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 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 EDTNielsen-Reidemeister indices for multivalued mapshttps://projecteuclid.org/euclid.bbms/1576206349<strong>L. Bernal-González</strong>, <strong>H.J.Cabana Méndez</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 25, Number 4, 481--492.</p><p><strong>Abstract:</strong><br/>
Let us consider the following two norms in the vector space \,$\mathcal{P}$ \,of all complex polynomials: $$ \|p\|_{D_{r}}:= \sup\{|p(z)|: |z|<r\}, \text{ and } \|p\|_{1}:=\sum_{i=0}^{n}|a_{i}|, $$ where \,$p(z) = \sum_{i=0}^{n} a_{i} z^{i}$. In this note we show that, if $0 <\varepsilon < \varepsilon' < 1 < r < r'$, then $$ \|\cdot\|_{D_{\varepsilon}}\prec\|\cdot\|_{D_{\varepsilon'}}\prec\|\cdot\|_{D_{1}}\prec \|\cdot\|_{1}\prec \|\cdot\|_{D_{r}}\prec \|\cdot\|_{D_{r'}}, $$ where \,$\prec$ \,represents the natural (strict) partial order in their corresponding induced topologies.
</p>projecteuclid.org/euclid.bbms/1576206349_20191212220622Thu, 12 Dec 2019 22:06 ESTA best proximity point approach to existence of solutions for a system of ordinary differential equationshttps://projecteuclid.org/euclid.bbms/1576206350<strong>Moosa Gabeleh</strong>, <strong>Calogero Vetro</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 25, Number 4, 493--503.</p><p><strong>Abstract:</strong><br/>
We establish the existence of a solution for the following system of differential equations \begin{equation*} \label{system}\begin{cases}x'(t) = f (t, x(t)), & x(t_0) = x^*,\\ y'(t) = g (t, y(t)), & y(t_0) = x^{**}, \end{cases} \end{equation*} in the space of all bounded and continuous real functions on $[0,+\infty[$. We use best proximity point methods and measure of noncompactness theory under suitable assumptions on $f$ and $g$. Some new best proximity point theorems play a key role in the above result.
</p>projecteuclid.org/euclid.bbms/1576206350_20191212220622Thu, 12 Dec 2019 22:06 ESTQuasianalytic ultradifferentiability cannot be tested in lower dimensionshttps://projecteuclid.org/euclid.bbms/1576206353<strong>Armin Rainer</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 25, Number 4, 505--517.</p><p><strong>Abstract:</strong><br/>
We show that, in contrast to the real analytic case, quasianalytic ultradifferentiability can never be tested in lower dimensions. Our results are based on a construction due to Jaffe.
</p>projecteuclid.org/euclid.bbms/1576206353_20191212220622Thu, 12 Dec 2019 22:06 ESTTopological groups have representable actionshttps://projecteuclid.org/euclid.bbms/1576206354<strong>Francesca Cagliari</strong>, <strong>Maria Manuel Clementino</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 25, Number 4, 519--526.</p><p><strong>Abstract:</strong><br/>
This paper shows that the group of auto-homeomorphisms of a topological group can be endowed with a topology so that the resulting topological group plays, for topological groups, the role of the group of automorphisms of a group: it represents the internal actions on the given topological group.
</p>projecteuclid.org/euclid.bbms/1576206354_20191212220622Thu, 12 Dec 2019 22:06 ESTA note on monotonically star $\sigma$-compact spaceshttps://projecteuclid.org/euclid.bbms/1576206355<strong>Yan-Kui Song</strong>, <strong>Wei-Feng Xuan</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 25, Number 4, 527--534.</p><p><strong>Abstract:</strong><br/>
A space $X$ is {\it monotonically star $\sigma$-compact} if one assigns to each open cover $\mathcal U$ of $X$ a subspace $s(\mathcal U)\subseteq X$, called a kernel, such that $s(\mathcal U)$ is a $\sigma$-compact subset of $X$, and $st(s(\mathcal U),\mathcal U)=X$, and if $\mathcal V$ refines $\mathcal U$ then $s(\mathcal U)\subseteq s(\mathcal V)$, where $st(s(\mathcal U),\mathcal U)=\bigcup\{U\in \mathcal U:U\cap s(\mathcal U)\neq\emptyset\}.$ In this paper, we investigate the relationship between monotonically star $\sigma$-compact spaces and related spaces, and also study topological properties of monotonically star $\sigma$-compact spaces.
