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 EDTTwo-transitive pairs in $ \mathrm{PSL}(2,q)$http://projecteuclid.org/euclid.bbms/1457560852<strong>Francis Buekenhout</strong>, <strong>Julie De Saedeleer</strong>, <strong>Dimitri Leemans</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 23, Number 1, 33--55.</p><p><strong>Abstract:</strong><br/>
For every group $ \mathrm{PSL}(2,q)$, $q$ a prime power, we
classify all two-transitive pairs $(U,U_0)$ consisting of a subgroup
$U$ of $ \mathrm{PSL}(2,q)$ and a subgroup $U_0$ of $U$ such that the
action of $U$ on the cosets of $U_0$ is two-transitive. We obtain
twenty classes up to conjugacy in $ \mathrm{PSL}(2,q)$ or fusion in
$P\Gamma L (2,q)$ except for two cases in which we don't have that
control.
</p>projecteuclid.org/euclid.bbms/1457560852_20160309170054Wed, 09 Mar 2016 17:00 ESTOn bijections, isometries and expansive mapshttp://projecteuclid.org/euclid.bbms/1457560853<strong>Alessandro Fedeli</strong>, <strong>Attilio Le Donne</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 23, Number 1, 57--61.</p><p><strong>Abstract:</strong><br/>
In this paper we show when a bijection on a set $X$ can be made
either an isometry or an expansive map with respect to a non-discrete
metric on $X$. As a corollary we obtain that any bijection on an
infinite set can be made biLipschitz by a non-discrete metric.
</p>projecteuclid.org/euclid.bbms/1457560853_20160309170054Wed, 09 Mar 2016 17:00 ESTApproximation and Schur properties for Lipschitz free spaces over
compact metric spaceshttp://projecteuclid.org/euclid.bbms/1457560854<strong>P. Hájek</strong>, <strong>G. Lancien</strong>, <strong>E. Pernecká</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 23, Number 1, 63--72.</p><p><strong>Abstract:</strong><br/>
We prove that for any separable Banach space $X$, there exists a
compact metric space which is homeomorphic to the Cantor space and
whose Lipschitz-free space contains a complemented subspace isomorphic
to $X$. As a consequence we give an example of a compact metric space
which is homeomorphic to the Cantor space and whose Lipschitz-free
space fails the approximation property and we prove that there exists
an uncountable family of topologically equivalent distances on the
Cantor space whose free spaces are pairwise non isomorphic. We also
prove that the free space over a countable compact metric space has
the Schur property. These results answer questions by G. Godefroy.
</p>projecteuclid.org/euclid.bbms/1457560854_20160309170054Wed, 09 Mar 2016 17:00 ESTDouble point-homogeneous spherical curveshttp://projecteuclid.org/euclid.bbms/1457560855<strong>Guy Valette</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 23, Number 1, 73--86.</p><p><strong>Abstract:</strong><br/>
A curve is, in this paper, the image of the circle $S^1$ under an
immersion $f$ into $S^2$, $\mathbb{R}^2$ or the real projective plane
$P_2(\mathbb{R})$, such that every multiple point of $f$ is an
ordinary double point. Such a curve $C$ is double point-homogeneous or
DP-homogeneous when the group of diffeomorphisms (of $S^2,
\mathbb{R}^2$ or $P_2(\mathbb{R})$) preserving $C$ has a transitive
action on the set of its double points. The orbits of DP-homogeneous
curves in $S^2$ are totally determined; using combinatorial methods,
we prove that they fall into five countably infinite families ; the
description of every family is illustrated by drawings of some
representatives with a small number of double points. As a corollary,
we obtain a similar classification of the DP-homogeneous curves in
$\mathbb{R}^2$. We also propose a conjecture about the classification
of DP-homogeneous curves in $P_2(\mathbb{R})$.
</p>projecteuclid.org/euclid.bbms/1457560855_20160309170054Wed, 09 Mar 2016 17:00 ESTCauchy transformation and mutual dualities between
$A^{-\infty}(\Omega)$ and $A^\infty(\complement\Omega)$ for Carathéodory
domainshttp://projecteuclid.org/euclid.bbms/1457560856<strong>A.V. Abanin</strong>, <strong>Le Hai Khoi</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 23, Number 1, 87--102.</p><p><strong>Abstract:</strong><br/>
Let $\Omega$ be a Carathéodory domain in the complex plane $\mathbb
C$, $A^{-\infty}(\Omega)$ the space of functions that are holomorphic
in $\Omega$ with polynomial growth near the boundary $\partial\Omega$,
and $A^\infty(\complement\Omega)$ the space of holomorphic functions
in the interior of $\complement\Omega:=\overline{\mathbb
C}\setminus\Omega$, vanishing at infinity and being in
$C^\infty(\complement\Omega)$. We prove that the Cauchy transformation
of analytic functionals establishes a mutual duality between spaces
$A^{-\infty}(\Omega)$ and $A^\infty(\complement\Omega)$. This result,
together with those of [3], gives a solution to duality problem for
the space $A^{-\infty}(\Omega)$ in both one and several complex
variables.
</p>projecteuclid.org/euclid.bbms/1457560856_20160309170054Wed, 09 Mar 2016 17:00 ESTA complete classification of real hypersurfaces in
$\mathbb{C}P^{2}$ and $\mathbb{C}H^{2}$ with generalized $\xi-$parallel
Jacobi structure Operatorhttp://projecteuclid.org/euclid.bbms/1457560857<strong>Th. Theofanidis</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 23, Number 1, 103--113.</p><p><strong>Abstract:</strong><br/>
The aim of the present paper is the classification of real
hypersurfaces $M$, whose Jacobi structure Operator is
\emph{generalized $\xi-$parallel}. The notion of generalized
$\xi-$parallel Jacobi structure Operator is rather new and much weaker
than $\xi-$ parallel Jacobi structure Operator which has been studied
so far.
