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 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 ESTDivergent series of Taylor coefficients on almost all sliceshttps://projecteuclid.org/euclid.bbms/1553047225<strong>Piotr Kot</strong>, <strong>Marek Karaś</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 26, Number 1, 1--9.</p><p><strong>Abstract:</strong><br/>
We show that there exists a holomorphic function, continuous to the boundary in a bounded, balanced, strictly pseudoconvex domain $\Omega$ with $C^{2}$ boundary such that almost every slice function has a series of Taylor coefficients divergent with every power $p\in(0,2)$.
</p>projecteuclid.org/euclid.bbms/1553047225_20190319220044Tue, 19 Mar 2019 22:00 EDTDynamics of multidimensional Cesáro operatorshttps://projecteuclid.org/euclid.bbms/1553047226<strong>J. Alberto Conejero</strong>, <strong>A. Mundayadan</strong>, <strong>J.B. Seoane-Sepúlveda</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 26, Number 1, 11--20.</p><p><strong>Abstract:</strong><br/>
We study the dynamics of the multi-dimensional Ces\`aro integral operator on $L^p(I^n)$, for $I$ the unit interval, $1<p<\infty$, and $n\ge 2$, that is defined as \begin{multline*} \displaystyle \mathcal{C}(f)(x_1,\ldots,x_n)=\frac {1} {x_1x_2\cdots x_n} \int_0^{x_1}\ldots\int_{0}^{x_n} f(u_1,\ldots,u_n)du_1\ldots du_n\\ \quad \text{ for } f\in L^p(I^n). \end{multline*} This operator is already known to be bounded. As a consequence of the Eigenvalue Criterion, we show that it is hypercyclic as well. Moreover, we also prove that it is Devaney chaotic and frequently hypercyclic.
</p>projecteuclid.org/euclid.bbms/1553047226_20190319220044Tue, 19 Mar 2019 22:00 EDTGevrey series in compensators linearizing a planar resonant vector field and its unfoldinghttps://projecteuclid.org/euclid.bbms/1553047227<strong>Patrick Bonckaert</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 26, Number 1, 21--62.</p><p><strong>Abstract:</strong><br/>
We consider a planar vector field $X$ near a saddle type $p:-q$ resonant singular point. Assuming that it has a normal form with a Gevrey-$d$ expansion (like $d=p+q$ which is in particular the case when starting from an analytic vector field) we show that $X$ can be linearized working with a change of coordinates that is of Gevrey order $d$ in certain $\log$-like variables, called compensators or also tags, multiplied by the first integral $u=x^qy^p$ of the linear part. Next we consider the unfolding of such a resonance, and provide (weaker) Gevrey-type linearization using compensators.
</p>projecteuclid.org/euclid.bbms/1553047227_20190319220044Tue, 19 Mar 2019 22:00 EDTOn a population model with nonlinear boundary conditions arising in ecosystemshttps://projecteuclid.org/euclid.bbms/1553047228<strong>S.H. Rasouli</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 26, Number 1, 63--69.</p><p><strong>Abstract:</strong><br/>
In this paper we study a model of population which is described by positive solutions to the nonlinear boundary value problem $$ \left\{\begin{array}{ll} -\Delta u = au-bu^{2}-c\frac{u^{2}}{1+u^{2}}-\epsilon, & x\in \Omega,\\ \mathbf{n}.\nabla u+ g(u)=0 , & x\in\partial \Omega.\\ \end{array}\right. $$ Here $\Omega$ is a bounded smooth domain of $\mathbb{R}^{N},$ $\Delta$ is the Laplacian operator, $a,$ $b,$ $c,$ $\epsilon$ are positive parameters and $g \in C^{1}\Big([0,\infty),$ $[\theta,\infty)\Big)$ is decreasing for some $\theta > 0.$ This model describes the dynamics of the fish populations. Our existence results are established via the well-known sub-super solution method.
</p>projecteuclid.org/euclid.bbms/1553047228_20190319220044Tue, 19 Mar 2019 22:00 EDTAbel Convergence of the Sequence of Positive Linear Operators in $L_{p,q}\left( loc\right) $https://projecteuclid.org/euclid.bbms/1553047229<strong>Nilay Şahin Bayram</strong>, <strong>Cihan Orhan</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 26, Number 1, 71--83.</p><p><strong>Abstract:</strong><br/>
In this paper, we study a Korovkin type approximation theorem for a sequence of positive linear operators acting from $L_{p,q}\left( loc\right) $ into itself with the use of Abel method which is a sequence-to-function transformation. Using the modulus of continuity for $L_{p,q}\left( loc\right) $ we also give the rate of Abel convergence of these operators.