</p>projecteuclid.org/euclid.bbms/1576206355_20191212220622Thu, 12 Dec 2019 22:06 ESTHypersurfaces of the homogeneous nearly Kähler $\mathbb{S}^6$ and $\mathbb{S}^3\times\mathbb{S}^3$ with anticommutative structure tensorshttps://projecteuclid.org/euclid.bbms/1576206356<strong>Zejun Hu</strong>, <strong>Zeke Yao</strong>, <strong>Xi Zhang</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 25, Number 4, 535--549.</p><p><strong>Abstract:</strong><br/>
Each hypersurface of a nearly Kähler manifold is naturally equipped with two tensor fields of $(1,1)$-type, namely the shape operator $A$ and the induced almost contact structure $\phi$. In this paper, we show that, in the homogeneous nearly Kähler $\mathbb{S}^6$ a hypersurface satisfies the condition $A\phi+\phi A=0$ if and only if it is totally geodesic; moreover, similar as for the non-flat complex space forms, the homogeneous nearly Kähler manifold $\mathbb{S}^3\times\mathbb{S}^3$ does not admit a hypersurface that satisfies the condition $A\phi+\phi A=0$.
</p>projecteuclid.org/euclid.bbms/1576206356_20191212220622Thu, 12 Dec 2019 22:06 ESTAn averaging formula for the coincidence Reidemeister tracehttps://projecteuclid.org/euclid.bbms/1576206357<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, 551--570.</p><p><strong>Abstract:</strong><br/>
This papers examines the general differential equation \[y''(z)+a(z) y'(z)+ b(z)y(z)=0\] in the unit disk of the complex plane, and finds conditions on the analytic functions $a$ and $b$ that ensures the solutions are Janowski starlike. Also studied is Janowski convexity of solutions to \[z (1-z)y''(z)+ a(z) y'(z)+ \alpha y(z) =0,\] where $\alpha$ is a given constant. Janowski starlikeness and Janowski convexity encompass various widely studied classes of classical starlikeness and convexity. As application, we give convexity and starlikeness geometric description of solutions to differential equations related to several important special functions.
</p>projecteuclid.org/euclid.bbms/1576206357_20191212220622Thu, 12 Dec 2019 22:06 ESTDiscontinuity at fixed points with applicationshttps://projecteuclid.org/euclid.bbms/1576206358<strong>R. P. Pant</strong>, <strong>Nihal Yilmaz Özgür</strong>, <strong>Nihal Taş</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 25, Number 4, 571--589.</p><p><strong>Abstract:</strong><br/>
In this paper, we study new contractive conditions which are strong enough to generate fixed points but which do not force the map to be continuous at fixed points. In this context, we give new results on the fixed-circle problem. We investigate some applications to complex-valued metric spaces and to discontinuous activation functions in real and complex valued neural networks.
</p>projecteuclid.org/euclid.bbms/1576206358_20191212220622Thu, 12 Dec 2019 22:06 ESTDecidability, Arithmetic Subsequences and Eigenvalues of Morphic Subshiftshttps://projecteuclid.org/euclid.bbms/1576206359<strong>Fabien Durand</strong>, <strong>Valérie Goyheneche</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 25, Number 4, 591--618.</p><p><strong>Abstract:</strong><br/>
We prove decidability results on the existence of constant subsequences of uniformly recurrent morphic sequences along arithmetic progressions. We use spectral properties of the subshifts they generate to give a first algorithm deciding whether, given $p\in \mathbb{N}$, there exists such a constant subsequence along an arithmetic progression of common difference $p$. In the special case of uniformly recurrent automatic sequences we explicitly describe the sets of such $p$ by means of automata.
