Extracta Mathematicae
https://revista-em.unex.es/index.php/EM
<p style="margin-bottom: 0cm; line-height: 100%;"> </p> <p><span style="color: #000000;"><span style="font-family: Latin Modern Math;"><span style="font-size: medium;">Welcome to the new (as of February 2024) page of Extracta Mathematicae. We have tried our best, but in case any user detects inaccuracy or malfunction, please contact us <a href="https://revista-em.unex.es/index.php/EM/about/contact">here</a> and we will solve it as soon as possible. <br /></span></span></span></p> <p><span style="color: #000000;"><span style="font-family: Latin Modern Math;"><span style="font-size: medium;">Extracta Mathematicae (E.M.) publishes quality research papers that contain innovative contributions in the <a href="https://revista-em.unex.es/index.php/EM/covered">areas covered</a> by the members of the <a href="https://revista-em.unex.es/index.php/EM/editorial">Editorial Board</a>. E.M. is also open to consider well written survey papers.</span></span></span></p> <p><span style="color: #000000;"><span style="font-family: Latin Modern Math;"><span style="font-size: medium;">Publishing in E.M. is exempt from fees of any kind, and all documents are freely available for reading. E.M. publishes two issues a year under a <a href="https://creativecommons.org/licenses/by-nc/3.0/legalcode" target="_blank" rel="noopener">Creative Commons License Attribution-Non Commercial 3.0 Unported</a> license. The online version is free and open access. E.M. uses a <a href="https://publicationethics.org/files/Ethical_Guidelines_For_Peer_Reviewers_2.pdf">standard blind peer review process</a>, following the <a href="https://publicationethics.org/files/Ethical_guidelines_for_peer_reviewers_0.pdf">COPE Code of Conduct</a>.</span></span></span></p> <p><span style="color: #000000;"><span style="font-family: Latin Modern Math;"><span style="font-size: medium;">E.M. is edited and published in Badajoz (Spain) by the <a href="https://www.eweb.unex.es/eweb/imuex/" target="_blank" rel="noopener">Instituto de Matemáticas de la Universidad de Extremadura (IMUEX)</a>, under the auspices of this university and the cooperation of the <a href="http://matematicas.unex.es/" target="_blank" rel="noopener">Departamento de Matemáticas</a> and the <a href="https://www.unex.es/organizacion/servicios-universitarios/servicios/servicio_publicaciones?set_language=en&cl=en" target="_blank" rel="noopener">Servicio de Publicaciones</a>. </span></span></span></p> <p><span style="color: #000000;"><span style="font-family: Latin Modern Math;"><span style="font-size: medium;">We are uploading the previous issues <a href="https://revista-em.unex.es/index.php/EM/issue/archive">here</a>. In the meanwhile, all volumes, published uninterruptedly since 1986, are available online at: <a href="http://www.eweb.unex.es/eweb/extracta/Extracta_Published_volumes.html">UNEx-Extracta</a> or <a href="https://dialnet.unirioja.es/servlet/revista?codigo=579">Dialnet</a></span></span></span></p> <p><span style="color: #000000;"><span style="font-family: Latin Modern Math;"><span style="font-size: medium;">E.M. has been recently evaluated and </span></span></span><strong><span style="color: #000000;"><span style="font-family: Latin Modern Math;"><span style="font-size: medium;">accepted</span></span></span></strong><span style="color: #000000;"><span style="font-family: Latin Modern Math;"><span style="font-size: medium;"> for inclusion in Scopus (Scopus Sources List, <a href="https://www.elsevier.com/?a=91122">Accepted titles</a>). These are</span></span></span><span style="color: #000000;"><span style="font-family: Latin Modern Math;"><span style="font-size: medium;"> the latest volumes of E.M. in <a href="https://www.scopus.com/results/results.uri?sid=ba5d3a69aecc7a73cdde93fb38647c25&src=s&sot=b&sdt=b&origin=searchbasic&rr=&sl=15&s=ISSN(2605-5686)&searchterm1=2605-5686&searchTerms=&connectors=&field1=ISSN&fields=">Scopus.</a> </span></span></span></p> <p><span style="color: #000000;"><span style="font-family: Latin Modern Math;"><span style="font-size: medium;">E.M. is abstracted and indexed in <a href="http://www.ams.org/publications/math-reviews/math-reviews">Mathematical Reviews</a> and <a href="https://zbmath.org/">Zentralblatt MATH</a>. The AMS-Mathematical Citation Quotient (MCQ) average (2000-2017) for E.M. is 0.25 (all publications MCQ average 2000-2017 is 0.22) and the 2022-MCQ is 0.45 (2021-MCQ all journal median is 0.20). The printed version is exchanged with 117 journals in 36 countries all over the world.