</p>projecteuclid.org/euclid.bbms/1553047229_20190319220044Tue, 19 Mar 2019 22:00 EDTGroups whose set of vanishing elements is the union of at most three conjugacy classehttps://projecteuclid.org/euclid.bbms/1553047230<strong>Sajjad Mahmood Robati</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 26, Number 1, 85--89.</p><p><strong>Abstract:</strong><br/>
Let $G$ be a finite group. We say that an element $g$ in $G$ is a vanishing element if there exists some irreducible character $\chi$ of $G$ such that $\chi(g)=0$. In this paper, we prove that if the set of vanishing elements of $G$ is the union of at most three conjugacy classes, then $G$ is solvable.
</p>projecteuclid.org/euclid.bbms/1553047230_20190319220044Tue, 19 Mar 2019 22:00 EDTDissipative property for non local evolution equationshttps://projecteuclid.org/euclid.bbms/1553047231<strong>Severino H. da Silva</strong>, <strong>Antonio R. G. Garcia</strong>, <strong>Bruna E. P. Lucena</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 26, Number 1, 91--117.</p><p><strong>Abstract:</strong><br/>
In this work we consider the non local evolution problem \[ \begin{cases} \partial_t u(x,t)=-u(x,t)+g(\beta K(f\circ u)(x,t)+\beta h), ~x \in\Omega, ~t\in[0,\infty[;\\ u(x,t)=0, ~x\in\mathbb{R}^N\setminus\Omega, ~t\in[0,\infty[;\\ u(x,0)=u_0(x),~x\in\mathbb{R}^N, \end{cases} \] where $\Omega$ is a smooth bounded domain in $\mathbb{R}^N; ~g,f: \mathbb{R}\to\mathbb{R}$ satisfying\linebreak certain growing condition and $K$ is an integral operator with symmetric kernel, $ Kv(x)=\int_{\mathbb{R}^{N}}J(x,y)v(y)dy.$ We prove that Cauchy problem above is well posed, the solutions are smooth with respect to initial conditions, and we show the existence of a global attractor. Furthermore, we exhibit a Lyapunov's functional, concluding that the flow generated by this equation has the gradient property.
</p>projecteuclid.org/euclid.bbms/1553047231_20190319220044Tue, 19 Mar 2019 22:00 EDTPointwise version of contractibility of Banach algebras of locally compact groupshttps://projecteuclid.org/euclid.bbms/1553047232<strong>M. Soroushmehr</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 26, Number 1, 119--129.</p><p><strong>Abstract:</strong><br/>
In this paper, we introduce the concept of pointwise compactness for a locally compact group $G,$ and among other results, we show that pointwise compactness of $G$ is a necessary condition for pointwise contractibility of $L^1(G)$ in a commutative case. Also, pointwise contractibility of measure algebras in a general case is studied. Finally, applying the results, we study the pointwise contractibility of Fourier and Fourier-Stieltjes algebras in a commutative case.
</p>projecteuclid.org/euclid.bbms/1553047232_20190319220044Tue, 19 Mar 2019 22:00 EDTGrowth on Meromorphic Solutions of Non-linear Delay Differential Equationshttps://projecteuclid.org/euclid.bbms/1553047233<strong>Pei-Chu Hu</strong>, <strong>Qiong-Yan Wang</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 26, Number 1, 131--147.</p><p><strong>Abstract:</strong><br/>
By using Nevanlinna theory and linear algebra, we show that the number one is a lower bound of the hyper-order of any meromorphic solution of a non-linear delay differential equation under certain conditions.
