Extracta Mathematicae
type: channel
description: Welcome to the web page of Extracta Mathematicae. We have tried our best, but in case any user detects any inaccuracy or malfunction, please contact us here and we will solve it as soon as possible. Extracta Mathematicae (E.M.) publishes quality research papers that contain innovative contributions in the areas covered by the members of the Editorial Board. E.M. is also open to consider well written survey papers. 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 Creative Commons License Attribution-Non Commercial 4.0 Unported license. The online version is free and open access. E.M. uses a standard blind peer review process, following the COPE Code of Conduct. E.M. is edited and published in Badajoz (Spain) by the Instituto de Matemáticas de la Universidad de Extremadura (IMUEX), under the auspices of this university and the cooperation of the Departamento de Matemáticas and the Servicio de Publicaciones. We are uploading the previous issues here. In the meanwhile, all volumes, published uninterruptedly since 1986, are available online at: UNEx-Extracta or Dialnet E.M. has been recently evaluated and accepted for inclusion in Scopus (Scopus Sources List, Accepted titles). These are the latest volumes of E.M. in Scopus. E.M. is abstracted and indexed in Mathematical Reviews and Zentralblatt MATH. 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 2024-MCQ is 0.25 (2024-MCQ all journal median is 0.21). The printed version is exchanged with 117 journals in 36 countries all over the world. E.M. is indexed in DOAJ, the Directory of Open Access Journals, as well as in Latindex 2.0, and is a member of Free Journal Network. E.M. has obtained the Fecyt Quality seal 2021 and it was renewed in 2022, 2023 and 2024. E.M. uses Open Journal System OJS. 2024 data: From 1st January to 31th December 202…
publisher: Servicio de Publicaciones, Universidad de Extremadura
language: en
publication name: Extracta Mathematicae
issn: 0213-8743
items: Constructing g-fusion frames for operators
items: Cohomology of orthosymplectic contactomorphisms acting on λ-densities on the 1|n-supercircle
items: Some properties of (k, ψ)-Hadamard fractional integral
items: The dark side of categorical Banach space theory
items: On functional analytic approach for corona and Gleason’s problems for holomorphic Lipschitz algebras
items: Rationality conjecture for finite CW-complexes with unique spherical cohomology class and high-torsion lens spaces
items: On a cohomological characterization of free profinite products of three profinite groups with amalgamated subgroups
items: Two miniatures relating the 2 × 2 minors of a square matrix and the symmetric group
items: Tangent structures for divided power algebras
items: Binet’s formula for operator-valued recursive sequences and the operator moment problem
items: Cohomology of Tanabe algebras
items: Metrizability of the strong dual: equivalent topological characterizations
items: The polynomial cluster value problem for Banach spaces
items: Four-dimensional quasi-Einstein non-reductive homogeneous spaces are Einstein
items: Algebraic realization of chain maps in differential graded algebras over a principal ideal domain
items: Fourth Hankel and Toeplitz determinant estimates for certain analytic functions associated with Four Leaf function
items: Analytic infinite gaps
items: On lifts of linear tensor fields to Weil bundles
items: Spectrally distinguishing symmetric spaces II
items: On the coordinates of minimal vectors in a Minkowski-reduced basis
items: Isocanted cube: the lower Lebesgue volumes, incidence numbers and symmetries of this d–dimensional tile
items: The easiest polynomial differential systems in R^3 having an invariant cylinder
items: A study on W9-curvature tensor within the framework of Lorentzian para-Sasakian manifold
items: Accessible operators on ultraproducts of Banach spaces
items: Classes of homothetic convex sets
items: c-Continuous polynomials on l1
items: Some operators on finite-dimensional non-Archimedean normed spaces
items: Some applications of Q-points and Lebesgue filters to Banach spaces
items: A spectral theorem for a non-Archimedean valued field whose residue field is formally real
items: The Arens-Calderon theorem for commutative topological algebras