</span></span></span></p> <p><span style="color: #000000;"><span style="font-family: Latin Modern Math;"><span style="font-size: medium;">E.M. is indexed in <a href="https://www.doaj.org/toc/2605-5686?source=%7B">DOAJ</a>, the Directory of Open Access Journals, as well as in <a href="https://www.latindex.org/latindex/inicio">Latindex 2.0,</a> and is a member of <a href="https://freejournals.org/">Free Journal Network</a>. </span></span></span></p> <p><span style="color: #000000;"><span style="font-family: Latin Modern Math;"><span style="font-size: medium;">E.M. has obtained the <a href="https://evaluacionarce.fecyt.es/Publico/Resolucion/resolucion.aspx">Fecyt Quality seal 2021 </a>and it was renewed in <a href="https://calidadrevistas.fecyt.es/fecyt-publica-el-listado-provisional-de-revistas-que-renuevan-el-sello-de-calidad-en-2022">2022</a> and <a href="https://evaluacionarce.fecyt.es/Publico/Resolucion/__Recursos/2023ListadoProvisionalRenovacion.pdf" target="_blank" rel="noopener">2023</a>.</span></span></span></p> <p><span style="color: #000000;"><span style="font-family: Latin Modern Math;"><span style="font-size: medium;">E.M. uses Open Journal System <a href="https://openjournalsystems.com/">OJS</a>.</span></span></span></p> <p><span style="font-family: Latin Modern Math;"><span style="font-size: medium;"><span style="color: #000000;"><strong>2022 data:</strong><br />From 1st January to 31th December 2022, 71 manuscripts have been received in E.M., and 10 papers have been accepted for publication.<br />Regular number of reviewers for each manuscript: 2.<br />Speed (average):<br />Submission to first decision (all received manuscripts): 48 days<br />Submission to definitive decision (all received manuscripts): 66 days<br />Submission to first decision (accepted manuscripts): 127 days<br />Submission to definitive decision (accepted manuscripts): 134 days<br />Acceptance to online publication: 34 days<br />Acceptance to print publication: 145 days.</span></span></span></p>Servicio de Publicaciones, Universidad de ExtremaduraenExtracta Mathematicae0213-8743A topological characterization of an almost Boolean algebra
https://revista-em.unex.es/index.php/EM/article/view/2288
<p>For any Boolean space X and a discrete almost distributive lattice D, it is proved that the set C(X, D) of all continuous mappings of X into D, when D is equipped with the discrete topology, is an almost Boolean algebra under pointwise operations. Conversely, it is proved that any almost Boolean algebra is a homomorphic image of C(X,D) for a suitable Boolean space X and a discrete almost distributive lattice D.</p>
Articles in pressalmost distributive latticealmost Boolean algebramaximal elementdiscrete ADLdiscrete topologyBoolean spaceK. Ramanuja RaoK. Rama PrasadG. Vara LakshmiCh. Santhi Sundar Raj
Copyright (c) 2024 The authors
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2024-02-272024-02-2710.17398/The current state of play in the Landsberg-Berwald problem of Finsler geometry
https://revista-em.unex.es/index.php/EM/article/view/2287
<p>A progress report on the (still unresolved) Landsberg-Berwald problem of Finsler geometry: whether there can be non-Berwaldian regular Landsberg spaces.</p>
Articles in pressFinsler spacesLandsberg spacesBerwald spacesM. Crampin
Copyright (c) 2024 The author
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2024-02-202024-02-2010.17398/On discontinuity of derivations, inducing inequivalent complete metric topologies
https://revista-em.unex.es/index.php/EM/article/view/2286
<p>We give an elementary method for constructing commutative Fréchet algebras with non-unique Fréchet algebra topology. The result is applied to show that the action of any non-algebraic analytic function may fail to be uniquely defined among other useful applications. We give an affirmative answer to a question of Loy (1974) for Fréchet algebras. We also obtain the uniqueness of the Fréchet algebra topology of certain Fréchet algebras with finite dimensional radicals.</p>
Articles in pressFréchet algebra of power series in infinitely many indeterminatesderivation(in)equivalent Fréchet algebra topologiesLoy’s questionS.R. Patel
Copyright (c) 2024 Extracta Mathematicae
2024-01-152024-01-1510.17398/Continua whose hyperspace of subcontinua is infinite dimensional and a cone
https://revista-em.unex.es/index.php/EM/article/view/2605-5686.38.2.205