</p>projecteuclid.org/euclid.bbms/1553047233_20190319220044Tue, 19 Mar 2019 22:00 EDTLipsman mapping and dual topology of semidirect productshttps://projecteuclid.org/euclid.bbms/1553047234<strong>Aymen Rahali</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 26, Number 1, 149--160.</p><p><strong>Abstract:</strong><br/>
We consider the semidirect product $G = K \ltimes V$ where $K$ is a connected compact Lie group acting by automorphisms on a finite dimensional real vector space $V$ equipped with an inner product $\langle,\rangle$. We denote by $\widehat{G}$ the unitary dual of $G$ (note that we identify each representation $\pi\in\widehat{G}$ to its classes $[\pi]$) and by $\mathfrak{g}^\ddag/G$ the space of admissible coadjoint orbits, where $\mathfrak{g}$ is the Lie algebra of $G.$ It was pointed out by Lipsman that the correspondence between $\mathfrak{g}^\ddag/G$ and $\widehat{G}$ is bijective. Under some assumption on $G,$ we prove that the Lipsman mapping \begin{eqnarray*} \Theta:\mathfrak{g}^\ddag/G &\longrightarrow&\widehat{G}\\ \mathcal{O}&\longmapsto&\pi_\mathcal{O} \end{eqnarray*} is a homeomorphism.
</p>projecteuclid.org/euclid.bbms/1553047234_20190319220044Tue, 19 Mar 2019 22:00 EDTFonctions arithmétiques multiplicativement monotoneshttps://projecteuclid.org/euclid.bbms/1561687559<strong>Michel Balazard</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 26, Number 2, 161--176.</p><p><strong>Abstract:</strong><br/>
A real arithmetic function $f$ is \emph{multiplicatively monotonous} if $f(mn)-f(m)$ has constant sign for $m,n$ positive integers. Properties and examples of such functions are discussed, with applications to positive hermitian Toeplitz-multiplicative determinants.
</p>projecteuclid.org/euclid.bbms/1561687559_20190627220616Thu, 27 Jun 2019 22:06 EDTOn surfaces of finite Chen $III$-typehttps://projecteuclid.org/euclid.bbms/1561687560<strong>Hassan Al-Zoubi</strong>, <strong>Mutaz Al-Sabbagh</strong>, <strong>Stylianos Stamatakis</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 26, Number 2, 177--187.</p><p><strong>Abstract:</strong><br/>
In this paper, we study quadric surfaces in the 3-dimensional Euclidean space which are of finite $III$-type, that is, they are of finite type, in the sense of B.-Y. Chen, corresponding to the third fundamental form. We show that helicoids and spheres are the only quadric surfaces of finite $III$-type.
</p>projecteuclid.org/euclid.bbms/1561687560_20190627220616Thu, 27 Jun 2019 22:06 EDTA remark on the minimal dilation of the semigroup generated by a normal UCP-maphttps://projecteuclid.org/euclid.bbms/1561687561<strong>Yusuke Sawada</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 26, Number 2, 189--202.</p><p><strong>Abstract:</strong><br/>
There are three known ways to construct the minimal dilation of the discrete semigroup generated by a normal unital completely positive map on a von Neumann algebra, which are given by Arveson, Bhat-Skeide and Muhly-Solel. In this paper, we describe the relation between Bhat-Skeide's and Muhly-Solel's constructions, which is different from the one described by Skeide's commutant duality.
</p>projecteuclid.org/euclid.bbms/1561687561_20190627220616Thu, 27 Jun 2019 22:06 EDTNumerical evaluation of order six for fractional differential equations : stability and convergencyhttps://projecteuclid.org/euclid.bbms/1561687562<strong>Mohammad Shahbazi Asl</strong>, <strong>Mohammad Javidi</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 26, Number 2, 203--221.</p><p><strong>Abstract:</strong><br/>
In this paper, a novel high-order numerical method is formulated to solve fractional differential equations. The fractional derivative is described in the Caputo sense due to its applicability to real-world phenomena. First, the fractional differential equation is reduced into a Volterra-type integral equation by applying the Laplace and inverse Laplace transform. Then, the piecewise Lagrange interpolation polynomial of degree five is utilized to approximate unknown function. The truncation error estimates for the novel schemes is derived, and it is theoretically established that the order of convergence of the numerical method is $O(h^6)$. The stability analysis of the novel method is also carefully investigated. Numerical examples are given to show the accuracy, applicability and the effectiveness of the novel method.