</p>projecteuclid.org/euclid.bbms/1457560857_20160309170054Wed, 09 Mar 2016 17:00 ESTArithmetical pseudo-valuations associated to Dubrovin valuation
rings and prime divisors of bounded Krull ordershttp://projecteuclid.org/euclid.bbms/1457560858<strong>Freddy Van Oystaeyen</strong>, <strong>Nikolaas Verhulst</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 23, Number 1, 115--131.</p><p><strong>Abstract:</strong><br/>
We look at value functions of primes in simple Artinian rings and
associate arithmetical pseudo-valuations to Dubrovin valuation rings
which, in the Noetherian case, are $\mathbb{Z}$-valued. This allows a
divisor theory for bounded Krull orders.
</p>projecteuclid.org/euclid.bbms/1457560858_20160309170054Wed, 09 Mar 2016 17:00 ESTSlant helices in the Euclidean 3-space revisitedhttp://projecteuclid.org/euclid.bbms/1457560859<strong>Pascual Lucas</strong>, <strong>José Antonio Ortega-Yagües</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 23, Number 1, 133--150.</p><p><strong>Abstract:</strong><br/>
In this paper, we study the surfaces whose geodesics are slant
curves. We show that a unit speed curve $\gamma$ in the 3-dimensional
Euclidean space is a slant helix if and only if it is a geodesic of a
helix surface. We prove that the striction line of a helix surface is
a general helix; as a consequence, slant helices are characterized as
geodesics of the tangent surface of a general helix. Finally, we
provide two methods for constructing slant helices in helix
surfaces.
</p>projecteuclid.org/euclid.bbms/1457560859_20160309170054Wed, 09 Mar 2016 17:00 ESTUne note sur les dérivations localement nilpotentes dans les
catégories monoïdales symétriqueshttp://projecteuclid.org/euclid.bbms/1457560860<strong>Abhishek Banerjee</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 23, Number 1, 151--160.</p><p><strong>Abstract:</strong><br/>
In this paper, we construct the exponential morphism
$e^D:A\longrightarrow A$ associated to a locally nilpotent derivation
$D$ on a monoid $A$ in a symmetric monoidal category. Further, we show
that the kernel of $D$ is identical to the subobject of $A$ invariant
under $e^D$. Finally, we study how to extend a locally nilpotent
derivation on $A$ to its localization $A_S$, where $S\subseteq
Hom_{A-Mod}(A,A)$ is a multiplicatively closed subset.
</p>projecteuclid.org/euclid.bbms/1457560860_20160309170054Wed, 09 Mar 2016 17:00 ESTBoundaries and peak points in topological algebrashttp://projecteuclid.org/euclid.bbms/1464710112<strong>Rodia I. Hadjigeorgiou</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 23, Number 2, 161--189.</p><p><strong>Abstract:</strong><br/>
We examine the relation of the set of peak points with several
boundaries defined in the spectrum of a given topological algebra
relative to a subspace of it. In this respect, we show that the
peak points are contained in the Choquet boundary and, under
suitable conditions, are dense in the Šilov boundary.
Furthermore, the set of points at issue coincide with the Bishop
boundary if, and only if, it constitutes a weakly boundary set.
On the other hand, in appropriate topological algebras, the Bishop,
Choquet and strong boundaries coincide with the peak points, so
that they are dense in the Šilov boundary. Finally
there are topological algebras for which all the above boundaries
and points remain invariant, under restriction of the Gel'fand
transform algebras to subsets of the spectra of the topological
algebras involved, containing the Šilov boundary.
</p>projecteuclid.org/euclid.bbms/1464710112_20160531115513Tue, 31 May 2016 11:55 EDTMore on the locally convex space $(M(X),\beta(X))$ of a locally compact Hausdorff space $X$http://projecteuclid.org/euclid.bbms/1464710113<strong>Hossein Javanshiri</strong>, <strong>Rasoul Nasr-Isfahani</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 23, Number 2, 191--201.</p><p><strong>Abstract:</strong><br/>
In the previous paper [12] we introduced the definition of
the strict topology $\beta(X)$ on the measure space $M(X)$ for a
locally compact Hausdorff space $X$. In this paper, we consider on
$M(X)$ the topology $\beta(X)$ and we show that $\beta(X)$ is the
weak topology under all left multipliers induced by a function
space on $M(X)$. We then show that $\beta(X)$ can be considered as
a mixed topology. This result is not only of interest in its own
right, but also it paves the way to prove that $(M(X),\beta(X))$
is a Mazur space and the locally convex space $(M(S),\beta(S))$,
equipped with the convolution multiplication is a complete
semitopological algebra, for a wide class of locally compact
semigroups $S$.
</p>projecteuclid.org/euclid.bbms/1464710113_20160531115513Tue, 31 May 2016 11:55 EDTDisk-cyclic and Codisk-cyclic tuples of the adjoint weighted composition operators on Hilbert spaceshttp://projecteuclid.org/euclid.bbms/1464710114<strong>Yu-Xia Liang</strong>, <strong>Ze-Hua Zhou</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 23, Number 2, 203--215.</p><p><strong>Abstract:</strong><br/>
Some sufficient conditions under which the tuple of the adjoint of weighted composition operators $(C_{\omega_1,\varphi_1}^* , C_{\omega_2,\varphi_2}^*)$ on the Hilbert space $\mathcal{H}$ of analytic functions is disk-cyclic (or codisk-cyclic) were investigated.
</p>projecteuclid.org/euclid.bbms/1464710114_20160531115513Tue, 31 May 2016 11:55 EDTUpper-Lower and Left-Right Semi-Fredholmnesshttp://projecteuclid.org/euclid.bbms/1464710115<strong>C.S. Kubrusly</strong>, <strong>B.P. Duggal</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 23, Number 2, 217--233.</p><p><strong>Abstract:</strong><br/>
Upper-lower and left-right approaches coincide for semi-Fredholm operators
on Hilbert spaces but, in general, they are distinct for operators
on a Banach space. The purpose of this paper is to investigate the
difference between the upper-lower and left-right approaches for
semi-Fredholm operators on a Banach space and, in particular, to
verify when these approaches coincide. The program is based on the classes
$\Gamma_R[\X]$ and $\Gamma_N[\X]$ of all operators on a Banach space
$\X$ with complemented range and complemented kernel. It is shown that the
intersection ${\Gamma_R[\X]\cap\Gamma_N[\X]}$ is algebraically and
topologically large, and also that if $\Gamma_R[\X]$ and $\Gamma_N[\X]$ are
either open, or closed, or if they coincide, then there is no difference
between the upper-lower and left-right approaches for semi-Fredholm
operators on a Banach space.
