https://www.ajol.info/index.php/qm/issue/feed Quaestiones Mathematicae 2021-11-09T11:53:02+00:00 Publishing Manager publishing@nisc.co.za Open Journal Systems <p><em>Quaestiones Mathematicae</em> is devoted to research articles from a wide range of mathematical areas. Longer expository papers of exceptional quality are also considered. Published in English, the journal receives contributions from authors around the globe and serves as an important reference source for anyone interested in mathematics.</p><p>Read more about the journal <a href="http://www.nisc.co.za/products/12/journals/quaestiones-mathematicae" target="_blank">here</a>. </p> https://www.ajol.info/index.php/qm/article/view/217083 Practical central binomial coefficients 2021-11-08T14:13:55+00:00 Carlo Sanna carlo.sanna.dev@gmail.com <div class="page" title="Page 1"> <div class="layoutArea"> <div class="column"> <p>A practical number is a positive integer n such that all positive integers less than <em>n</em> can be written as a sum of distinct divisors of <em>n</em>. Leonetti and Sanna proved that, as <em>x → +∞</em>, the central binomial coefficient (<em>2n/n</em>) is a practical number <em>n </em>for all positive integers <em>n ≤ x</em> but at most <em>O</em>(<em>x<sup>0.88097</sup></em>) exceptions. We improve this result by reducing the number of exceptions to exp(<em>C</em>(log <em>x</em>)<sup>4/5</sup> log log <em>x</em>), where C &gt; 0 is a constant.</p> </div> </div> </div> 2021-11-08T00:00:00+00:00 Copyright (c) https://www.ajol.info/index.php/qm/article/view/217086 Weak compactness of almost L-weakly and almost M-weakly compact operators 2021-11-08T14:34:08+00:00 Farid Afkir farid.afkir94@gmail.com Khalid Bouras k.bouras@uae.ac.ma Aziz Elbour azizelbour@hotmail.com Safae El Filali safae.elfilali.pc@gmail.com <div class="page" title="Page 1"> <div class="layoutArea"> <div class="column"> <p>In this paper, we investigate conditions on a pair of Banach lattices <em>E</em> and <em>F</em> that tells us when every positive almost L-weakly compact (resp. almost M-weakly compact) operator <em>T : E −→ F</em> is weakly compact. Also, we present some necessary conditions that tells us when every weakly compact operator <em>T : E −→ F</em> is almost M-weakly compact (resp. almost L-weakly compact). In particular, we will prove that if every weakly compact operator from a Banach lattice E into a Banach space <em>X</em> is almost L-weakly compact, then <em>E</em> is a KB-space or <em>X</em> has the Dunford-Pettis property and the norm of <em>E</em> is order continuous.</p> </div> </div> </div> 2021-11-08T00:00:00+00:00 Copyright (c) https://www.ajol.info/index.php/qm/article/view/217087 Weak exceptional sequences 2021-11-08T14:38:14+00:00 Emre Sen emre-sen@uiowa.edu <div class="page" title="Page 1"> <div class="layoutArea"> <div class="column"> <p>We introduce weak exceptional sequence of modules which can be viewed as another modification of the standard case, different from the works of Igusa- Todorov [IT17] and Buan-Marsh [BM18]. For hereditary algebras it is equivalent to standard exceptional sequences. One important new feature is: if the global dimension of an algebra is greater than one, then the size of a full sequence can exceed the rank of the algebra. We use both cyclic and linear Nakayama algebras to test combinatorial aspects of this new sequence. For some particular classes, we give closed form formulas which returns the number of a full weak exceptional sequences, and compare them with the number of exceptional sequences of types A and linear radical square zero Nakayama algebras [Sen19-2].</p> </div> </div> </div> 2021-11-08T00:00:00+00:00 Copyright (c) https://www.ajol.info/index.php/qm/article/view/217088 Computations and global properties for traces of Bessel’s Dirichlet form 2021-11-08T14:42:15+00:00 Ali BenAmor ali.benamor@ipeit.rnu.tn Rafed Moussa rafed.moussa@gmail.com <div class="page" title="Page 1"> <div class="layoutArea"> <div class="column"> <p>By an approximation method we compute explicitly traces of the Dirichlet form related to the Bessel process with respect to discrete measures as well as measures of mixed type. Then some global properties of the obtained Dirichlet forms, such as conservativeness, irreducibility and compact embedding for their domains are discussed.