</p>projecteuclid.org/euclid.bbms/1561687562_20190627220616Thu, 27 Jun 2019 22:06 EDTSome fixed point theorems for Meir-Keeler condensing operators and application to a system of integral equationshttps://projecteuclid.org/euclid.bbms/1561687563<strong>Maha Belhadj</strong>, <strong>Afif Ben Amar</strong>, <strong>Mohamed Boumaiza</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 26, Number 2, 223--239.</p><p><strong>Abstract:</strong><br/>
We introduce the concept of Meir-Keeler condensing operator in a Banach space via an arbitrary measure of weak noncompactness. We prove some generalizations of Darbo's fixed point theorem by considering a measure of weak noncompactness which not necessary has the maximum property. We prove some coupled fixed point theorems and we apply them in order to establish the existence of weak solutions for a system of functional integral equations of Volterra type.
</p>projecteuclid.org/euclid.bbms/1561687563_20190627220616Thu, 27 Jun 2019 22:06 EDTOn the compatibility between the differential topological index and the analytic Bunke-Schick push-forward constructionhttps://projecteuclid.org/euclid.bbms/1561687564<strong>Adnane Elmrabty</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 26, Number 2, 241--253.</p><p><strong>Abstract:</strong><br/>
In this note we establish the compatibility between the topological index in the differential K-theory of Freed-Lott and the analytic push-forward construction in the differential K-theory of Bunke-Schick by a direct computation.
</p>projecteuclid.org/euclid.bbms/1561687564_20190627220616Thu, 27 Jun 2019 22:06 EDTGeneralizations of Connected and Compact Sets by $d_\delta$-Closure Operatorhttps://projecteuclid.org/euclid.bbms/1561687565<strong>Davinder Singh</strong>, <strong>Harshit Mathur</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 26, Number 2, 255--273.</p><p><strong>Abstract:</strong><br/>
In this paper, we introduce two new concepts, namely, a subset being $d_\delta$-connected relative to a topological space, and a subset being $D_\delta$-closed relative to the space. The former is a generalization of the concept of a subset being $\theta$-connected relative to a space, and the latter is analogous to the $H(i)$ space.
</p>projecteuclid.org/euclid.bbms/1561687565_20190627220616Thu, 27 Jun 2019 22:06 EDTDouble centralizers in Artin-Tits groupshttps://projecteuclid.org/euclid.bbms/1561687566<strong>Oussama Ajbal</strong>, <strong>Eddy Godelle</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 26, Number 2, 275--298.</p><p><strong>Abstract:</strong><br/>
We prove an analogue of the Centralizer Theorem in the context of Artin-Tits groups.
</p>projecteuclid.org/euclid.bbms/1561687566_20190627220616Thu, 27 Jun 2019 22:06 EDTPolynomial stability of evolution cocycles and Banach function spaceshttps://projecteuclid.org/euclid.bbms/1561687567<strong>Pham Viet Hai</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 26, Number 2, 299--314.</p><p><strong>Abstract:</strong><br/>
In this paper, we give characterizations for a polynomial stability in Banach spaces. This is done by using evolution cocycles and techniques of Banach function spaces. Our characterizations are new versions of the theorems of Datko type.
</p>projecteuclid.org/euclid.bbms/1561687567_20190627220616Thu, 27 Jun 2019 22:06 EDTAssociated Families of Surfaces in Warped Products and Homogeneous Spaceshttps://projecteuclid.org/euclid.bbms/1568685650<strong>Marie-Amélie Lawn</strong>, <strong>Miguel Ortega</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 26, Number 3, 321--339.</p><p><strong>Abstract:</strong><br/>
We classify Riemannian surfaces admitting associated families in three dimensional homogeneous spaces with four-dimensional isometry groups and in a wide family of (semi-Riemannian) warped products, with an extra natural condition (namely, rotating structure vector field). We prove that, provided the surface is not totally umbilical, such families exist in both cases if, and only if, the ambient manifold is a product and the surface is minimal. In particular, there exists no associated families of surfaces with rotating structure vector field in the Heisenberg group.
</p>projecteuclid.org/euclid.bbms/1568685650_20190916220116Mon, 16 Sep 2019 22:01 EDTSome Characterizations of Composition Operators on Weighted Dirichlet Spaceshttps://projecteuclid.org/euclid.bbms/1568685651<strong>Songxiao Li</strong>, <strong>Yecheng Shi</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 26, Number 3, 341--353.</p><p><strong>Abstract:</strong><br/>
In this paper, we give three different characterizations for the boundedness and compactness of composition operators between different weighted Dirichlet spaces in the unit disk.