Constructing g-fusion frames for operators
type: item
description: Fusion frames are a very active area of research because of a myriad of applications in pure mathematics, applied mathematics, image processing and related areas. In the current paper, we mainly establish an operator theoretic approach for constructing K-g-fusion frames in Hilbert spaces from operators satisfying suitable properties.
subject: Articles in press
  topic: section
subject: K-g-fusion frame
  topic: keywords
subject: regular operator
  topic: keywords
subject: EP operator
  topic: keywords
creator: Salah Eddine Oustani
creator: Choonkil Park
rights: Copyright (c) 2026 The authors https://creativecommons.org/licenses/by-nc-sa/4.0
date: 2026-06-08
publication date: 2026-06-08
starting page: 14 pp.
ending page: 14 pp.
doi: 10.17398/

Cohomology of orthosymplectic contactomorphisms acting on λ-densities on the 1|n-supercircle
type: item
description: We study the standard contact structure on the supercircle, S 1|n , and the associated supergroups of contactomorphisms E(1|n) and OPs(n|2) corresponding to Euclidean and projective geometries. In this work, we begin by computing the cohomology group of the orthosymplectic Lie group PC(n|2), taking values in the space of tensor densities, Fnλ . Second, we determine the s(2|n)-relative cohomology spaces H1diff (osp(n|2), s(2|n); Fnλ ) with H1diff indicating that only differential cochains are considered; meaning that only cochains given by differential operators are taken into account. We also explicitly determine the 1-cocycles generating these cohomology spaces.
subject: Articles in press
  topic: section
subject: Group of contactomorphisms
  topic: keywords
subject: euclidean structures
  topic: keywords
subject: orthosymplectic superalgebra
  topic: keywords
subject: supermanifolds
  topic: keywords
creator: Okba Basdouri
rights: Copyright (c) 2026 The author https://creativecommons.org/licenses/by-nc-sa/4.0
date: 2026-05-26
publication date: 2026-05-26
starting page: 20 pp.
ending page: 20 pp.
doi: 10.17398/

Some properties of (k, ψ)-Hadamard fractional integral
type: item
description: In this paper, we study the boundedness properties of the (k, ψ)-Hadamard fractional integral in various functional spaces, including C[a, b], C1 [a, b], and the weighted Lebesgue spaces Lpω (a, b). In addition, we establish several fundamental analytical results associated with this operator, such as a Mean Value Theorem and an Integration by Parts Theorem. These findings enhance the theoretical understanding of (k, ψ)-Hadamard type operators and provide a rigorous foundation for their application in the study of differential and integral equations exhibiting nonlocal behavior and variable-scaling effects.
subject: Articles in press
  topic: section
subject: (k, ψ)–Hadamard fractional integrals
  topic: keywords
subject: weighted Lebesgue space
  topic: keywords
subject: fractional integration by parts
  topic: keywords
creator: César E. Torres Ledesma
creator: Nemat Nyamoradi
creator: Hernán A. Cuti Gutiérrez
rights: Copyright (c) 2026 The authors https://creativecommons.org/licenses/by-nc-sa/4.0
date: 2026-05-20
publication date: 2026-05-20
starting page: 29 pp.
ending page: 29 pp.
doi: 10.17398/

The dark side of categorical Banach space theory
type: item
description: This paper could be considered the third in the series The Hitchhiker Guide to Categorical Banach Space Theory [24, 25]. We explore (quasi) Banach space formulations and applications for advanced categorical topics, such as relative homology (with either respect to size or relative to an operator ideal), Buchsbaum’s satellites (and homological derivation in quasi-Banach spaces), coherent functors and sheaves, Quillen’s adjunction theorem, Auslander’s formula, the Heart of the categories of Banach and quasi-Banach spaces, the vanishing of some Ext2 functors, Martsinkovsky-Russell stabilizations, nets of Banach spaces or 3-space problems.
subject: Categorical and Homological Algebra (applied)
  topic: section
subject: Categorical ideas in Banach space theory
  topic: keywords
subject: quasi-Banach spaces
  topic: keywords
subject: homological derivation
  topic: keywords
subject: Operator ideals and relative homology
  topic: keywords
subject: functor categories and the heart of Banach spaces
  topic: keywords
subject: coherent and effaceable functors in Banach spaces
  topic: keywords
subject: extension of compact operators
  topic: keywords
subject: tensors and Tor in Banach spaces
  topic: keywords
subject: Rochberg spaces
  topic: keywords
subject: Quillen’s theorem
  topic: keywords
subject: Serre subcategories and 3-space problems
  topic: keywords
creator: Jesús Castillo
rights: Copyright (c) 2026 The author https://creativecommons.org/licenses/by-nc-sa/4.0
date: 2026-06-07
publication date: 2026-06-07
starting page: 25
ending page: 110
doi: 10.17398/2605-5686.41.1.25