</p>projecteuclid.org/euclid.bbms/1576206359_20191212220622Thu, 12 Dec 2019 22:06 ESTRings in which elements are a sum of a central and a unit elementhttps://projecteuclid.org/euclid.bbms/1576206360<strong>Yosum Kurtulmaz</strong>, <strong>Sait Halicioglu</strong>, <strong>Abdullah Harmanci</strong>, <strong>Huanyin Chen</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 25, Number 4, 619--631.</p><p><strong>Abstract:</strong><br/>
In this paper we introduce a new class of rings whose elements are a sum of a central and a unit element, namely a ring $R$ is called $CU$ if each element $a\in R$ has a decomposition $a = c + u$ where $c$ is central and $u$ is unit. One of the main results in this paper is that if $F$ is a field which is not isomorphic to $\Bbb Z_2$, then $M_2(F)$ is a $CU$ ring. This implies, in particular, that any square matrix over a field which is not isomorphic to $\Bbb Z_2$ is the sum of a central matrix and a unit matrix.
</p>projecteuclid.org/euclid.bbms/1576206360_20191212220622Thu, 12 Dec 2019 22:06 ESTOn lineability of additive surjective functionshttps://projecteuclid.org/euclid.bbms/1576206361<strong>Krzysztof Płotka</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 25, Number 4, 633--639.</p><p><strong>Abstract:</strong><br/>
We prove that the class of additive perfectly everywhere surjective functions contains (with the exception of the zero function) a vector space of maximal possible dimension ($2^\cont$). Additionally, we show under the assumption of regularity of $\cont$ that the family of additive everywhere surjective functions that are not strongly everywhere surjective contains (with the exception of the zero function) a vector space of dimension $\cont^+$.
</p>projecteuclid.org/euclid.bbms/1576206361_20191212220622Thu, 12 Dec 2019 22:06 ESTLinear representation stable bounds for the integral cohomology of pure mapping class groupshttps://projecteuclid.org/euclid.bbms/1579402815<strong>Rita Jiménez Rolland</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 26, Number 5, 641--658.</p><p><strong>Abstract:</strong><br/>
In this paper we study the integral cohomology of pure mapping class groups of surfaces, and other related groups and spaces, as $\mathsf{FI}$-modules. We use recent results from Church, Miller, Nagpal and Reinhold to obtain explicit linear bounds for their presentation degree and to give an inductive description of these $\mathsf{FI}$-modules. Furthermore, we establish new results on representation stability, in the sense of Church and Farb, for the rational cohomology of pure mapping class groups of non-orientable surfaces.
</p>projecteuclid.org/euclid.bbms/1579402815_20200118220031Sat, 18 Jan 2020 22:00 ESTSymmetric connectedness in $T_0$-quasi-metric spaceshttps://projecteuclid.org/euclid.bbms/1579402816<strong>Filiz Yıldız</strong>, <strong>Hans-Peter A. Künzi</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 26, Number 5, 659--679.</p><p><strong>Abstract:</strong><br/>
We continue the study of asymmetry in $T_0$-quasi-metric spaces. In this context we introduce the property of symmetric connectedness for a $T_0$-quasi-metric space. We present some methods in order to find the symmetrically connected pairs of a $T_0$-quasi-metric space. We also show that the problem to determine the symmetry components of points turns out to be easier when formulated for the induced $T_0$-quasi-metric of an asymmetrically normed real vector space. In addition, as a kind of opposite to the notion of a metric space, we define antisymmetric $T_0$-quasi-metric spaces. Subsequently some useful results about antisymmetry can be emphasized by describing the property of antisymmetric connectedness for a $T_0$-quasi-metric space. Finally, we observe that there are natural relations between the theory of (anti)symmetrically connected $T_0$-quasi-metric spaces and the theory of connectedness in the sense of graph theory.
</p>projecteuclid.org/euclid.bbms/1579402816_20200118220031Sat, 18 Jan 2020 22:00 ESTOn Bernstein-Chlodovsky operators preserving $e^{-2x} $https://projecteuclid.org/euclid.bbms/1579402817<strong>Tuncer Acar</strong>, <strong>Mirella Cappelletti Montano</strong>, <strong>Pedro Garrancho</strong>, <strong>Vita Leonessa</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 26, Number 5, 681--698.</p><p><strong>Abstract:</strong><br/>
In this paper we introduce a generalization of Bernstein-Chlodovsky operators that preserves the exponential function $e^{-2x}$ $(x \geq 0)$. We study its approximation properties in several function spaces, and we evaluate the rate of convergence by means of suitable moduli of continuity. Throughout some estimates of the rate of convergence, we prove better error estimation than the original operators on certain intervals.