</p> </div> </div> </div> 2021-11-08T00:00:00+00:00 Copyright (c) https://www.ajol.info/index.php/qm/article/view/217089 Infinitely many solutions for a class of sublinear fractional Schrödinger-Poisson systems 2021-11-08T15:14:34+00:00 Wen Guan mathguanw@163.com Lu-Ping Ma 974531947@qq.com Da-Bin Wang wangdb96@163.com Jin-Long Zhang Zhangjllut@163.com <div class="page" title="Page 1"> <div class="layoutArea"> <div class="column"> <p>In this paper, we consider the following nonlinear fractional Schr<span style="font-weight: 400;">ö</span>dinger-Poisson system <span style="font-weight: 400;">{(<em>−∆)</em></span><em><sup><span style="font-weight: 400;">s</span></sup><span style="font-weight: 400;">u + V (x)u + K(x)φu = a(x)|u|</span><sup><span style="font-weight: 400;">q−1</span></sup><span style="font-weight: 400;">u, x ∈ R</span><sup><span style="font-weight: 400;">3</span></sup><span style="font-weight: 400;">, (−∆)</span><sup><span style="font-weight: 400;">t</span></sup><span style="font-weight: 400;">φ = K(x)u</span><sup><span style="font-weight: 400;">2</span></sup><span style="font-weight: 400;">, x ∈ R</span><sup><span style="font-weight: 400;">3</span></sup></em><span style="font-weight: 400;">} </span>where <em>s,t</em> ∈ (0,1) and <em>4s + 2t</em> ≥ 3,0 &lt; q &lt; 1, and a,K,V ∈ L∞(R<sup>3</sup>). When <em>a, V</em> both change sign in R<sup>3</sup>, by applying the symmetric mountain pass theorem, we prove that the problem has infinitely many solutions under appropriate assumptions on <em>a, K, V</em>.</p> </div> </div> </div> 2021-11-08T00:00:00+00:00 Copyright (c) https://www.ajol.info/index.php/qm/article/view/217091 A note on Tingley’s problem and Wigner’s theorem in the unit sphere of L<sup>∞</sup>(Г)-type spaces 2021-11-08T15:24:05+00:00 Dongni Tan tandongni0608@sina.cn Xiaolei Xiong 719179931@qq.com <div class="page" title="Page 1"> <div class="layoutArea"> <div class="column"> <p>Suppose that <em>f : S<sub>X</sub> → S<sub>Y</sub></em> is a surjective map between the unit spheres of two real L<sup>∞</sup>(Γ)-type spaces <em>X</em> and <em>Y</em> satisfying the following equation<em> {∥f(x) + f(y)∥,∥f(x) − f(y)∥} = {∥x + y∥,∥x − y∥} (x,y ∈ SX).&nbsp;</em>We show that such a mapping <em>f</em> is phase equivalent to an isometry, i.e., there exists a function <em>ε : SX</em> → {−1,1} such that <em>εf</em> is an isometry. We further show that this isometry is the restriction of a linear isometry between the whole spaces. These results can be seen as a combination of Tingley’s problem and Wigner’s theorem for L∞(Γ)-type spaces.</p> </div> </div> </div> 2021-11-08T00:00:00+00:00 Copyright (c) https://www.ajol.info/index.php/qm/article/view/217153 Shephard type problem for <i>L<sub>p</sub></i>-mixed Blaschke-Minkowski homomorphisms 2021-11-09T10:54:21+00:00 Bin Chen chenb121223@163.com Weidong Wang wangwd722@163.com Peibiao Zhao pbzhao@njust.edu.cn <div class="page" title="Page 1"> <div class="layoutArea"> <div class="column"> <p>In 2006, Schuster introduced the concept of Blaschke-Minkowski homomorphism of convex bodies. In this paper, we introduce the <em>L<sub>p-</sub></em>mixed Blaschke-Minkowski homomorphism in <em>L<sub>p</sub></em>-Brunn-Minkowski theory. We then further study the Shephard type problem involving an affirmative answer and two negative answers for <em>L<sub>p</sub></em>-mixed Blaschke-Minkowski homomorphism.</p> </div> </div> </div> 2021-11-09T00:00:00+00:00 Copyright (c) https://www.ajol.info/index.php/qm/article/view/217156 On best proximity points of interpolative proximal contractions 2021-11-09T11:00:02+00:00 Ishak Altun ishak.altun@tdtu.edu.vn Ayşenur Taşdemir aysenur.tasdemirr@gmail.com <div class="page" title="Page 1"> <div class="layoutArea"> <div class="column"> <div class="page" title="Page 1"> <div class="layoutArea"> <div class="column"> <p>In this paper, we introduce some kinds of interpolative proximal contractions named as Reich-Rus-<span style="font-weight: 400;">Ć</span>iri<span style="font-weight: 400;">ć</span> and Kannan types. Then taking into account the aforementioned mappings, we give a few best proximity point results. As special cases we obtain some fixed point results for interpolative contractions. To support the theory, some examples are provided.