On functional analytic approach for corona and Gleason’s problems for holomorphic Lipschitz algebras
type: item
description: We study Lipschitz algebras of holomorphic functions of the order k, 0 ≤ k ≤ ∞, and the exponent α, α ∈ (0, 1]. The Gel’fand theory and maximal ideal spaces of these algebras are discussed. Further, we solve the corona problem (1962) and Gleason’s problem (1964) for these algebras on certain bounded pseudoconvex/poly domains G in Cn (e.g., the ball and polydisc). As a welcome bonus, we affirmatively solve Fornæss and Øvrelid’s problem (1983) for holomorphic Hölder and Lipschitz spaces. In fact, we establish an equivalency between the two problems for these algebras. As an application, we establish the I.J. Schark’s theorem for Lipschitz algebras on these G’s. Indeed, we extend our recent work on Gleason’s problem, based on the functional analytic approach, as well as extend recent results of Clos for these algebras, and apply the usual Banach algebra method.
subject: Complex Variable
  topic: section
subject: Corona problem
  topic: keywords
subject: Gleason’s problem
  topic: keywords
subject: Gel’fand theory
  topic: keywords
subject: locally Stein algebras
  topic: keywords
subject: finitely generated maximal ideal
  topic: keywords
subject: Lipschitz algebras of holomorphic functions
  topic: keywords
subject: Gleason A-property
  topic: keywords
creator: S.R. Patel
rights: Copyright (c) 2026 The author https://creativecommons.org/licenses/by-nc-sa/4.0
date: 2026-06-07
publication date: 2026-06-07
starting page: 159
ending page: 184
doi: 10.17398/2605-5686.41.1.159

Rationality conjecture for finite CW-complexes with unique spherical cohomology class and high-torsion lens spaces
type: item
description: This paper examines the weak Rationality Conjecture for (r −1)-connected CW-complexes X admitting a unique spherical cohomology class u ∈ Hr (X, Z) for some r ≥ 2. We affirm this conjecture for such complexes of dimension kr where uk ̸= 0. We provide a non-exhaustive list of finite CW-complexes satisfying the conjecture. Furthermore, we investigate some high-torsion Lens spaces Lm2n+1, which are defined as orbit spaces S2n+1 /Zm . The generating functions of these lens spaces confirm both the Weak and Strong Rationality Conjectures under certain conditions.
subject: Algebraic Topology
  topic: section
subject: (Higher) Topological complexity
  topic: keywords
subject: Hopf invariant
  topic: keywords
subject: Zero-divisor-cup-length
  topic: keywords
subject: spherical cohomology class
  topic: keywords
creator: K. Boutahir
creator: A. El Houari
creator: Y. Rami
rights: Copyright (c) 2026 The authors https://creativecommons.org/licenses/by-nc-sa/4.0
date: 2026-06-07
publication date: 2026-06-07
starting page: 143
ending page: 157
doi: 10.17398/2605-5686.41.1.143

On a cohomological characterization of free profinite products of three profinite groups with amalgamated subgroups
type: item
description: Let C be the class of all finite solvable groups and n ≥ 2 be an integer. In this paper, we present constructions of free pro-C products of n pro-C groups with amalgamated subgroups, and of free pro-C products of n pro-C groups with commuting subgroups. We also provide conditions under which a given free pro-C product of three pro-C groups with amalgamated subgroups can be written as a free pro-C product with amalgamated subgroup of two free pro-C products with amalgamated subgroups. Furthermore, we characterize –using cohomological conditions– when a pro-C group is the free pro-C product of three of its subgroups with amalgamated subgroups. Finally, we obtain a similar characterization for free pro-C products of two pro-C groups with commuting subgroups.
subject: Group Theory
  topic: section
subject: pro-C group
  topic: keywords
subject: pro-C topology
  topic: keywords
subject: free pro-C product of pro-C groups with amalgamation
  topic: keywords
subject: free pro-C product of pro-C groups with commuting subgroups
  topic: keywords
subject: group of continuous derivations
  topic: keywords
creator: S. Douboula
creator: N. Temate
creator: G. Mantika
creator: D. Tieudjo
rights: Copyright (c) 2026 The authors https://creativecommons.org/licenses/by-nc-sa/4.0
date: 2026-06-07
publication date: 2026-06-07
starting page: 111
ending page: 132
doi: 10.17398/2605-5686.41.1.111