<p>We determine several classes of continua whose hyperspaces of subcontinua are infinite dimensional and homeomorphic to cones over (usually) other continuum. In particular, we obtain many Peano continua with such a property.</p>
General Topology and Measure Theoryconvex metricHilbert cubeHilbert cube manifoldn-fold hyperspacePeano continuumsmooth fanS. Macı́asS.B. Nadler
Copyright (c) 2023 The authors
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2023-12-012023-12-0120521910.17398/2605-5686.38.2.205Radon-Nikodýmification of arbitrary measure spaces
https://revista-em.unex.es/index.php/EM/article/view/2605-5686.38.2.139
<p style="margin-bottom: 0cm; line-height: 100%;">We study measurable spaces equipped with a σ-ideal of negligible sets. We find conditions under which they admit a localizable locally determined version – a kind of fiber space that locally describes their directions – defined by a universal property in an appropriate category that we introduce. These methods allow to promote each measure space (X, A , µ) to a strictly localizable version (X̂, Â, µ̂), so that the dual of L<sub>1</sub> (X, A , µ) is L<sub>∞</sub> (X̂, Â, µ̂). Corresponding to this duality is a generalized Radon-Nikodým theorem. We also provide a characterization of the strictly localizable version in special cases that include integral geometric measures, when the negligibles are the purely unrectifiable sets in a given dimension.</p>
General Topology and Measure TheoryMeasurable space with negligiblesRadon-Nikodým Theoremstrictly localizable measure spaceintegral geometric measurepurely unrectifiableP. BouafiaT. De Pauw
Copyright (c) 2023 The authors
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2023-12-012023-12-0113920310.17398/2605-5686.38.2.139Results on Lie ideals of prime rings with homoderivations
https://revista-em.unex.es/index.php/EM/article/view/2605-5686.38.2.125
<p>Let R be a prime ring of characteristic not 2 and U be a noncentral square closed Lie ideal of R. An additive mapping H on R is called a homoderivation if H(xy) = H(x)H(y)+H (x) y+xH(y) for all x, y ∈ R. In this paper we investigate homoderivations satisfying certain differential identities on square closed Lie ideals of prime rings.</p>
Rings and Algebrasprime ringLie idealhomoderivationcommutativityA. SarikayaÖ. Gölbaşi
Copyright (c) 2023 The authors
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2023-12-012023-12-0112513710.17398/2605-5686.38.2.125Tensorial and Hadamard product inequalities for functions of selfadjoint operators in Hilbert spaces in terms of Kantorovich ratio
https://revista-em.unex.es/index.php/EM/article/view/2605-5686.38.2.237
<p style="margin-bottom: 0cm; line-height: 100%;">Let <em>H</em> be a Hilbert space. In this paper we show among others that, if <em>f</em>, <em>g</em> are continuous on the interval <em>I</em> with</p> <p style="margin-bottom: 0cm; font-style: normal; line-height: 100%;"> </p> <p style="margin-bottom: 0cm; line-height: 100%;" align="center"><span style="font-style: normal;">0 <γ ≤ </span><em>f</em><span style="font-style: normal;">(</span><em>t</em><span style="font-style: normal;">)/</span><em>g</em><span style="font-style: normal;">(</span><em>t</em><span style="font-style: normal;">)≤ Γ </span>for t ∈ I</p> <p style="margin-bottom: 0cm; line-height: 100%;"> </p> <p style="margin-bottom: 0cm; line-height: 100%;">and if <em>A</em> and <em>B</em> are selfadjoint operators with Sp (<em>A</em>), Sp (<em>B</em>) ⊂ <em>I</em>, then</p> <p style="margin-bottom: 0cm; line-height: 100%;"> </p> <p style="margin-bottom: 0cm; line-height: 100%;"> </p> <p style="margin-bottom: 0cm; line-height: 100%;"><span style="font-size: large;">[</span>f<sup><span style="font-size: large;">1−ν</span></sup>(A) g<sup><span style="font-size: large;">ν</span></sup> (A)<span style="font-size: large;">]</span> ⊗ <span style="font-size: large;">[</span>f<sup><span style="font-size: large;">ν</span></sup>(B) g<sup><span style="font-size: large;">1−ν</span></sup> (B)<span style="font-size: large;">] </span> ≤ (1 − ν) f (A) ⊗ g (B) + ν g (A) ⊗ f (B)</p> <p style="margin-bottom: 0cm; line-height: 100%;"> ≤ <span style="font-size: large;">[</span>(γ + Γ) <sup><span style="font-size: large;">2</span></sup>/4γΓ<span style="font-size: large;">]</span><sup><span style="font-size: large;">R </span></sup><span style="font-size: large;">[</span><span style="font-size: medium;">f</span><sup><span style="font-size: