaza</strong>, <strong>Iheb Elouaer</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 25, Number 5, 777--792.</p><p><strong>Abstract:</strong><br/>
In this paper, we will discuss the period length of the continued fraction of the product of a polynomial with a quadratic power series over a finite field. Furthermore, we will give the first example of bounded continued fraction in characteristic 3 with not flat partial quotients.
</p>projecteuclid.org/euclid.bbms/1547780435_20190117220049Thu, 17 Jan 2019 22:00 EST