Two miniatures relating the 2 × 2 minors of a square matrix and the symmetric group
type: item
description: In the first miniature we recall a puzzle proposed by Martin Gardner in 1957 and refreshed by Blasco in 2014. We prove some properties of the matrices involved. We show that Gardner magical matrices are tropically singular. In the second miniature we construct a counterexample to the following conjecture by R. Flores: for a square matrix A = (aij ) of size n, if for each permutation σ there exists a 2 × 2 minor of A such that aσ(k)k aσ(l)l - aσ(k)l aσ(l)k vanishes, then determinant of A vanishes.
subject: Linear Algebra
  topic: section
subject: determinant
  topic: keywords
subject: rank
  topic: keywords
subject: minor
  topic: keywords
subject: symmetric group
  topic: keywords
subject: variant of magic square
  topic: keywords
creator: Marı́a Jesús de la Puente
rights: Copyright (c) 2026 The author https://creativecommons.org/licenses/by-nc-sa/4.0
date: 2026-06-07
publication date: 2026-06-07
starting page: 133
ending page: 141
doi: 10.17398/2605-5686.41.1.133

Tangent structures for divided power algebras
type: item
description: We build a tangent structure on the category of divided power algebras using a particular notion of semidirect product. We show that this tangent structure admits an adjoint tangent structure, which involves a version of Khäler differentials, and which is similar to the Zariski cotangent space for affine schemes. We study vector fields and differential bundles for these two structures, which correspond respectively to a notion of special derivation, and to the category of modules over the underlying commutative algebra of a given divided power algebra.
subject: Categorical and Homological Algebra (applied)
  topic: section
subject: Divided power algebras
  topic: keywords
subject: Tangent categories
  topic: keywords
subject: Khäler differentials
  topic: keywords
creator: Sacha Ikonicoff
rights: Copyright (c) 2026 The author https://creativecommons.org/licenses/by-nc-sa/4.0
date: 2026-06-07
publication date: 2026-06-07
starting page: 1
ending page: 24
doi: 10.17398/2605-5686.41.1.1

Binet’s formula for operator-valued recursive sequences and the operator moment problem
type: item
description: We derive a Binet-type formula for operator-valued sequences satisfying linear recurrence relations, extending the classical scalar case to the setting of bounded operators on Hilbert spaces. In this framework, we analyze the operator moment problem as an application, establishing new connections between recursive operator sequences and moment sequences.
subject: Functional Analysis and Operator Theory
  topic: section
subject: Binet formula
  topic: keywords
subject: recursive operator-valued sequences
  topic: keywords
subject: operator moment problem
  topic: keywords
subject: representing measures
  topic: keywords
subject: flat extension
  topic: keywords
creator: A. Ech-charyfy
creator: A. Ghanmi
creator: K. Idrissi
creator: A. Salhi
rights: Copyright (c) 2025 The authors https://creativecommons.org/licenses/by-nc-sa/4.0
date: 2025-12-17
publication date: 2025-12-17
starting page: 181
ending page: 195
doi: 10.17398/2605-5686.40.2.181

Cohomology of Tanabe algebras
type: item
description: In this paper we study the (co)homology of Tanabe algebras, which are a family of subalgebras of the partition algebras exhibiting a Schur–Weyl duality with certain complex reflection groups. The homology of the partition algebras has been shown to be related to the homology of the symmetric groups by Boyd–Hepworth–Patzt and the results they obtain depend on a parameter. In all known results, the homology of a diagram algebra is dependent on one of two things: the invertibility of a parameter in the ground ring or the parity of the positive integer indexing the number of pairs of vertices. We show that the (co)homology of Tanabe algebras is isomorphic to the (co)homology of the symmetric groups and that this is independent of both the parameter and the parity of the index. To the best of our knowledge, this is the first example of a result of this sort. Along the way we will also study the (co)homology of uniform block permutation algebras and totally propagating partition algebras as well collecting cohomological analogues of known results for the homology of partition algebras and Jones annular algebras.
subject: Homological Algebra
  topic: section
subject: diagram algebras
  topic: keywords
subject: cohomology of algebras
  topic: keywords
subject: partition algebras
  topic: keywords
subject: Tanabe algebras
  topic: keywords
creator: Andrew Fisher
creator: Daniel Graves
rights: Copyright (c) 2025 The authors https://creativecommons.org/licenses/by-nc-sa/4.0
date: 2025-12-17
publication date: 2025-12-17
starting page: 235
ending page: 252
doi: 10.17398/2605-5686.40.2.235