large;">1−ν</span></sup><span style="font-size: medium;">(A) g</span><sup><span style="font-size: large;">ν</span></sup><span style="font-size: medium;"> (A)</span><span style="font-size: large;">]</span><span style="font-size: medium;"> ⊗ </span><span style="font-size: large;">[</span><span style="font-size: medium;">f</span><sup><span style="font-size: large;">ν</span></sup><span style="font-size: medium;">(</span><span style="font-size: medium;">B</span><span style="font-size: medium;">) g</span><sup><span style="font-size: large;">1−ν</span></sup><span style="font-size: medium;"> (</span><span style="font-size: medium;">B</span><span style="font-size: medium;">)</span><span style="font-size: large;">]. </span></p> <p style="margin-bottom: 0cm; line-height: 100%;"> </p> <p style="margin-bottom: 0cm; line-height: 100%;">The above inequalities also hold for the Hadamard product “ ◦ ” instead of tensorial product “ ⊗ ”.</p>
Operator TheoryTensorial productHadamard ProductSelfadjoint operatorsConvex functionsS.S. Dragomir
Copyright (c) 2023 The author
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2023-12-012023-12-0123725010.17398/2605-5686.38.2.237Estimates of Generalized Nevanlinna Counting Function and Applications to Composition Operators
https://revista-em.unex.es/index.php/EM/article/view/2281
<p>Let φ be a holomorphic self-map of the unit disc. We study the relationship between the generalized Nevanlinna counting function associated with φ and the norms of φn in the Dirichlet spaces. We give examples of Hilbert-Schmidt composition operators on the Dirichlet spaces.</p>
Operator TheoryGeneralized Nevanlinna counting functionDirichlet spacescomposition operatorsHilbert-Schmidt operatorsZ. BendaoudF. KorrichiL. MerghniA. Yagoub
Copyright (c) 2023 Extracta Mathematicae
2023-12-212023-12-2122123410.17398/Virtually (r; r_1, ... , r_n ; s)-nuclear multilinear operators
https://revista-em.unex.es/index.php/EM/article/view/2280
<p>In this paper, the space of virtually (r; r_1, ... , r_n; s)-nuclear multilinear operators between Banach spaces is introduced, some of its properties are described and its topological dual is characterized as a Banach space of multiple absolutely (r'; r'_1, ... , r'_n; s')-summing multilinear operators.</p>
Operator TheoryMultilinear operatorsnuclear operatorssumming operatorsDahmane AchourAmar Belacel
Copyright (c) 2023 Extracta Mathematicae
2015-12-012015-12-0123525010.17398/Powers in Alternating Simple Groups
https://revista-em.unex.es/index.php/EM/article/view/2279
<p>C. Martínez and E. Zelmanov proved in [12] that for every natural number d and every finite simple group G, there exists a function N = N(d) such that either G^d = 1 or G = {a_1^d, ... , a_N^d : ai \in G}.</p> <p>In a more general context the problem of finding words w such that the word map (g1; ...; gd) --> w(g1; ... ; gd) is surjective for any finite non abelian simple group is a major challenge in Group Theory. In [8] authors give the first example of a word map which is surjective on all finite non-abelian simple groups, the commutator [x; y] (Ore Conjecture).</p> <p>In [11] the conjecture that this is also the case for the word x2y2 is formulated. This conjecture was solved in [9] and, independently, in [6], using deep results of algebraic simple groups and representation theory. An elementary proof of this result for alternating simple groups is presented here.</p>
Group TheoryAlternating groupssimple groupspower subgroupsword mapsJ. Martínez Carracedo
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2015-12-012015-12-0125126210.17398/On Additive Preservers of Certain Classes of Algebraic Operators
https://revista-em.unex.es/index.php/EM/article/view/2278
<p>In this article we provide a complete description of all additive surjective unital maps in the algebra of all bounded linear operators acting on an in nite-dimensional Hilbert space, preserving in both directions the set of non-invertible algebraic operators or the set of invertible algebraic operators.</p>
Operator TheoryAlgebraic operatorsLinear preserver problemsKhalid Souilah
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2015-12-012015-12-0120722010.17398/Preservation Results for New Spectral Properties
https://revista-em.unex.es/index.php/EM/article/view/2277