</p>projecteuclid.org/euclid.bbms/1464710115_20160531115513Tue, 31 May 2016 11:55 EDT$f-$statistical convergence, completeness and $f-$cluster pointshttp://projecteuclid.org/euclid.bbms/1464710116<strong>M. C. Listán-García</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 23, Number 2, 235--245.</p><p><strong>Abstract:</strong><br/>
We study $f-$statistical convergence, which is a generalization of the classical statistical convergence. In terms of it, we give a characterization of completeness in a normed space. We also introduce `$f-$statistical cluster points', which is a richer concept than the classic one. Namely, each (usual) limit point of a sequence is an $f-$statistical cluster point for some $f$.
</p>projecteuclid.org/euclid.bbms/1464710116_20160531115513Tue, 31 May 2016 11:55 EDTImproved direct and converse theorems in weighted Lorentz
spaceshttp://projecteuclid.org/euclid.bbms/1464710117<strong>Ramazan Akgün</strong>, <strong>Yunus Emre Yıldırır</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 23, Number 2, 247--262.</p><p><strong>Abstract:</strong><br/>
In the present work we prove the equivalence of the fractional modulus of
smoothness to the realization functional and to the Peetre K-functional in
weighted Lorentz spaces. Using this equivalence we obtain an improvement of
the direct approximation theorem. Furthermore we prove the improved converse
theorem in this space.
</p>projecteuclid.org/euclid.bbms/1464710117_20160531115513Tue, 31 May 2016 11:55 EDTOn a frictional contact problem with adhesion in piezoelectricityhttp://projecteuclid.org/euclid.bbms/1464710118<strong>Mohamed Selmani</strong>, <strong>Lynda Selmani</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 23, Number 2, 263--284.</p><p><strong>Abstract:</strong><br/>
We consider a mathematical model describing the quasistatic frictional
contact between an electro-elasto-viscoplastic body and an adhesive
conductive foundation. The contact is described with a normal compliance
condition with adhesion, the associated general version of Coulomb's law of
dry friction in which the adhesion of contact surfaces is taken into
account and a regularized electrical conductivity condition. The existence
of a unique weak solution is established under smallness assumption on the
surface conductance. The proof is based on arguments of time-dependent
variational inequalities, differential equations and Banach fixed point
theorem.
</p>projecteuclid.org/euclid.bbms/1464710118_20160531115513Tue, 31 May 2016 11:55 EDTUniform and
pointwise Bernstein-Walsh-type inequalities on a quasidisk in the complex
planehttp://projecteuclid.org/euclid.bbms/1464710119<strong>F.G. Abdullayev</strong>, <strong>P. Özkartepe</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 23, Number 2, 285--310.</p><p><strong>Abstract:</strong><br/>
In this present work, we continue studying the Bernstein-Walsh type
estimations for complex algebraic polynomials in the bounded and unbounded
regions with quasiconformal boundary.
</p>projecteuclid.org/euclid.bbms/1464710119_20160531115513Tue, 31 May 2016 11:55 EDTWhen are enriched strong monads double exponential monads?http://projecteuclid.org/euclid.bbms/1464710120<strong>Christopher Townsend</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 23, Number 2, 311--319.</p><p><strong>Abstract:</strong><br/>
Some categorical conditions are given that are sufficient to show that an enriched monad with a strength is a double exponential monad. The conditions hold for the double power locale monad (enriched over posets) and so as an application it is shown that the double power locale monad is a double exponential monad. A benefit is that this result about the double power locale monad can be established without the need for any detailed discussion of frame presentations or topos theory.
</p>projecteuclid.org/euclid.bbms/1464710120_20160531115513Tue, 31 May 2016 11:55 EDTGrassmannians of arbitrary rankhttp://projecteuclid.org/euclid.bbms/1473186508<strong>Simon Huggenberger</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 23, Number 3, 321--343.</p><p><strong>Abstract:</strong><br/>
We introduce a generalization of Grassmannians of projective spaces that
allows us to consider subspaces of any (possibly infinite) rank as points of
the Grassmannian. We show that the spaces that we obtain, carry in a
natural way the structure of a twin building.
</p>projecteuclid.org/euclid.bbms/1473186508_20160906142833Tue, 06 Sep 2016 14:28 EDTYamabe solitons on three-dimensional Kenmotsu manifoldshttp://projecteuclid.org/euclid.bbms/1473186509<strong>Yaning Wang</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 23, Number 3, 345--355.</p><p><strong>Abstract:</strong><br/>
Let the Riemannian metric of a three-dimensional Kenmotsu manifold be a Yamabe soliton. In this paper, we prove that the Kenmotsu manifold is of constant sectional curvature $-1$ and the Yamabe soliton is expanding with the soliton constant $\lambda=-6$.
</p>projecteuclid.org/euclid.bbms/1473186509_20160906142833Tue, 06 Sep 2016 14:28 EDTOn the simplicity of induced modules for reductive Lie algebrashttp://projecteuclid.org/euclid.bbms/1473186510<strong>Chaowen Zhang</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 23, Number 3, 357--371.</p>projecteuclid.org/euclid.bbms/1473186510_20160906142833Tue, 06 Sep 2016 14:28 EDTNon-Archimedean meromorphic solutions of functional equationshttp://projecteuclid.org/euclid.bbms/1473186511<strong>Pei-Chu Hu</strong>, <strong>Yong-Zhi Luan</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 23, Number 3, 373--383.</p><p><strong>Abstract:</strong><br/>
We discuss meromorphic solutions of functional equations over non-Archimedean fields, and prove difference analogues of the Clunie lemma, Malmquist-type theorems and the Mokhon'ko theorem.