Metrizability of the strong dual: equivalent topological characterizations
type: item
description: This short article presents several equivalent topological characterizations for the metrizability of the strong dual of a locally convex Hausdorff space. Among our key findings, we establish that the metrizability of the strong dual is precisely equivalent to it being a q-space.
subject: Functional Analysis and Operator Theory
  topic: section
subject: Locally convex space
  topic: keywords
subject: dual space
  topic: keywords
subject: bounded sets
  topic: keywords
subject: strong topology
  topic: keywords
subject: metrizability
  topic: keywords
creator: Subiman Kundu
creator: Varun Jindal
rights: Copyright (c) 2025 Subiman Kundu, Varun Jindal https://creativecommons.org/licenses/by-nc-sa/4.0
date: 2025-12-17
publication date: 2025-12-17
starting page: 173
ending page: 179
doi: 10.17398/2605-5686.40.2.173

The polynomial cluster value problem for Banach spaces
type: item
description: We reduce the polynomial cluster value problem for the algebra of bounded analytic functions, H ∞ , on the ball of Banach spaces X to the same polynomial cluster value problem for H ∞ but on the ball of those spaces which are `1 -sums of finite dimensional spaces.
subject: Functional Analysis and Operator Theory
  topic: section
creator: Isidro H. Munive Lima
creator: Sofía Ortega Castillo
rights: Copyright (c) 2025 The authors https://creativecommons.org/licenses/by-nc-sa/4.0
date: 2025-12-17
publication date: 2025-12-17
starting page: 159
ending page: 172
doi: 10.17398/2605-5686.40.2.159

Four-dimensional quasi-Einstein non-reductive homogeneous spaces are Einstein
type: item
description: We investigate quasi-Einstein structures on four-dimensional non-reductive homogeneous spaces. We show that contrary to the Ricci solitons structures, quasi-Einstein structures display a strong rigidity in the sense that every such a structure is necessarily Einstein.
subject: Differential Geometry
  topic: section
subject: non-reductive
  topic: keywords
subject: homogeneous space
  topic: keywords
subject: quasi-Einstein
  topic: keywords
creator: Mohamed Tahar Kadaoui Abbassi
creator: Khadija Boulagouaz
rights: Copyright (c) 2025 The authors https://creativecommons.org/licenses/by-nc-sa/4.0
date: 2025-12-17
publication date: 2025-12-17
starting page: 253
ending page: 275
doi: 10.17398/2605-5686.40.2.253

Algebraic realization of chain maps in differential graded algebras over a principal ideal domain
type: item
description: Let R be a principal ideal domain, and let (T (V ), ∂) and (T (W ), δ) be two free differential graded R-algebras. Let (V, d) and (W, d0 ) denote the chain complexes of the indecomposables of (T (V ), ∂) and (T (W ), δ), respectively. Given a chain map ξ* : (V, d) → (W, d'), this paper addresses the problem of determining whether there exists a DGA-map α : (T (V ), ∂) → (T (W ), δ) such that H* (α) = H* (ξ* ).
subject: Homological Algebra
  topic: section
subject: Free chain algebras
  topic: keywords
subject: n-characteristic extensions
  topic: keywords
subject: Coherent morphisms
  topic: keywords
subject: Adams-Hilton model
  topic: keywords
creator: M. Benkhalifa
rights: Copyright (c) 2025 The author https://creativecommons.org/licenses/by-nc-sa/4.0
date: 2025-12-17
publication date: 2025-12-17
starting page: 219
ending page: 234
doi: 10.17398/2605-5686.40.2.219