<p>A bounded linear operator T is said to satisfy property (SBaw) if </p> <p>s_a(T) \ s_SBF (T) = E_a^0 (T)</p> <p>where s_a(T) is the approximate point spectrum of T; s_SBF (T) is the upper semi-B-Weyl spectrum of T and E_a^0(T) is the set of all eigenvalues of T of finite multiplicity that are isolated in its approximate point spectrum.</p> <p>In this paper we give a characterization of this spectral property for a bounded linear operator having SVEP on the complementary of its upper semi-B-Weyl spectrum, and we study its stability under commuting Riesz-type perturbations. Analogous results are obtained for the properties (SBb); (SBab) and (SBw). The theory is exemplified in the case of some special classes of operators.</p>
Operator Theorya-Browder's theoremupper semi-Weyl spectrumSVEPRiesz operatorHassan Zariouh
Copyright (c) 2023 Extracta Mathematicae
2015-12-012015-12-0119120510.17398/Jordan Derivations on Triangular Matrix Rings
https://revista-em.unex.es/index.php/EM/article/view/2276
<p>Guided by the research line introduced by Martindale III in [5] on the study of the additivity of maps, this article aims establish conditions on triangular matrix rings in order that an map φ satisfying</p> <p>φ(ab + ba) = φ(a)b + aφ(b) + φ(b)a + bφ(a)</p> <p>for all a, b in a triangular matrix ring becomes additive.</p>
Operator TheoryAdditivityJordan derivationtriangular matrix ringnest algebrasBruno Ferreira
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2015-12-012015-12-0118119010.17398/Banach Lattices with the Positive Dunford-Pettis Relatively Compact Property
https://revista-em.unex.es/index.php/EM/article/view/2275
<p>The paper is devoted to such Banach lattices E that every Dunford-Pettis and weakly null sequence (xn) E with disjoint terms is norm null (the positive Dunford-Pettis relatively compact property). It is established that a Banach lattice E has the positive Dunford-Pettis relatively compact property if and only if its almost Dunford-Pettis subsets are L-weakly compact. Consequently, we derive the following result: Banach lattices with the property that their almost Dunford-Pettis subsets are relatively compact, are precisely the discrete KB-spaces.</p>
Banach Spacespositive Dunford-Pettis relatively compact propertyalmost Dunford-Pettis completely continuous operatoralmost Dunford-Pettis setBanach latticeKamal El FahriNabil MachrafiMohammed Moussa
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2015-12-012015-12-0116117910.17398/Real Analytic Version of Lévy’s Theorem
https://revista-em.unex.es/index.php/EM/article/view/2274
<p>We obtain real analytic version of the classical theorem of Lévy on absolutely convergent power series. Whence, as a consequence, its harmonic version.</p>
Banach SpacesFourier seriesLévy’s theoremweight functionweihgted algebracommutative Banach algebraHermitian Banach algebraGelfand spacefunctional calculusreal analytic functionharmonic functionA. El KinaniL. Bouchikhi
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2015-12-012015-12-0115315910.17398/The fundamental theorem of affine geometry
https://revista-em.unex.es/index.php/EM/article/view/2605-5686.38.2.221
<p>We deal with a natural generalization of the classical Fundamental Theorem of Affine Geometry to the case of non bijective maps. This extension geometrically characterizes semiaffine morphisms. It was obtained by W. Zick in 1981, although it is almost unknown. Our aim is to present and discuss a simplified proof of this result.</p>
GeometryFundamental Theoremsemiaffine morphismsparallel morphismsJ.B. Sancho de Salas
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2023-12-012023-12-0122123510.17398/2605-5686.38.2.221On Jordan ideals with left derivations in 3-prime near-rings
https://revista-em.unex.es/index.php/EM/article/view/2605-5686.38.1.51
<p>We will extend in this paper some results about commutativity of Jordan ideals proved in [2] and [6]. However, we will consider left derivations instead of derivations, which is enough to get good results in relation to the structure of near-rings. We will also show that the conditions imposed in the paper cannot be removed.</p>
Algebras (associative, non associative, topological)3-prime near-ringsJordan idealsLeft derivationsA. En-guadyA. Boua
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2023-01-232023-01-23516610.17398/2605-5686.38.1.51Topologies, posets and finite quandles
https://revista-em.unex.es/index.php/EM/article/view/2605-5686.38.1.1