</p>projecteuclid.org/euclid.bbms/1579402817_20200118220031Sat, 18 Jan 2020 22:00 ESTHypercyclicity, existence and approximation results for convolution operators on spaces of entire functionshttps://projecteuclid.org/euclid.bbms/1579402818<strong>Vinícius V. Fávaro</strong>, <strong>Ariosvaldo Jatobá</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 26, Number 5, 699--723.</p><p><strong>Abstract:</strong><br/>
In this work we shall prove new results on the theory of convolution operators on spaces of entire functions. The focus is on hypercyclicity results for convolution operators on spaces of entire functions of a given type and order; and existence and approximation results for convolution equations on spaces of entire functions of a given type and order. In both cases we give a general method to prove new results that recover, as particular cases, several results of the literature. Applications of these more general results are given, including new hypercyclicity results for convolution operators on spaces on entire functions on $\mathbb{C}^n.$
</p>projecteuclid.org/euclid.bbms/1579402818_20200118220031Sat, 18 Jan 2020 22:00 ESTPermanence properties of the second nilpotent product of groupshttps://projecteuclid.org/euclid.bbms/1579402819<strong>Román Sasyk</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 26, Number 5, 725--742.</p><p><strong>Abstract:</strong><br/>
We show that amenability, the Haagerup property, the Kazhdan's property (T) and exactness are preserved under taking second nilpotent product of groups. We also define the restricted second nilpotent wreath product of groups, this is a semi-direct product akin to the restricted wreath product but constructed from the second nilpotent product. We then show that if two discrete groups have the Haagerup property, the restricted second nilpotent wreath product of them also has the Haagerup property. We finally show that if a discrete group is abelian, then the restricted second nilpotent wreath product constructed from it is unitarizable if and only if the acting group is amenable.
</p>projecteuclid.org/euclid.bbms/1579402819_20200118220031Sat, 18 Jan 2020 22:00 ESTAsymptotic Distributions of Record Values under Exponential Normalizationhttps://projecteuclid.org/euclid.bbms/1579402820<strong>H. M. Barakat</strong>, <strong>E. M. Nigm</strong>, <strong>E. O. Abo Zaid</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 26, Number 5, 743--758.</p><p><strong>Abstract:</strong><br/>
In this paper, we study the limit distribution of the record values under nonlinear normalization of the form $${\cal T}_n(x)=\exp\{u_{n}(| \log |x||)^{v_{n}}\mbox{sign}(\log |x|)\}\mbox{sign}(x),$$ which is called exponential norming ($e-$norming). The corresponding limit laws of the upper extremes are called $e$-max stable laws (denoted by $U(.)$). In this paper, we show that the limit distributions of the record values under exponential norming are of the form $ {\cal N}(-\log (-\log U(x))),$ where ${\cal N}(.)$ is the standard normal distribution. Moreover, we study the domains of attraction for these types of limit laws. Finally, some illustrative examples are given.
</p>projecteuclid.org/euclid.bbms/1579402820_20200118220031Sat, 18 Jan 2020 22:00 EST$L^2$ concentration of blow-up solutions for the mass-critical NLS with inverse-square potentialhttps://projecteuclid.org/euclid.bbms/1579402821<strong>Abdelwahab Bensouilah</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 26, Number 5, 759--771.</p><p><strong>Abstract:</strong><br/>
In this paper, we prove a refined version of a compactness lemma and we use it to establish mass-concentration for the focusing nonlinear Schrödinger equation with an inverse-square potential.