Fourth Hankel and Toeplitz determinant estimates for certain analytic functions associated with Four Leaf function
type: item
description: The objective of this paper is to establish initial coefficient inequalities, Upper bounds to the Hankel and Toeplitz determinants for certain normalized univalent functions defined on the open unit disk D in the complex plane related to the analytic function ϕ4L (z) = 1 + 5z/6 + z5/6 that maps the open unit disk in the complex plane onto the interior of four leaf shaped domain in the right half of the complex plane.
subject: Complex Variable
  topic: section
subject: Hankel determinants
  topic: keywords
subject: Starlike functions
  topic: keywords
subject: Coefficient inequalities
  topic: keywords
subject: Four Leaf domain
  topic: keywords
subject: Toeplitz determinants
  topic: keywords
creator: R. Rudrani
creator: R. Bharavi Sharma
creator: S. Sambasiva Rao
rights: Copyright (c) 2025 The authors https://creativecommons.org/licenses/by-nc-sa/4.0
date: 2025-12-17
publication date: 2025-12-17
starting page: 197
ending page: 217
doi: 10.17398/2605-5686.40.2.197

Analytic infinite gaps
type: item
description: We provide infinite-dimensional versions of analytic gap dichotomies, in the sense that a sequence of analytic hereditary families {Ip }p<ω of subsets of a countable set Ω is either countably separated or there is a tree structure inside Ω in which p-chains are sets from Ip . A topological version of this is that if K is a separable Rosenthal compact space, then either K is a continuous image of a finite-to-one preimage of a metric compactum or there is a tree structure inside K in which p-chains inside every branch form a relatively discrete family of sets.
subject: General Topology
  topic: section
subject: Analytic gaps
  topic: keywords
subject: Rosenthal compacta
  topic: keywords
subject: infinite-dimensional dichotomies
  topic: keywords
creator: Antonio Avilés
creator: Stevo Todorcevic
rights: Copyright (c) 2025 The authors https://creativecommons.org/licenses/by-nc/4.0/
date: 2025-12-17
publication date: 2025-12-17
starting page: 143
ending page: 158
doi: 10.17398/2605-5686.40.2.143

On lifts of linear tensor fields to Weil bundles
type: item
description: In this paper, we generalize for an arbitrary double vector bundle, some results on linear tensor fields. Moreover we study some properties of their lifts with respect to a product preserving bundle functor.
subject: Differential Geometry
  topic: section
subject: Double vector bundle
  topic: keywords
subject: local triviality
  topic: keywords
subject: duality
  topic: keywords
subject: linear section
  topic: keywords
subject: Weil bundle functor
  topic: keywords
subject: lift
  topic: keywords
creator: Ezekiel Kilanta
creator: Achille Ntyam
rights: Copyright (c) 2025 The authors https://creativecommons.org/licenses/by-nc/4.0/
date: 2025-06-07
publication date: 2025-06-07
starting page: 57
ending page: 90
doi: 10.17398/2605-5686.40.1.57

Spectrally distinguishing symmetric spaces II
type: item
description: The action of the subgroup G2 of SO(7) (resp. Spin(7) of SO(8)) on the Grassmannian space M = SO(7)/(SO(5)×SO(2)) (resp. M = SO(8)/(SO(5)×SO(3)) ) is still transitive. We prove that the spectrum (i.e. the collection of eigenvalues of its Laplace-Beltrami operator) of a symmetric metric g0 on M coincides with the spectrum of a G2-invariant (resp. Spin(7)-invariant) metric g on M only if g0 and g are isometric. As a consequence, each non-flat compact irreducible symmetric space of non-group type is spectrally unique among the family of all currently known homogeneous metrics on its underlying differentiable manifold.
subject: Differential Geometry
  topic: section
subject: Isospectrality
  topic: keywords
subject: first eigenvalue
  topic: keywords
subject: homogeneous metric
  topic: keywords
subject: symmetric space
  topic: keywords
subject: nu-stability
  topic: keywords
creator: Emilio A. Lauret
creator: Juan S. Rodrı́guez
rights: Copyright (c) 2025 The authors https://creativecommons.org/licenses/by-nc/4.0/
date: 2025-06-07
publication date: 2025-06-07
starting page: 91
ending page: 120
doi: 10.17398/2605-5686.40.1.91