<p>An Alexandroff space is a topological space in which every intersection of open sets is open. There is one to one correspondence between Alexandroff T<sub>0</sub> -spaces and partially ordered sets (posets). We investigate Alexandroff T<sub>0</sub> -topologies on finite quandles. We prove that there is a non-trivial topology on a finite quandle making right multiplications continuous functions if and only if the quandle has more than one orbit. Furthermore, we show that right continuous posets on quandles with n orbits are n-partite. We also find, for the even dihedral quandles, the number of all possible topologies making the right multiplications continuous. Some explicit computations for quandles of cardinality up to five are given.</p>
TopologyquandlestopologyposetM. ElhamdadiH. LahraniT. Gona
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2023-06-012023-06-0111510.17398/2605-5686.38.1.1Construction of Hom-pre-Jordan algebras and Hom-J-dendriform algebras
https://revista-em.unex.es/index.php/EM/article/view/2605-5686.38.1.27
<p>The aim of this work is to introduce and study the notions of Hom-pre-Jordan algebra and Hom-J-dendriform algebra which generalize Hom-Jordan algebras. Hom-pre-Jordan algebras are regarded as the underlying algebraic structures of the Hom-Jordan algebras behind the Rota-Baxter operators and O-operators introduced in this paper. Hom-pre-Jordan algebras are also analogues of Hom-pre-Lie algebras for Hom-Jordan algebras. The anti-commutator of a Hom-pre-Jordan algebra is a Hom-Jordan algebra and the left multiplication operator gives a representation of a Hom-Jordan algebra. On the other hand, a Hom-J-dendriform algebra is a Hom-Jordan algebraic analogue of a Hom-dendriform algebra such that the anti-commutator of the sum of the two operations is a Hom-pre-Jordan algebra.</p>
Algebras (associative, non associative, topological)Hom-Jordan algebraHom-pre-Jordan algebraHom-J-dendriform algebraO-operatorT. ChtiouiS. MabroukA. Makhlouf
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2023-06-012023-06-01275010.17398/2605-5686.38.1.27A note on isomorphisms of quantum systems
https://revista-em.unex.es/index.php/EM/article/view/2605-5686.38.1.17
<p>We consider the question as to whether a quantum system is uniquely determined by all values of all its observables. For this, we consider linearly nuclear GB*-algebras over W*-algebras as models of quantum systems.</p>
Algebras (associative, non associative, topological)quantum systemobservablesGB*-algebraJordan homomorphismMartin Weigt
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2023-06-012023-06-01172510.17398/2605-5686.38.1.17On Lie ideals satisfying certain differential identities in prime rings
https://revista-em.unex.es/index.php/EM/article/view/2605-5686.38.1.67
<p>Let R be a prime ring of characteristic not 2, L a nonzero square closed Lie ideal of R and let F : R → R, G : R → R be generalized derivations associated with derivations d : R → R, g : R → R respectively. In this paper, we study several conditions that imply that the Lie ideal is central. Moreover, it is shown that the assumption of primeness of R can not be removed.</p>
Algebras (associative, non associative, topological)Prime ringderivationgeneralized derivationLie idealB. DharaS. GhoshG.S. Sandhu
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2023-06-012023-06-01678410.17398/2605-5686.38.1.67Estimating the number of limit cycles for one step perturbed homogeneous degenerate centers
https://revista-em.unex.es/index.php/EM/article/view/2605-5686.38.1.85
<p>We consider a homogeneous degenerate center of order 2m + 1 and perturb it by a homogeneous polynomial of order 2m. We study the Lyapunov constants around the origin to estimate the number of limit cycles. To do it, we classify the parameters and study their effect on the number of limit cycles. Finally, we find that the perturbed degenerate center without any condition has at least two limit cycles, and the number of the bifurcated limit cycles could reach 2m + 3.</p>
Limit CirclesDegenerate CenterLimit cycleLyapunov constantM. MolaeiDerakhtenjaniO. RabieiMotlaghH.M. MohammadiNejad
Copyright (c) 2023 The authors
2023-06-012023-06-018510410.17398/2605-5686.38.1.85The character variety of one relator groups
https://revista-em.unex.es/index.php/EM/article/view/2605-5686.38.1.105
<p>We consider some families of one relator groups arising as fundamental groups of 3-dimensional manifolds, and calculate their character varieties in SL(2, <strong>C</strong>). Then we give simple geometrical descriptions of such varieties, and determine the number of their irreducible components. Our paper relates to the work of Baker-Petersen, Qazaqzeh and Morales-Marcén on the character variety of certain classes of one relator groups, but we use different methods based on the concept of palindrome presentations of given groups.</p>