</p>projecteuclid.org/euclid.bbms/1579402821_20200118220031Sat, 18 Jan 2020 22:00 ESTBlow-up and exponential decay of solutions to a class of pseudo-parabolic equationhttps://projecteuclid.org/euclid.bbms/1579402822<strong>Jun Zhou</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 26, Number 5, 773--785.</p><p><strong>Abstract:</strong><br/>
In this paper, we consider a class of pseudo-parabolic equation, which was studied extensively in recent years, and the main results on blow-up depend on the initial energy $J(u_0)$ (see (1.5)) and the mountain-pass level $d$ (see (1.7)). By using eigenfunction, we give a new blow-up result which does not depend on $J(u_0)$ and $d$. Moreover, we obtain the energy functional $J(u)$ (see (1.5)) decays exponentially. These results extend the previous studies on this equation.
</p>projecteuclid.org/euclid.bbms/1579402822_20200118220031Sat, 18 Jan 2020 22:00 ESTThe non-split symplectic period of a residual Eisenstein series on $Sp_{2n}$https://projecteuclid.org/euclid.bbms/1579402823<strong>Cesar Valverde</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 26, Number 5, 787--799.</p><p><strong>Abstract:</strong><br/>
Let $\field{F}$ be a number field with ring of adeles $\field{A}$, let $\field{K}$ be a quadratic extension of $\field{F}$ with ring of adeles $\field{A}_\field{K}$. Let $\eta$ be an irreducible, automorphic, cuspidal, self-dual representation of $GL_{2n}(\field{A})$ and let $\phi \in Ind_{P(\field{A})}^{Sp_{2n}(\field{A})}\eta$, where $P$ is the standard Siegel parabolic. We present an identity between the $Sp_n(\field{A}_\field{K})$-period of the residual Eisenstein series on $Sp_{2n}(\field{A})$ associated to $\phi$ and the $GL_n(\field{A}_\field{K})$- period of $\phi$. This is a non-split version of a result of Ginzburg, Soudry and Rallis.
</p>projecteuclid.org/euclid.bbms/1579402823_20200118220031Sat, 18 Jan 2020 22:00 ESTField of Iterated Laurent Series and its Brauer Grouphttps://projecteuclid.org/euclid.bbms/1590199296<strong>Adam Chapman</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 27, Number 1, 1--6.</p><p><strong>Abstract:</strong><br/>
The symbol length of ${_pBr}(k(\!(\alpha_1)\!)\dots(\!(\alpha_n)\!))$ for an algebraically closed field $k$ of $\operatorname{char}(k) \neq p$ is known to be $\lfloor \frac{n}{2} \rfloor$. We prove that the symbol length for the case of $\operatorname{char}(k) = p$ is rather $n-1$. We also show that pairs of anisotropic quadratic or bilinear $n$-fold Pfister forms over this field need not share an $(n-1)$-fold factor.
</p>projecteuclid.org/euclid.bbms/1590199296_20200522220144Fri, 22 May 2020 22:01 EDTOn block basic sequences in non-Archimedean Köthe spaceshttps://projecteuclid.org/euclid.bbms/1590199299<strong>Wiesław Śliwa</strong>, <strong>Agnieszka Ziemkowska-Siwek</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 27, Number 1, 7--16.</p><p><strong>Abstract:</strong><br/>
We prove that any two Schauder bases $(x_n)$ and $(y_n)$ in non-normable Köthe spaces $E$ and $F$ (over a non-Archimedean field $\mathbb K$) have block basic sequences $(u_n)$ and $(v_n)$, respectively, that are equivalent. Moreover we show that any Schauder basis in a non-normable Köthe space has a block basic sequence that is equivalent to the coordinate Schauder basis in some generalized power series space of infinite type; the generalized power series spaces are the most known and important examples of nuclear Köthe spaces. It follows that any two non-normable Köthe spaces $E$ and $F$, have closed subspaces $E_0$ and $F_0$, respectively, that are isomorphic to the same generalized power series space of infinite type $D_g(a,\infty)$ for some $g\in \Phi_c$ and $a\in \Gamma$.