On the coordinates of minimal vectors in a Minkowski-reduced basis
type: item
description: Finding the shortest non-zero vectors in a lattice is a computationally hard problem (NP-hard in general dimensions), making results in low dimensions particularly important in lattice reduction theory. This paper focuses on the coordinates of minimal lattice vectors when expressed in a Minkowski-reduced basis. By applying Ryskov’s findings on admissible centerings and Tammela’s work characterizing Minkowski-reduced forms via a finite set of inequalities (up to dimension 6), we demonstrate sharp bounds on the absolute values of these coordinates. Specifically, we show that for dimensions n ≤ 6, the absolute values of the coordinates of any minimal vector with respect to a Minkowski-reduced basis are bounded by 1 (for n = 2, 3), 2 (for n = 4, 5), and 3 (for n = 6). This refines bounds implicitly available from Tammela’s results by combining geometric arguments from lattice theory, admissible centering theory, and reduction theory.
subject: Geometry
  topic: section
subject: Dirichlet-Voronoi cell
  topic: keywords
subject: minimum vector of a lattice
  topic: keywords
subject: Minkowski-reduction
  topic: keywords
subject: admissible centering
  topic: keywords
subject: positive quadratic forms
  topic: keywords
creator: Ákos G. Horváth
rights: Copyright (c) 2025 The author https://creativecommons.org/licenses/by-nc/4.0/
date: 2025-06-07
publication date: 2025-06-07
starting page: 27
ending page: 41
doi: 10.17398/2605-5686.40.1.27

Isocanted cube: the lower Lebesgue volumes, incidence numbers and symmetries of this d–dimensional tile
type: item
description: Let d ≥ 2. In this paper we prove that Id(ℓ, a) fills Rd face–to–face by translations. We prove that the symmetry group of Id(ℓ, a) contains the product of cyclic groups Cd × C2 as a subgroup. We compute the Lebesgue j–volume (i.e., the sum of the Lebesgue j–measures of the j–faces) of Id(ℓ, a), for 1 ≤ j < d. We compute the incidence numbers (as defined by Grünbaum) of the faces of Id(ℓ, a).
subject: Geometry
  topic: section
subject: tile space
  topic: keywords
subject: symmetry group
  topic: keywords
subject: face volume
  topic: keywords
subject: cubical zonotope
  topic: keywords
subject: isocanted cube
  topic: keywords
subject: incidence number
  topic: keywords
subject: perturbation
  topic: keywords
creator: María Jesús de la Puente
rights: Copyright (c) 2025 The author https://creativecommons.org/licenses/by-nc/4.0/
date: 2025-06-06
publication date: 2025-06-06
starting page: 1
ending page: 26
doi: 10.17398/2605-5686.40.1.1

The easiest polynomial differential systems in R^3 having an invariant cylinder
type: item
description: This paper answers the following two questions: What are the easiest polynomial differential systems in R3 having an invariant hyperbolic, parabolic or elliptic cylinder?, and for such polynomial differential systems what are their phase portraits on such invariant cylinders?
subject: Differential Equations
  topic: section
subject: Polynomial differential systems in R3
  topic: keywords
subject: hyperbolic cylinder
  topic: keywords
subject: parabolic cylinder
  topic: keywords
subject: elliptic cylinder
  topic: keywords
creator: J. Llibre
creator: L.P. Serantola
rights: Copyright (c) 2025 The authors https://creativecommons.org/licenses/by-nc/4.0/
date: 2025-06-06
publication date: 2025-06-06
starting page: 121
ending page: 141
doi: 10.17398/2605-5686.40.1.121