Group TheoryFinitely generated grouptorus linktorus bundlecharacter varietySL(2, C) representationKauffman bracket skein moduleA. CavicchioliF. Spaggiari
Copyright (c) 2023 The authors
2023-06-012023-06-0110512310.17398/2605-5686.38.1.105Smooth 2-homogeneous polynomials on the plane with a hexagonal norm
https://revista-em.unex.es/index.php/EM/article/view/2605-5686.37.2.243
<p>Motivated by the classifications of extreme and exposed 2-homogeneous polynomials on the plane with the hexagonal norm ||(x, y)|| = max{|y|, |x| + |y|/2} (see [15, 16]), we classify all smooth 2-homogeneous polynomials on R<sup>2</sup> with the hexagonal norm.</p>
Banach SpacesThe Krein-Milman theoremsmooth pointsextreme points2-homogeneous polynomials on the plane with the hexagonal normSung Guen Kim
Copyright (c) 2022 The author
2022-12-012022-12-0124325910.17398/2605-5686.37.2.243Extensions, crossed modules and pseudo quadratic Lie type superalgebras
https://revista-em.unex.es/index.php/EM/article/view/2605-5686.37.2.153
<p>Extensions and crossed modules of Lie type superalgebras are introduced and studied. We construct homology and cohomology theories of Lie-type superalgebras. The notion of left super-invariance for a bilinear form is defined and we consider Lie type superalgebras endowed with nondegenerate, supersymmetric and left super-invariant bilinear form. Such Lie type superalgebras are called pseudo quadratic Lie type superalgebras. We show that any pseudo quadratic Lie type superalgebra induces a Jacobi-Jordan superalgebra. By using the method of double extension, we study pseudo quadratic Lie type superalgebras and theirs associated Jacobi-Jordan superalgebras.</p>
Non-associative Rings and AlgebrasLie type superalgebrasJacobi-Jordan superalgebrasextensioncrossed modulehomologycohomologydouble extensionpseudo quadratic Lie type superalgebrasM. PouyeB. Kpamegan
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2022-12-012022-12-0115318410.17398/2605-5686.37.2.153Dynamics of products of nonnegative matrices
https://revista-em.unex.es/index.php/EM/article/view/2605-5686.37.2.223
<p>The aim of this manuscript is to understand the dynamics of products of nonnegative matrices. We extend a well known consequence of the Perron-Frobenius theorem on the periodic points of a nonnegative matrix to products of finitely many nonnegative matrices associated to a word and later to products of nonnegative matrices associated to a word, possibly of infinite length.</p>
Dynamical SystemsProducts of nonnegative matricescommon eigenvectorscommon periodic pointsorbits of infinite matrix productsS. JayaramanY.K. PrajapatyS. Sridharan
Copyright (c) 2022 The authors
2022-12-012022-12-0122324210.17398/2605-5686.37.2.223On a class of power associative LCC-loops
https://revista-em.unex.es/index.php/EM/article/view/2605-5686.37.2.185
<p>Let LWPC denote the identity (xy · x) · xz = x((yx · x)z), and RWPC the mirror identity. Phillips proved that a loop satisfies LWPC and RWPC if and only if it is a WIP PACC loop. Here, it is proved that a loop Q fulfils LWPC if and only if it is a left conjugacy closed (LCC) loop that fulfils the identity (xy · x)x = x(yx · x). Similarly, RWPC is equivalent to RCC and x(x · yx) = (x · xy)x. If a loop satisfies LWPC or RWPC, then it is power associative (PA). The smallest nonassociative LWPC-loop was found to be unique and of order 6 while there are exactly 6 nonassociative LWPC-loops of order 8 up to isomorphism. Methods of construction of nonassociative LWPC-loops were developed.</p>
Group Theoryleft (right) conjugacy closed looppower associativityLWPC-loopRWPC-loopO.O. GeorgeJ.O. OlaleruJ.O. Adénı́ranT.G. Jaiyéolá
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2022-12-012022-12-0118519410.17398/2605-5686.37.2.185Genus zero of projective symplectic groups
https://revista-em.unex.es/index.php/EM/article/view/2605-5686.37.2.195