</p> </div> </div> </div> </div> </div> </div> 2021-11-09T00:00:00+00:00 Copyright (c) https://www.ajol.info/index.php/qm/article/view/217157 On property (<i>A</i>) of the amalgamated duplication of a ring along an ideal 2021-11-09T11:10:24+00:00 Youssef Arssi youssefarssi4@gmail.com Samir Bouchiba s.bouchiba@fs.umi.ac.ma <div class="page" title="Page 1"> <div class="layoutArea"> <div class="column"> <p>The main purpose of this paper is to totally characterize when the amalgamated duplication <em>R</em> <span style="font-weight: 400;">⋈</span> <em>I</em> of a ring <em>R</em> along an ideal <em>I</em> is an <em>A</em>-ring as well as an <em>SA</em>-ring. In this regard, we prove that <em>R</em> ◃▹ <em>I</em> is an <em>SA</em>-ring if and only if <em>R</em> is an <em>SA</em>-ring and <em>I</em> is contained in the set of zero divisors Z(<em>R</em>) of <em>R</em>. As to the Property (<em>A</em>) of <em>R</em> <span style="font-weight: 400;">⋈</span> <em>I</em>, it turns out that its characterization involves a new concept that we introduce in [6] and that we term the Property (<em>A</em>) of a module <em>M</em> along an ideal <em>I</em>. In fact, we prove that <em>R </em><span style="font-weight: 400;">⋈ </span><em>I</em> is an <em>A</em>-ring if and only if <em>R</em> is an <em>A</em>-ring, <em>I</em> is an <em>A</em>-module along itself and if <em>p</em> is a prime ideal of <em>R</em> such that <em>p</em> ⊆ Z<em><sub>R</sub></em>(<em>I</em>)∪Z<em><sup>I</sup></em>(<em>R</em>), then either <em>p</em> ⊆ Z<em><sub>R</sub></em>(<em>I</em>) or <em>p</em> ⊆ Z<em><sup>I</sup></em> (<em>R</em>), where Z<em><sup>I</sup></em> (<em>R</em>) := {a ∈ <em>R</em> : a + <em>I</em> ⊆ Z(<em>R</em>)}.</p> </div> </div> </div> 2021-11-09T00:00:00+00:00 Copyright (c) https://www.ajol.info/index.php/qm/article/view/217158 Global behavior and oscillation of a third order difference equation 2021-11-09T11:24:28+00:00 R. Abo-Zeid abuzead73@yahoo.com <div class="page" title="Page 1"> <div class="layoutArea"> <div class="column"> <p>In this paper, we solve and study the global behavior of the admissible solutions of the difference equation <em><span style="font-weight: 400;">x</span></em><sub><span style="font-weight: 400;">n+1</span></sub><span style="font-weight: 400;"> = </span><em><span style="font-weight: 400;">x</span></em><sub><span style="font-weight: 400;">n</span></sub><em><span style="font-weight: 400;">x</span></em><span style="font-weight: 400;"><sub>n-2 / </sub></span><em><span style="font-weight: 400;">ax</span></em><sub><span style="font-weight: 400;">n-1</span></sub><span style="font-weight: 400;"> + </span><em><span style="font-weight: 400;">bx</span></em><sub><span style="font-weight: 400;">n-2&nbsp;</span></sub><span style="font-weight: 400;"><em>n</em> = 0,1,...., </span>where <em>a,b</em> &gt; 0 and the initial values <em>x</em><sub>−2</sub>, <em>x</em><sub>−1</sub>, <em>x</em><sub>0</sub> are real numbers. We study also the oscillation of the admissible solutions of the aforementioned difference equation and give some illustrative examples.</p> </div> </div> </div> 2021-11-09T00:00:00+00:00 Copyright (c) https://www.ajol.info/index.php/qm/article/view/217159 Addendum to: “Variations of classical selection principles: An overview” 2021-11-09T11:29:11+00:00 Ljubiŝa D.R. Kočinac lkocinac@gmail.com <div class="page" title="Page 1"> <div class="layoutArea"> <div class="column"> <p>In this addendum we give a few remarks about Subsection 6.2 of the paper “Variations of classical selection principles: An overview,” Quaestiones Mathematicae, https://doi.org/10.2989/16073606.2019.1601646.</p> </div> </div> </div> 2021-11-09T00:00:00+00:00 Copyright (c)