</p>projecteuclid.org/euclid.bbms/1568685651_20190916220116Mon, 16 Sep 2019 22:01 EDTThe simplicity of the first eigenvalue for an eigenvalue problem involving the Finsler $p$-Laplace operator and a nonlocal termhttps://projecteuclid.org/euclid.bbms/1568685652<strong>Andrei Grecu</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 26, Number 3, 355--363.</p><p><strong>Abstract:</strong><br/>
We investigate the simplicity of the lowest eigenvalue for an eigenvalue problem involving the Finsler $p$-Laplace operator and a nonlocal term on a bounded domain subject to the homogeneous Dirichlet boundary condition.
</p>projecteuclid.org/euclid.bbms/1568685652_20190916220116Mon, 16 Sep 2019 22:01 EDTModuli Spaces of Affine Homogeneous Spaceshttps://projecteuclid.org/euclid.bbms/1568685653<strong>Gregor Weingart</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 26, Number 3, 365--400.</p><p><strong>Abstract:</strong><br/>
Every affine homogeneous space is locally described by its curvature, its torsion and a slightly less tangible object, its connection. Using this description of the local geometry of an affine homogeneous space we construct a variety $\mathfrak{M}(\,\mathfrak{g}\,V\,)$, which serves as a coarse moduli space for the local isometry classes of affine homogeneous spaces. Infinitesimal deformations of an isometry class of affine homogeneous spaces in this moduli space are \linebreak described by the Spencer cohomology of a comodule associated to a point in $\mathfrak{M}_\infty(\,\mathfrak{g}\,V\,)$. In an appendix we discuss the relevance of this construction to the study of locally homogeneous spaces.
</p>projecteuclid.org/euclid.bbms/1568685653_20190916220116Mon, 16 Sep 2019 22:01 EDTOn compactly-fibered coset spaceshttps://projecteuclid.org/euclid.bbms/1568685654<strong>Hanfeng Wang</strong>, <strong>Wei He</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 26, Number 3, 401--411.</p><p><strong>Abstract:</strong><br/>
Topological properties of compactly-fibered coset spaces are investigated. It is proved that for a compactly-fibered coset space $X$ with $Nag(X)\leq\tau$, the closure of a family of $G_{\tau}$-sets is also a $G_{\tau}$-set in $X$. We also show that the equation $\chi(X)=\pi\chi(X)$ holds for any compactly-fibered coset space $X$. A Dichotomy Theorem for compactly-fibered coset spaces is established: every remainder of such a space has the Baire property, or is $\sigma$-compact.
</p>projecteuclid.org/euclid.bbms/1568685654_20190916220116Mon, 16 Sep 2019 22:01 EDTFinite codimensional maximal ideals in subalgebras of ultrametric uniformly continuous functionshttps://projecteuclid.org/euclid.bbms/1568685655<strong>Monique Chicourrat</strong>, <strong>Bertin Diarra</strong>, <strong>Alain Escassut</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 26, Number 3, 413--420.</p><p><strong>Abstract:</strong><br/>
Let $\rm I\!E$ be a complete ultrametric space, let $\rm I\!E$ be a perfect complete ultrametric field and let $A$ be a Banach $\rm I\!E$-algebra which is either a full $\rm I\!E$-subalgebra of the algebra of continuous functions from $\rm I\!E$ to $\rm I\!E$ owning all characteristic functions of clopens of $\rm I\!E$, or a full $\rm I\!E$-subalgebra of the algebra of uniformly continuous functions from $\rm I\!E$ to $\rm I\!E$ owning all characteristic functions of uniformly open subsets of $\rm I\!E$. We prove that all maximal ideals of finite codimension of $A$ are of codimension $1$.