<p>A transitive subgroup <em>G ≤ S<sub>N</sub></em> is called a genus zero group if there exist non identity elements <em>x<sub>1</sub> , . . . , x<sub>r</sub>∈G</em> satisfying <em>G =<x</em><sub>1</sub><em>, . . . , x<sub>r</sub>>, x</em><sub>1</sub><em>·...·x<sub>r</sub></em>=1 and <em>ind x<sub>1</sub>+...+ind x<sub>r</sub> = </em>2<em>N −</em> 2. The Hurwitz space H<sup>in</sup><sub>r</sub>(<em>G</em>) is the space of genus zero coverings of the Riemann sphere <strong>P</strong><sup>1</sup> with <em>r</em> branch points and the monodromy group <em>G</em>.<br>In this paper, we assume that <em>G</em> is a finite group with <em>PSp</em>(4, <em>q</em>) ≤ <em>G</em> ≤ <em>Aut</em>(<em>PSp</em>(4, <em>q</em>)) and <em>G</em> acts on the projective points of 3-dimensional projective geometry <em>PG</em>(3, <em>q</em>), <em>q</em> is a prime power. We show that <em>G</em> possesses no genus zero group if <em>q</em> > 5. Furthermore, we study the connectedness of the Hurwitz space H<sup>in</sup><sub>r</sub>(<em>G</em>) for a given group <em>G</em> and <em>q</em> ≤ 5.</p>
Group Theorysymplectic groupfixed pointgenus zero groupH.M Mohammed SalihRezhna M. Rezhna M. Hussein
Copyright (c) 2022 The authors
2022-12-012022-12-0119521010.17398/2605-5686.37.2.195Second derivative Lipschitz type inequalities for an integral transform of positive operators in Hilbert spaces
https://revista-em.unex.es/index.php/EM/article/view/2605-5686.37.2.261
<p style="margin-bottom: 0cm; line-height: 100%;">For a continuous and positive function w (λ), λ > 0 and µ a positive measure on (0, ∞) we consider the following integral transform</p> <p style="margin-bottom: 0cm; line-height: 100%;">D (w, µ) (T ) := <span style="font-family: Liberation Serif, serif;">∫</span><sub>0</sub><sup>∞</sup>w (λ) (λ + T ) <sup>−1</sup> dµ (λ) ,</p> <p style="margin-bottom: 0cm; line-height: 100%;">where the integral is assumed to exist for T a positive operator on a complex Hilbert space H. We show among others that, if A ≥ m 1 > 0, B ≥ m 2 > 0, then</p> <p style="margin-bottom: 0cm; line-height: 100%;">||D (w, µ) (B) − D (w, µ) (A) − D (D (w, µ)) (A) (B − A)||</p> <p style="margin-bottom: 0cm; line-height: 100%;">≤|B − A|<sup>2</sup>×[D(w,µ)(m<sub>2</sub>)−D(w,µ)(m<sub>1</sub>)−(m<sub>2</sub>- m<sub>1</sub>)D’(w,µ)(m<sub>1</sub>)]/(m<sub>2</sub>−m<sub>1</sub>)<sup>2 </sup>if m<sub>1</sub><span style="font-family: Liberation Serif, serif;">≠</span>m<sub>2</sub>,</p> <p style="margin-bottom: 0cm; line-height: 100%;">≤ D’’(w, µ)(m)/2 if m<sub>1</sub>=m<sub>2</sub>=m,</p> <p style="margin-bottom: 0cm; line-height: 100%;">where D (D (w, µ)) is the Fréchet derivative of D (w, µ) as a function of operator and D’’(w, µ) is the second derivative of D (w, µ) as a real function.</p> <p style="margin-bottom: 0cm; line-height: 100%;">We also prove the norm integral inequalities for power r ∈ (0, 1] and A, B ≥ m > 0,</p> <p style="margin-bottom: 0cm; line-height: 100%;"><span style="font-family: Liberation Serif, serif;">||</span><span style="font-family: Liberation Serif, serif;">∫</span><sub>0</sub><sup>1</sup>((1−t)A+tB)<sup>r−1</sup>dt−((A+B)/2)<sup>r−1</sup><span style="font-family: Liberation Serif, serif;">||</span> ≤ (1−r) (2−r) m<sup>r−3</sup><span style="font-family: Liberation Serif, serif;">||</span>B−A<span style="font-family: Liberation Serif, serif;">||</span><sup>2</sup>/24</p> <p style="margin-bottom: 0cm; line-height: 100%;">and</p> <p style="margin-bottom: 0cm; line-height: 100%;"><span style="font-family: Liberation Serif, serif;">||</span>((A<sup>r−1</sup>+B<sup>r−1 </sup>)/2) <span style="font-family: Liberation Serif, serif;">− </span><span style="font-family: Liberation Serif, serif;">∫</span><sub>0</sub><sup>1</sup>((1−t) A+tB)<sup>r−1</sup>dt<span style="font-family: Liberation Serif, serif;">||</span> ≤ (1−r) (2−r) m<sup>r−3</sup><span style="font-family: Liberation Serif, serif;">||</span>B − A<span style="font-family: Liberation Serif, serif;">||</span><sup>2</sup>/12.</p> <p style="margin-bottom: 0cm; line-height: 100%;"> </p>
Operator Theoryoperator monotone functionsoperator convex functionsoperator inequalitiesmidpoint inequalitytrapezoid inequalityS.S. Dragomir
Copyright (c) 2022 The author
2022-12-012022-12-0126128210.17398/2605-5686.37.2.261Topological Hausdorff dimension and Poincaré inequality
https://revista-em.unex.es/index.php/EM/article/view/2605-5686.37.2.211
<p>A relationship between Poincaré inequalities and the topological Hausdorff dimension is exposed—a lower bound on the dimension of Ahlfors regular spaces satisfying a weak (1, p)-Poincaré inequality is given.</p>
TopologyPoincaré inequalitymetric spaceCantor setstopological dimensionHausdorff dimensionbi-Lipschitz mapAhlfors regularC.A. DiMarco
Copyright (c) 2022 The author
2022-12-012022-12-0121122110.17398/2605-5686.37.2.211