</p>projecteuclid.org/euclid.bbms/1473186511_20160906142833Tue, 06 Sep 2016 14:28 EDTA criterion of strong density of operator subalgebrashttp://projecteuclid.org/euclid.bbms/1473186512<strong>Antoni Wawrzyńczyk</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 23, Number 3, 385--389.</p><p><strong>Abstract:</strong><br/>
The purpose of the note is to show the usefulness of a simple criterion of density of a subalgebra $\mathcal A\subset L(X)$ in the strong operator topology for arbitrary real or complex locally convex vector space $X$. After proving the criterion we observe its efficiency obtaining short proofs of three important known density theorems plus a new one.
</p>projecteuclid.org/euclid.bbms/1473186512_20160906142833Tue, 06 Sep 2016 14:28 EDTCharacterization of metric spaces whose free space is isometric to $\ell_1$http://projecteuclid.org/euclid.bbms/1473186513<strong>Aude Dalet</strong>, <strong>Pedro L. Kaufmann</strong>, <strong>Antonín Procházka</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 23, Number 3, 391--400.</p><p><strong>Abstract:</strong><br/>
We characterize metric spaces whose Lipschitz free space is isometric to $\ell_1$.
In particular, we show that the Lipschitz free space over an ultrametric space is not isometric to $\ell_1(\Gamma)$ for any set $\Gamma$. We give a lower bound for the Banach-Mazur distance in the finite case.
</p>projecteuclid.org/euclid.bbms/1473186513_20160906142833Tue, 06 Sep 2016 14:28 EDTStructures Associated with Real Closed Fields and the Axiom of Choicehttp://projecteuclid.org/euclid.bbms/1473186514<strong>Merlin Carl</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 23, Number 3, 401--419.</p><p><strong>Abstract:</strong><br/>
An integer part $I$ of a real closed field $K$ is a discretely ordered subring of $K$ with minimal positive element $1$
such that, for every $x\in K$, there is $i\in I$ with $i\leq x<i+1$.
Mourgues and Ressayre showed in [MR] that every real closed field has an integer part. Their construction implicitly uses the Axiom of Choice.
We show that $AC$ is actually necessary to obtain the result by constructing a transitive model of $ZF$ which contains a real
closed field without an integer part. Then we analyze some cases where the Axiom of Choice is not necessary for obtaining an integer part.
On the way, we demonstrate that a class of questions containing the question whether the Axiom of Choice is necessary for the proof of a certain $ZFC$-theorem
is algorithmically undecidable. We further apply the methods to show that it is independent of $ZF$ whether every real closed field has a value group section and a residue field section.
This also sheds some light on the possibility to effectivize constructions of integer parts and value group sections which was considered e.g. in [DKKL]
and [KL]
</p>projecteuclid.org/euclid.bbms/1473186514_20160906142833Tue, 06 Sep 2016 14:28 EDTLagrangian submanifolds in para-complex Euclidean spacehttp://projecteuclid.org/euclid.bbms/1473186515<strong>Henri Anciaux</strong>, <strong>Maikel Antonio Samuays</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 23, Number 3, 421--437.</p><p><strong>Abstract:</strong><br/>
We address the study of some curvature equations for distinguished submanifolds in para-Kähler geometry. We first observe that a para-complex submanifold of a para-Kähler manifold is minimal. Next we describe the extrinsic geometry of Lagrangian submanifolds in the para-complex Euclidean space $\mathbb{D}^n$ and discuss a number of examples, such as graphs and normal bundles. We also
characterize those Lagrangian surfaces of $\mathbb{D}^2$ which are minimal and have indefinite metric. Finally we describe those Lagrangian self-similar solutions of the Mean Curvature Flow (with respect to the neutral metric of $\mathbb{D}^n$) which are $SO(n)$-equivariant.
</p>projecteuclid.org/euclid.bbms/1473186515_20160906142833Tue, 06 Sep 2016 14:28 EDTCurves of low positive genus and low degree on a general heptic hypersurface of $\mathbb {P}^5$http://projecteuclid.org/euclid.bbms/1473186516<strong>E. Ballico</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 23, Number 3, 439--464.</p><p><strong>Abstract:</strong><br/>
We study the non-existence of smooth curves of low degree and low positive genus
on a general heptic hypersurface of $\mathbb {P}^5$. The genus $0$ case was proved for
the same degrees by Hana - Johnsen and Cotterill.
</p>projecteuclid.org/euclid.bbms/1473186516_20160906142833Tue, 06 Sep 2016 14:28 EDTDirichlet-Ford domains and Double Dirichlet domainshttp://projecteuclid.org/euclid.bbms/1473186517<strong>E. Jespers</strong>, <strong>S. O. Juriaans</strong>, <strong>A. Kiefer</strong>, <strong>A. de A. e Silva</strong>, <strong>A. C. Souza Filho</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 23, Number 3, 465--479.</p><p><strong>Abstract:</strong><br/>
We continue investigations started by Lakeland on Fuchsian and Kleinian groups which have a Dirichlet fundamental domain that also is a Ford domain in the upper half-space model of hyperbolic $2$- and $3$-space, or which have a Dirichlet domain with multiple centers. Such domains are called DF-domains and Double Dirichlet domains respectively. Making use of earlier obtained concrete formulas for the bisectors defining the Dirichlet domain of center $i \in \mathbb H^2$ or center $j \in \mathbb H^3$, we obtain a simple condition on the matrix entries of the side-pairing transformations of the fundamental domain of a Fuchsian or Kleinian group to be a DF-domain. Using the same methods, we also complement a result of Lakeland stating that a cofinite Fuchsian group has a DF domain (or a Dirichlet domain with multiple centers) if and only if it is an index $2$ subgroup of the discrete group G of reflections in a hyperbolic polygon.