</p>projecteuclid.org/euclid.bbms/1568685655_20190916220116Mon, 16 Sep 2019 22:01 EDTOn the compressed essential graph of a commutative ringhttps://projecteuclid.org/euclid.bbms/1568685656<strong>Shiroyeh Payrovi</strong>, <strong>Sakineh Babaei</strong>, <strong>Esra Sengelen Sevim</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 26, Number 3, 421--429.</p><p><strong>Abstract:</strong><br/>
Let $R$ be a commutative ring. In this paper, we introduce and study the compressed essential graph of $R$, $EG_E(R)$. The compressed essential graph of $R$ is a graph whose vertices are equivalence classes of non-zero zero-divisors of $R$ and two distinct vertices $[x]$ and $[y]$ are adjacent if and only if $\ann(xy)$ is an essential ideal of $R$. It is shown if $R$ is reduced, then $EG_E(R)=\Gamma_E(R)$, where $\Gamma_E(R)$ denotes the compressed zero-divisor graph of $R$. Furthermore, for a non-reduced Noetherian ring $R$ with $3<|EG_E(R)|<\infty $, it is shown that $EG_E(R)=\Gamma_E(R)$ if and only if \begin{itemize} \item[(i)] $\Nil(R)=\ann(Z(R))$. \item[(ii)] Every non-zero element of $\Nil(R)$ is irreducible in $Z(R)$. \end{itemize}
</p>projecteuclid.org/euclid.bbms/1568685656_20190916220116Mon, 16 Sep 2019 22:01 EDTSome drift exponentially fitted stochastic Runge-Kutta methods for solving It\^{o} SDE systemshttps://projecteuclid.org/euclid.bbms/1568685657<strong>Sadegh Amiri</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 26, Number 3, 431--451.</p><p><strong>Abstract:</strong><br/>
In this paper, we introduce a family of drift exponentially fitted stochastic Runge-Kutta (DEFSRK) methods for multi-dimensional It\^{o} stochastic differential equations (SDEs). For the presented class of DEFSRK methods, the regions of mean-square stability (MS-stability) are obtained with reasonable results. Also, general order conditions for the coefficients and the random variables of the DEFSRK methods are extracted. Then, a set of order conditions for a subclass with stochastic weak second order is obtained. Some numerical examples are presented to establish the efficiency and accuracy of the new schemes.
</p>projecteuclid.org/euclid.bbms/1568685657_20190916220116Mon, 16 Sep 2019 22:01 EDTOrder theoretic and topological Characterizations of the Divided Spectrum of a Ringhttps://projecteuclid.org/euclid.bbms/1568685658<strong>Othman Echi</strong>, <strong>Adel Khalfallah</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 26, Number 3, 453--467.</p><p><strong>Abstract:</strong><br/>
Let $R$ be a commutative ring with identity. We denote by $\mathcal{D}\mathrm{iv}(R)$ the divided spectrum of $R$ (the set of all divided prime ideals of $R$). By a divspectral space, we mean a topological space homeomorphic with the subspace $\mathcal{D}\mathrm{iv}(R)$ of $\mathrm{Spec}(R)$ endowed with the Zariski topology, for some ring $R$. A divspectral set is a poset which is order isomorphic to $(\mathcal{D}\mathrm{iv}(R),\subseteq)$, for some ring $R$. The main purpose of this paper is to provide some topological (resp., algebraic) characterizations of of divspectral spaces (resp., sets).
</p>projecteuclid.org/euclid.bbms/1568685658_20190916220116Mon, 16 Sep 2019 22:01 EDTOn the $C^*$-algebra generated by the Koopman representation of a topological full grouphttps://projecteuclid.org/euclid.bbms/1568685659<strong>Eduardo Scarparo</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 26, Number 3, 469--479.</p><p><strong>Abstract:</strong><br/>
Let $(X,T,\mu)$ be a Cantor minimal system and $[[T]]$ the associated topological full group. We analyze $C^*_\pi([[T]])$, where $\pi$ is the Koopman representation attached to the action of $[[T]]$ on $(X,\mu)$. Specifically, we show that $C^*_\pi([[T]])=C^*_\pi([[T]]')$ and that the kernel of the character $\tau$ on $C^*_\pi([[T]])$ coming from containment of the trivial representation is a hereditary $C^*$-subalgebra of $C(X)\rtimes\mathbb{Z}$. Consequently, $\ker\tau$ is stably isomorphic to $C(X)\rtimes\mathbb{Z}$, and $C^*_\pi([[T]]')$ is not AF. We also prove that if $G$ is a finitely generated, elementary amenable group and $C^ *(G)$ has real rank zero, then $G$ is finite.
</p>projecteuclid.org/euclid.bbms/1568685659_20190916220116Mon, 16 Sep 2019 22:01 EDT