</p>projecteuclid.org/euclid.bbms/1590199299_20200522220144Fri, 22 May 2020 22:01 EDTA class of monotonic quantities along the Yamabe flowhttps://projecteuclid.org/euclid.bbms/1590199300<strong>Farzad Daneshvar</strong>, <strong>Asadollah Razavi</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 27, Number 1, 17--27.</p><p><strong>Abstract:</strong><br/>
Let $(M,g(t))$ be a closed Riemannian manifold of dimension $n\geq 2$. In this paper we obtain the evolution formula for the lowest constant $\lambda^{b}_{a}(g)$ under the normalized and unnormalized Yamabe flow such that the equation \begin{equation*} -{\rm \Delta} f + af\log f + bRf= \lambda^{b}_{a}(g) f, \end{equation*} with $\int_M f^2\, {\rm dV}=1,$ has positive solutions, where $a$ and $b$ are two real constants. Then we construct various monotonic quantities under the normalized and unnormalized Yamabe flow. We also show that the scalar curvature of a steady Yamabe breather with nonnegative scalar curvature is identically zero.
</p>projecteuclid.org/euclid.bbms/1590199300_20200522220144Fri, 22 May 2020 22:01 EDTThe inverse and the Moore-Penrose inverse of a $k$-circulant matrix with binomial coefficientshttps://projecteuclid.org/euclid.bbms/1590199301<strong>Biljana Radičić</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 27, Number 1, 29--42.</p><p><strong>Abstract:</strong><br/>
Let $k$ be a non-zero complex number. In this paper, we consider a $k$-circulant matrix with binomial coefficients. The inverse of such invertible matrix is determined. We also obtain the Moore\,-\,Penrose inverse (and the group inverse) of such singular matrix. The obtained results are illustrated by examples at the end of this paper.
</p>projecteuclid.org/euclid.bbms/1590199301_20200522220144Fri, 22 May 2020 22:01 EDTThe classification of fully filial torsion-free ringshttps://projecteuclid.org/euclid.bbms/1590199302<strong>Karol Pryszczepko</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 27, Number 1, 43--47.</p><p><strong>Abstract:</strong><br/>
A ring in which the relation of being an ideal is transitive is called fully filial. The aim of this paper is to give the classification theorem for torsion-free fully filial rings.
</p>projecteuclid.org/euclid.bbms/1590199302_20200522220144Fri, 22 May 2020 22:01 EDTComposition operators and closures of $\mathcal{Q}_K(p,q)$-type spaces in the Logarithmic Bloch spacehttps://projecteuclid.org/euclid.bbms/1590199303<strong>Xiangling Zhu</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 27, Number 1, 49--60.</p><p><strong>Abstract:</strong><br/>
Closures of $\mathcal{Q}_K(p,q)$-type spaces in the Logarithmic Bloch space are investigated in this paper. Moreover, we characterize the boundedness and compactness of composition operators from the Logarithmic Bloch space to the closure of $\mathcal{Q}_K(p,q)$ type spaces in the Logarithmic Bloch space
</p>projecteuclid.org/euclid.bbms/1590199303_20200522220144Fri, 22 May 2020 22:01 EDTGeneralized Mrówka spaces and diagonal propertieshttps://projecteuclid.org/euclid.bbms/1590199304<strong>Wei-Feng Xuan</strong>, <strong>Yan-Kui Song</strong>, <strong>Wei-Xue Shi</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 27, Number 1, 61--69.</p><p><strong>Abstract:</strong><br/>
In this paper, we prove that if $2^\lambda < \kappa$ and $\mathcal A \subset [\kappa]^{\lambda}$ is a MADF then the generalized Mrówka space $\Psi (\mathcal A\setminus \mathcal B)$ has no $G_\lambda$-diagonal, where $\mathcal B \subset \mathcal A$ and $|\mathcal B|\le\lambda$. If a topological space $X$ has a regular $G_\lambda$-diagonal and a local decreasing base of cardinality $\chi(X)$ for each $x \in X$, then $|X| \le 2^{dc(X) \cdot \chi(X) \cdot \lambda}$, where $dc(X)$ is the discrete cellularity of $X$ and $\chi(X)$ is the character of $X$. As a corollary, we prove that if $X$ is a DCCC (and hence, $DC(\omega_1)$, weakly Lindelöf or star Lindelöf) first countable space with a regular $G_\delta$-diagonal then $|X|\le 2^\omega$, which gives a positive answer to a question in [17]. Finally, we give another counterexample to a question of Ginsburg and Woods [6], which has nicer properties than the counterexamples constructed in [15] and [16].