</p>projecteuclid.org/euclid.bbms/1473186517_20160906142833Tue, 06 Sep 2016 14:28 EDTPrimitive arcs on curveshttp://projecteuclid.org/euclid.bbms/1480993581<strong>Julien Sebag</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 23, Number 4, 481--486.</p><p><strong>Abstract:</strong><br/>
We introduce the notion of \emph{primitive arc} of a curve defined over a field $k$ and study criterions for the existence of such objects in terms of the geometry of the curve. We prove that this notion provides a criterion which determines when the normalization of an irreductible curve singularity $(X,x)$ induces an isomorphism between the formal neighborhoods of the associated arc schemes at the constant arc $x$ and its lifting $\bar x$ to the normalization $\bar X$. We also show that the existence of a primitive arc at $x\in X$ is equivalent to the smoothness of the analytically irreducible curve $X$ at $x$. In this end, we interpret this notion in terms of the formal deformations of the constant arc $x$ in the associated arc scheme.
</p>projecteuclid.org/euclid.bbms/1480993581_20161205220633Mon, 05 Dec 2016 22:06 ESTFaber Polynomial Coefficient Estimates for a
Comprehensive Subclass of Analytic Bi-Univalent Functions Defined by Subordinationhttp://projecteuclid.org/euclid.bbms/1480993582<strong>Ahmad Zireh</strong>, <strong>E. Analouei Adegani</strong>, <strong>Serap Bulut</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 23, Number 4, 487--504.</p><p><strong>Abstract:</strong><br/>
In this paper, we find coefficient estimates by a new method making use of
the Faber polynomial expansions for a comprehensive subclass of
analytic bi-univalent functions, which is defined by subordinations
in the open unit disk. The coefficient bounds presented in this
paper would generalize and improve some recent works appeared in the
literature.
</p>projecteuclid.org/euclid.bbms/1480993582_20161205220633Mon, 05 Dec 2016 22:06 ESTAlgebrability of some subsets of the disk algebrahttp://projecteuclid.org/euclid.bbms/1480993583<strong>Mary Lilian Lourenço</strong>, <strong>Daniela M. Vieira</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 23, Number 4, 505--514.</p><p><strong>Abstract:</strong><br/>
We show that the subset of the disk algebra of the functions that are not in some Dales-Davie algebra is algebrable. In other words, the set $\Big\{f\in\mathcal{A}(D)\,:\,\sum_{n=0}^{\infty}\dfrac{\|f^{(n)}\|}{n!}=+\infty\Big\}$ is shown to be algebrable.
</p>projecteuclid.org/euclid.bbms/1480993583_20161205220633Mon, 05 Dec 2016 22:06 ESTOn linear extendability of isometrical embeddingshttp://projecteuclid.org/euclid.bbms/1480993584<strong>Hossein Khodaiemehr</strong>, <strong>Fereshteh Sady</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 23, Number 4, 515--527.</p><p><strong>Abstract:</strong><br/>
In this paper we first investigate linear extendability of an
isometric embedding $T:\mathcal U \longrightarrow \mathcal Y$ from an open subset
$\mathcal U$ of a real Banach space $\mathcal X$ into a real Banach space $\mathcal Y$
in the case where $\mathcal Y$ is either the space $C_\Bbb R(K)$ of
continuous real-valued functions on a compact space $K$, or is a
strictly convex Banach space. Then we obtain similar results for
the case where $\mathcal Y$ is an arbitrary real Banach space and $T:\mathcal U
\longrightarrow \mathcal Y$ is an isometry whose range satisfies some
additional conditions.
</p>projecteuclid.org/euclid.bbms/1480993584_20161205220633Mon, 05 Dec 2016 22:06 ESTFixed point properties for semigroups of non-expansive mappings in conjugate Banach spaceshttp://projecteuclid.org/euclid.bbms/1480993585<strong>Khadime Salame</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 23, Number 4, 529--544.</p><p><strong>Abstract:</strong><br/>
In this paper we study common fixed point properties of non-linear actions of semi-topological semigroups on non-void weak* compact convex sets in dual Banach spaces. Among other things, we derive from our main result Theorem 1, the existence of a common fixed point property for semigroups of non-expansive mappings acting on non-empty weakly compact convex sets, generalizing a result of Hsu [13], Mitchell [25].
</p>projecteuclid.org/euclid.bbms/1480993585_20161205220633Mon, 05 Dec 2016 22:06 ESTWeak amenability of Banach algebras with respect to charactershttp://projecteuclid.org/euclid.bbms/1480993586<strong>Rasoul Nasr-Isfahani</strong>, <strong>Somayeh Shahmoradi</strong>, <strong>Sima Soltani Renani</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 23, Number 4, 545--558.</p><p><strong>Abstract:</strong><br/>
For a Banach algebra ${\cal A}$, we introduce and investigate weak amenability of ${\cal A}$
with respect to a character. We give some necessary conditions for the weak
amenability of $\cal A$ with respect to a character and describe a class of Banach
algebras that are not weakly amenable with respect to characters.
Finally, we give examples of Banach algebras which are
weakly amenable with respect to characters but neither weakly amenable nor amenable
with respect to characters.
</p>projecteuclid.org/euclid.bbms/1480993586_20161205220633Mon, 05 Dec 2016 22:06 ESTFlag-transitive point-primitive non-symmetric $2$-$(v,k,2)$ designs with alternating soclehttp://projecteuclid.org/euclid.bbms/1480993587<strong>Hongxue Liang</strong>, <strong>Shenglin Zhou</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 23, Number 4, 559--571.</p><p><strong>Abstract:</strong><br/>
We prove that if $\mathcal{D}$ is a non-trivial non-symmetric $2$-$(v,k,2)$ design
admitting a flag-transitive point-primitive automorphism group $G$ with $Soc(G)=A_{n}$ for $n\geq5$,
then $\mathcal{D}$ is a $2$-$(6,3,2)$ or $2$-$(10,4,2)$ design.
</p>projecteuclid.org/euclid.bbms/1480993587_20161205220633Mon, 05 Dec 2016 22:06 ESTOn the Frobenius vector of some simplicial affine semigroupshttp://projecteuclid.org/euclid.bbms/1480993588<strong>Ali Mahdavi</strong>, <strong>Farhad Rahmati</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 23, Number 4, 573--582.</p><p><strong>Abstract:</strong><br/>
We give a formula for a Frobenius vector of a Gorenstein simplicial affine semigroup $S$, and when the semigroup is Cohen-Macaulay we give an algorithm computing the set of minimal Frobenius vectors of $S$ for a special class of semigroups.
</p>projecteuclid.org/euclid.bbms/1480993588_20161205220633Mon, 05 Dec 2016 22:06 ESTOptimization through dense setshttp://projecteuclid.org/euclid.bbms/1480993589<strong>C. R. Jayanarayanan</strong>, <strong>T. S. S. R. K. Rao</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 23, Number 4, 583--594.</p><p><strong>Abstract:</strong><br/>
In this paper, we study two optimization problems where solutions on a dense set yield global solution. We study these problems for spaces of Bochner integrable functions and for spaces of continuous functions.
The first one deals with expressing the length of a vector as a sum of the distance to a best approximation and minimal best approximation and the second one relates to approximating a subsequence of a minimizing sequence with a sequence of proximinal vectors.
</p>projecteuclid.org/euclid.bbms/1480993589_20161205220633Mon, 05 Dec 2016 22:06 ESTWeighted composition operators on algebras of differentiable functionshttp://projecteuclid.org/euclid.bbms/1480993590<strong>S. Amiri</strong>, <strong>A. Golbaharan</strong>, <strong>H. Mahyar</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 23, Number 4, 595--608.</p><p><strong>Abstract:</strong><br/>
Let $X$ be a perfect compact plane set, $n\in \mathbb{N}$ and $D^n(X)$ be
the algebra of complex-valued functions on $X$ with continuous
$n$-th derivative. In this paper we study weighted composition
operators on algebras $D^n(X)$. We give a necessary and sufficient
condition for these operators to be compact. As a consequence, we
characterize power compact composition operators on these
algebras. Then we determine the spectra of Riesz weighted
composition operators on these algebras.
</p>projecteuclid.org/euclid.bbms/1480993590_20161205220633Mon, 05 Dec 2016 22:06 ESTInjective mappings in $\mathbb{R}^\mathbb{R}$ and lineabilityhttp://projecteuclid.org/euclid.bbms/1480993591<strong>P. Jiménez-Rodríguez</strong>, <strong>S. Maghsoudi</strong>, <strong>G.A. Muñoz-Fernández</strong>, <strong>J.B. Seoane-Sepúlveda</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 23, Number 4, 609--623.</p><p><strong>Abstract:</strong><br/>
It is known that there is not a two dimensional linear space in $\mathbb R^\mathbb R$ every non-zero element of which is an injective function. Here, we generalize this result to arbitrarily large dimensions. We also study the convolution of non-differentiable functions which gives, as a result, a differentiable function. In this latter case, we are able to show the existence of linear spaces of the largest possible dimension formed by functions enjoying the previous property. By doing this we provide both positive and negative results to the recent field of lineability. Some open questions are also provided.
</p>projecteuclid.org/euclid.bbms/1480993591_20161205220633Mon, 05 Dec 2016 22:06 ESTTransitive parallelism of residues in buildingshttp://projecteuclid.org/euclid.bbms/1480993592<strong>Antoine Clais</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 23, Number 4, 625--640.</p><p><strong>Abstract:</strong><br/>
We study the buildings in which parallelism of residues is an equivalence relation. If the building admits a group action, we describe how parallel residues are related to residues with equal stabilizers. This permits to retrieve the fact that in a Coxeter group or in a graph product, intersections of parabolic subgroups are parabolic.
</p>projecteuclid.org/euclid.bbms/1480993592_20161205220633Mon, 05 Dec 2016 22:06 ESTCoalgebras governing both weighted Hurwitz products and their pointwise transformshttp://projecteuclid.org/euclid.bbms/1483671619<strong>Richard Garner</strong>, <strong>Ross Street</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 23, Number 5, 643--666.</p><p><strong>Abstract:</strong><br/>
We give further insights into the weighted Hurwitz product and the
weighted tensor product of Joyal species. Our first group of results
relate the Hurwitz product to the pointwise product, including the
interaction with Rota--Baxter operators. Our second group of results
explain the first in terms of convolution with suitable bialgebras,
and show that these bialgebras are in fact obtained in a
particularly straightforward way by freely generating from pointed
coalgebras. Our third group of results extend this from linear
algebra to two-dimensional linear algebra, deriving the existence of
weighted Hurwitz monoidal structures on the category of species
using convolution with freely generated bimonoidales. Our final
group of results relate Hurwitz monoidal structures with
equivalences of Dold--Kan type.
</p>projecteuclid.org/euclid.bbms/1483671619_20170105220101Thu, 05 Jan 2017 22:01 ESTA criterion for reflectiveness of normal extensionshttp://projecteuclid.org/euclid.bbms/1483671620<strong>Andrea Montoli</strong>, <strong>Diana Rodelo</strong>, <strong>Tim Van der Linden</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 23, Number 5, 667--691.</p><p><strong>Abstract:</strong><br/>
We give a new sufficient condition for the normal extensions in an
admissible Galois structure to be reflective. We then show that
this condition is indeed fulfilled when $\mathbb{X}$ is the (protomodular)
reflective subcategory of $\mathcal{S}$-special objects of a Barr-exact
$\mathcal{S}$-protomodular category $\mathbb{C}$, where $\mathcal{S}$ is the class of
split epimorphic trivial extensions in $\mathbb{C}$. Next to some
concrete examples where the criterion may be applied, we also
study the adjunction between a Barr-exact unital category and its
abelian core, which we prove to be admissible.