</p>projecteuclid.org/euclid.bbms/1590199304_20200522220144Fri, 22 May 2020 22:01 EDTFitted second order numerical method for a singularly perturbed Fredholm integro-differential equationhttps://projecteuclid.org/euclid.bbms/1590199305<strong>Gabil M. Amiraliyev</strong>, <strong>Muhammet Enes Durmaz</strong>, <strong>Mustafa Kudu</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 27, Number 1, 71--88.</p><p><strong>Abstract:</strong><br/>
In this paper, we consider the linear first order singularly perturbed Fredholm integro-differential equation. For the solution of this problem, fitted difference scheme is constructed on a Shishkin mesh. The method is based on the method of integral identities with the use of exponential basis functions and interpolating quadrature rules with the weight and remainder terms in integral form. The method is proved to be second-order convergent in the discrete maximum norm. Also, numerical results are given to support theoretical analysis.
</p>projecteuclid.org/euclid.bbms/1590199305_20200522220144Fri, 22 May 2020 22:01 EDTUniform convergence of trigonometric series with $p$-bounded variation coefficientshttps://projecteuclid.org/euclid.bbms/1590199306<strong>Mateusz Kubiak</strong>, <strong>Bogdan Szal</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 27, Number 1, 89--110.</p><p><strong>Abstract:</strong><br/>
In the present paper we introduce a new class of sequences called $GMS\left(p, \beta ,r\right) ,$ which is the generalization of a class considered by Tikhonov in [9] and Szal in [10]. Moreover, we obtained in this note sufficient and necessary conditions for the uniform convergence of sine and cosine series with $\left(p,\beta ,r\right) -$ general monotone coefficients.
</p>projecteuclid.org/euclid.bbms/1590199306_20200522220144Fri, 22 May 2020 22:01 EDTSome Remarks on Schauder Bases in Lipschitz Free Spaceshttps://projecteuclid.org/euclid.bbms/1590199307<strong>Matěj Novotný</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 27, Number 1, 111--126.</p><p><strong>Abstract:</strong><br/>
We show that the basis constant of every retractional Schauder basis on the Free space of a graph circle increases with the radius. As a consequence, there exists a uniformly discrete subset $M\subseteq\R^2$ such that $\F(M)$ does not have a retractional Schauder basis. Furthermore, we show that for any net $ N\subseteq\R^n$, $n\geq 2$, there is no retractional unconditional basis on the Free space $\mathcal F(N)$.
</p>projecteuclid.org/euclid.bbms/1590199307_20200522220144Fri, 22 May 2020 22:01 EDTA viscosity iterative algorithm for a family of monotone inclusion problems in an Hadamard spacehttps://projecteuclid.org/euclid.bbms/1590199308<strong>G.N. Ogwo</strong>, <strong>C. Izuchukwu</strong>, <strong>K.O. Aremu</strong>, <strong>O.T. Mewomo</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 27, Number 1, 127--152.</p><p><strong>Abstract:</strong><br/>
In this paper, we introduce a viscosity-type proximal point algorithm which comprises of a finite sum of resolvents of monotone operators, and a generalized asymptotically nonexpansive mapping. We prove that the algorithm converges strongly to a common zero of a finite family of monotone operators, which is also a fixed point of a generalized asymptotically nonexpansive mapping in an Hadamard space. Furthermore, we give two numerical examples of our algorithm in finite dimensional spaces of real numbers and one numerical example in a non-Hilbert space setting, in order to show the applicability of our results.
</p>projecteuclid.org/euclid.bbms/1590199308_20200522220144Fri, 22 May 2020 22:01 EDTThe association scheme on the points off a quadrichttps://projecteuclid.org/euclid.bbms/1590199309<strong>F. Vanhove</strong>. <p><strong>Source: </strong>Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 27, Number 1, 153--160.</p><p><strong>Abstract:</strong><br/>
The parameters of the association scheme on the points off a quadric are computed. This corrects a mistake in the literature.
</p>projecteuclid.org/euclid.bbms/1590199309_20200522220144Fri, 22 May 2020 22:01 EDT