</p>projecteuclid.org/euclid.bbms/1483671620_20170105220101Thu, 05 Jan 2017 22:01 ESTThe Projective Class Rings of a family of pointed Hopf algebras of Rank twohttp://projecteuclid.org/euclid.bbms/1483671621<strong>Hui-Xiang Chen</strong>, <strong>Hassen Suleman Esmael Mohammed</strong>, <strong>Weijun Lin</strong>, <strong>Hua Sun</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 23, Number 5, 693--711.</p><p><strong>Abstract:</strong><br/>
In this paper, we compute the projective class rings of the tensor product
$\mathcal{H}_n(q)=A_n(q)\ot A_n(q^{-1})$ of Taft algebras $A_n(q)$ and $A_n(q^{-1})$, and its
cocycle deformations $H_n(0,q)$ and $H_n(1,q)$, where $n>2$ is a positive integer
and $q$ is a primitive $n$-th root of unity. It is shown that the projective class rings $r_p(\mathcal{H}_n(q))$,
$r_p(H_n(0,q))$ and $r_p(H_n(1,q))$ are commutative rings generated by three elements, three elements and
two elements subject to some relations, respectively.
It turns out that even $\mathcal{H}_n(q)$, $H_n(0,q)$ and $H_n(1,q)$
are cocycle twist-equivalent to each other, they are of different representation types: wild, wild and tame, respectively.
</p>projecteuclid.org/euclid.bbms/1483671621_20170105220101Thu, 05 Jan 2017 22:01 ESTCurved Rota-Baxter systemshttp://projecteuclid.org/euclid.bbms/1483671622<strong>Tomasz Brzeziński</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 23, Number 5, 713--720.</p><p><strong>Abstract:</strong><br/>
Rota-Baxter systems are modified by the inclusion of a curvature term. It is shown that, subject to specific properties of the curvature form, curved Rota-Baxter systems $(A,R,S,\omega)$ induce associative and (left) pre-Lie products on the algebra $A$. It is also shown that if both Rota-Baxter operators coincide with each other and the curvature is $A$-bilinear, then the (modified by $R$) Hochschild cohomology ring over $A$ is a curved differential graded algebra.
</p>projecteuclid.org/euclid.bbms/1483671622_20170105220101Thu, 05 Jan 2017 22:01 ESTAlgebra depth in tensor categorieshttp://projecteuclid.org/euclid.bbms/1483671623<strong>Lars Kadison</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 23, Number 5, 721--752.</p><p><strong>Abstract:</strong><br/>
Study of the quotient module of a finite-dimensional Hopf subalgebra pair in order to compute its depth yields a relative Maschke Theorem, in which semisimple extension is characterized as being separable, and is therefore an ordinary Frobenius extension. We study the core Hopf ideal of a Hopf subalgebra, noting that the length of the annihilator chain of tensor powers of the quotient module is linearly related to the depth, if the Hopf algebra is semisimple. A tensor categorical definition of depth is introduced, and a summary from this new point of view of previous results are included. It is shown in a last section that the depth, Bratteli diagram and relative cyclic homology of algebra extensions are Morita invariants.
</p>projecteuclid.org/euclid.bbms/1483671623_20170105220101Thu, 05 Jan 2017 22:01 ESTPicard-Vessiot and categorically normal extensions in differential-difference Galois theoryhttp://projecteuclid.org/euclid.bbms/1483671624<strong>G. Janelidze</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 23, Number 5, 753--768.</p><p><strong>Abstract:</strong><br/>
The connection between categorical and differential Galois theories established by the author (published in 1989) is extended to the context that includes difference Galois theory.
</p>projecteuclid.org/euclid.bbms/1483671624_20170105220101Thu, 05 Jan 2017 22:01 ESTA note on the restricted universal enveloping algebra of a restricted Lie-Rinehart Algebrahttp://projecteuclid.org/euclid.bbms/1483671625<strong>Peter Schauenburg</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 23, Number 5, 769--777.</p><p><strong>Abstract:</strong><br/>
Lie-Rinehart algebras, also known as Lie algebroids, give rise to Hopf algebroids by a universal enveloping algebra construction, much as the universal enveloping algebra of an ordinary Lie algebra gives a Hopf algebra, of infinite dimension. In finite characteristic, the universal enveloping algebra of a restricted Lie algebra admits a quotient Hopf algebra which is finite-dimensional if the Lie algebra is. Rumynin has shown that suitably defined restricted Lie algebroids allow to define restricted universal enveloping algebras that are finitely generated projective if the Lie algebroid is. This note presents an alternative proof and possibly fills a gap that might, however, only be a gap in the author's understanding.
</p>projecteuclid.org/euclid.bbms/1483671625_20170105220101Thu, 05 Jan 2017 22:01 ESTRepresentations of the small quasi-quantum group ${\operatorname{Q}}\mathbf{u}_{q}(\mathfrak{sl}_{2})$http://projecteuclid.org/euclid.bbms/1483671626<strong>Gongxiang Liu</strong>, <strong>Fred Van Oystaeyen</strong>, <strong>Yinhuo Zhang</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 23, Number 5, 779--800.</p><p><strong>Abstract:</strong><br/>
The quasi-Frobenius-Lusztig kernel ${\operatorname{Q}}\mathbf{u}_{q}(\mathfrak{sl}_{2})$
associated with $\mathfrak{sl}_{2}$ has been constructed in [9]. In this paper we study the representations of this small quasi-quantum group. We give a complete list of non-isomorphic indecomposables and the tensor product decomposition rules for simples and projectives. A description of the Grothendieck ring is also provided.
</p>projecteuclid.org/euclid.bbms/1483671626_20170105220101Thu, 05 Jan 2017 22:01 ESTFrom finite groups to finite-dimensional Hopf algebrashttp://projecteuclid.org/euclid.bbms/1489888812<strong>Miriam Cohen</strong>, <strong>Sara Westreich</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 24, Number 1, 1--14.</p>projecteuclid.org/euclid.bbms/1489888812_20170318220020Sat, 18 Mar 2017 22:00 EDTA finite-dimensional Lie algebra arising from a Nichols algebra of diagonal type (rank 2)http://projecteuclid.org/euclid.bbms/1489888813<strong>Nicolás Andruskiewitsch</strong>, <strong>Iván Angiono</strong>, <strong>Fiorela Rossi Bertone</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 24, Number 1, 15--34.</p><p><strong>Abstract:</strong><br/>
Let ${\mathcal{B}}_{\mathfrak{q}}$ be a finite-dimensional Nichols algebra of diagonal type corresponding to a matrix $\mathfrak{q} \in {\mathbf{k}}^{\theta \times \theta}$.
Let ${\mathcal{L}}_{\mathfrak{q}}$ be the Lusztig algebra associated to ${\mathcal{B}}_{\mathfrak{q}}$.
We present ${\mathcal{L}}_{\mathfrak{q}}$ as an extension (as braided Hopf algebras) of ${\mathcal{B}}_{\mathfrak{q}}$ by ${\mathfrak Z}_{\mathfrak{q}}$ where ${\mathfrak Z}_{\mathfrak{q}}$ is isomorphic to the universal enveloping algebra of a Lie algebra ${\mathfrak{n}}_\mathfrak{q}$. We compute the Lie algebra ${\mathfrak{n}}_{\mathfrak{q}}$ when $\theta = 2$.
</p>projecteuclid.org/euclid.bbms/1489888813_20170318220020Sat, 18 Mar 2017 22:00 EDTPartial actions: what they are and why we carehttp://projecteuclid.org/euclid.bbms/1489888814<strong>Eliezer Batista</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 24, Number 1, 35--71.</p><p><strong>Abstract:</strong><br/>
We present a survey of recent developments in the theory of partial actions of groups and Hopf algebras.
</p>projecteuclid.org/euclid.bbms/1489888814_20170318220020Sat, 18 Mar 2017 22:00 EDTThree natural subgroups of the Brauer-Picard group of a
Hopf algebra with applicationshttp://projecteuclid.org/euclid.bbms/1489888815<strong>Simon Lentner</strong>, <strong>Jan Priel</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 24, Number 1, 73--106.</p><p><strong>Abstract:</strong><br/>
In this article we construct three explicit natural subgroups of the
Brauer-Picard group of the category of representations of a
finite-dimensional Hopf algebra. In examples the Brauer Picard group decomposes
into an ordered product of these subgroups, somewhat similar to a Bruhat
decomposition.
Our construction returns for any Hopf algebra three types of braided
autoequivalences and correspondingly three families of invertible bimodule
categories. This gives examples of so-called (2-)Morita
equivalences and defects in topological field theories. We have a closer
look at the case of quantum groups and Nichols algebras and give
interesting applications. Finally, we briefly discuss the three families of
group-theoretic extensions.
</p>projecteuclid.org/euclid.bbms/1489888815_20170318220020Sat, 18 Mar 2017 22:00 EDTA simplicial approach to multiplier bimonoidshttp://projecteuclid.org/euclid.bbms/1489888816<strong>Gabriella Böhm</strong>, <strong>Stephen Lack</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 24, Number 1, 107--122.</p><p><strong>Abstract:</strong><br/>
Although multiplier bimonoids in general are not known to correspond to
comonoids in any monoidal category, we classify them in terms of maps from the
Catalan simplicial set to another suitable simplicial set; thus they can be
regarded as (co)monoids in something more general than a monoidal
category (namely, the simplicial set itself).
We analyze the particular simplicial maps corresponding to that class of
multiplier bimonoids which can be regarded as comonoids.
</p>projecteuclid.org/euclid.bbms/1489888816_20170318220020Sat, 18 Mar 2017 22:00 EDTA criterion for $p$-henselianity in characteristic $p$http://projecteuclid.org/euclid.bbms/1489888817<strong>Zoé Chatzidakis</strong>, <strong>Milan Perera</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 24, Number 1, 123--126.</p><p><strong>Abstract:</strong><br/>
Let $p$ be a prime. In this paper we give a proof of the following
result: A valued field $(K,v)$ of characteristic $p > 0$ is
$p$-henselian if and only if every element of strictly positive
valuation is of the form $x^p - x$ for some $x \in K$.
</p>projecteuclid.org/euclid.bbms/1489888817_20170318220020Sat, 18 Mar 2017 22:00 EDTComplex of injective words revisitedhttp://projecteuclid.org/euclid.bbms/1489888818<strong>Wee Liang Gan</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 24, Number 1, 127--134.</p><p><strong>Abstract:</strong><br/>
We give a simple proof that (a generalization of) the complex of injective words has vanishing homology in all except the top degree.
</p>projecteuclid.org/euclid.bbms/1489888818_20170318220020Sat, 18 Mar 2017 22:00 EDTSolvability of a fractional integral equation with the concept of measure of noncompactnesshttp://projecteuclid.org/euclid.bbms/1489888819<strong>Kishin Sadarangani</strong>, <strong>Bessem Samet</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 24, Number 1, 135--151.</p><p><strong>Abstract:</strong><br/>
We study the existence of solutions for a new class of integral equations involving a fractional integral with respect to another function. Our techniques are based on the measure of non-compactness concept combined with a generalized version of Darbo's theorem. Some examples are presented to illustrate the obtained results.
</p>projecteuclid.org/euclid.bbms/1489888819_20170318220020Sat, 18 Mar 2017 22:00 EDTVanishing theorems of the basic harmonic forms on a complete foliated Riemannian manifoldhttp://projecteuclid.org/euclid.bbms/1489888820<strong>Seoung Dal Jung</strong>, <strong>Huili Liu</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 24, Number 1, 153--160.</p><p><strong>Abstract:</strong><br/>
A well-known result by M. Min-Oo et al. states that
there are no nontrivial basic harmonic $r (0<
r<q={\rm codim}\mathcal F)$-forms
on a compact foliated Riemannian manifold $(M,\mathcal F)$. We extend this result to a complete foliated Riemannian
manifold.
</p>projecteuclid.org/euclid.bbms/1489888820_20170318220020Sat, 18 Mar 2017 22:00 EDT