A study on W9-curvature tensor within the framework of Lorentzian para-Sasakian manifold
type: item
description: This article focuses on the study of Lorentzian para-Sasakian manifolds Mn . It demonstrates that a W9-semisymmetric Lorentzian para-Sasakian manifold is a W9-flat manifold. Additionally, we explore Lorentzian para-Sasakian manifolds that satisfy the ζ-W9-flat condition, revealing that they represent a special type of η-Einstein manifold. Furthermore, it is shown that a W9-flat Lorentzian para-Sasakian manifold is a flat manifold. We also investigate Lorentzian para-Sasakian manifolds that meet W9-recurrent and ϕ-W9-semisymmetric conditions, presenting several significant results from this analysis. At last, we explore η-Ricci Solitons on Lorentzian para-Sasakian manifold satisfying W9(ζ, F1 ) · S = 0.
subject: Differential Geometry
  topic: section
subject: W9 -curvature tensor
  topic: keywords
subject: Lorentzian para-Sasakian manifolds
  topic: keywords
subject: η-Einstein manifolds
  topic: keywords
subject: η-Ricci solitons
  topic: keywords
creator: G.P. Singh
creator: S.S. Mishra
creator: P. Sharma
rights: Copyright (c) 2025 The authors https://creativecommons.org/licenses/by-nc/4.0/
date: 2025-06-06
publication date: 2025-06-06
starting page: 43
ending page: 56
doi: 10.17398/2605-5686.40.1.43

Accessible operators on ultraproducts of Banach spaces
type: item
description: We address a question by Henry Towsner about the possibility of representing linear operators between ultraproducts of Banach spaces by means of ultraproducts of nonlinear maps. We provide a bridge between these “accessible” operators and the theory of twisted sums through the so-called quasilinear maps. Thus, for many pairs of Banach spaces X and Y , there is an “accessible” operator XU → YU that is not the ultraproduct of a family of operators X → Y if and only if there is a short exact sequence of quasi-Banach spaces and operators 0 → Y → Z → X → 0 that does not split. We then adapt classical work by Ribe and Kalton–Peck to exhibit pretty concrete examples of accessible functionals and endomorphisms for the sequence spaces lp The paper is organized so that the main ideas are accessible to readers working on ultraproducts and requires only a rustic knowledge of Banach space theory.
subject: Banach Space Theory
  topic: section
subject: Ultraproduct
  topic: keywords
subject: quasi-Banach space
  topic: keywords
subject: operator
  topic: keywords
subject: exact sequence
  topic: keywords
subject: quasilinear map
  topic: keywords
subject: K-space
  topic: keywords
creator: Félix Cabello Sánchez
rights: Copyright (c) 2025 The author https://creativecommons.org/licenses/by-nc/4.0/
date: 2025-01-03
publication date: 2025-01-03
starting page: 207
ending page: 234
doi: 10.17398/2605-5686.39.2.207

Classes of homothetic convex sets
type: item
description: This is a survey of known results and still open problems on characteristic properties of classes of homothetic convex sets in the n-dimensional Euclidean space. These properties are formulated in terms of orthogonal projections, plane sections, homothety classes, Choquet simplices, and homothetic tilings and partitions.
subject: Convex Geometry
  topic: section
subject: convex
  topic: keywords
subject: homothetic
  topic: keywords
subject: symmetric
  topic: keywords
subject: section
  topic: keywords
subject: projection
  topic: keywords
subject: partition
  topic: keywords
subject: tiling
  topic: keywords
creator: Valeriu Soltan
rights: Copyright (c) 2024 The author https://creativecommons.org/licenses/by-nc/4.0/
date: 2025-01-03
publication date: 2025-01-03
starting page: 135
ending page: 171
doi: 10.17398/2605-5686.39.2.135

c-Continuous polynomials on l1
type: item
description: In this article we study the n-homogeneous polynomials P that are c-continuous on bounded subsets of l1 . We show that P can be decomposed in the form R + Q, where Q and R are n-homogeneous polynomials, with R weakly star continuous and Q (x) = 0 for all x ∈ ker u for u = (1, 1, . . . , 1, . . . ). We conclude that P = Σ un−j ⊗ Rj , where R is a weakly star continuous j-homogeneous polynomial for j = 0, 1, . . . , n.
subject: Banach Space Theory
  topic: section
subject: Polynomials
  topic: keywords
subject: Banach
  topic: keywords
subject: holomorphic
  topic: keywords
subject: weak
  topic: keywords
creator: Humberto D. Carrión
rights: Copyright (c) 2024 The author https://creativecommons.org/licenses/by-nc/4.0/
date: 2025-01-03
publication date: 2025-01-03
starting page: 189
ending page: 206
doi: 10.17398/2605-5686.39.2.189

Some operators on finite-dimensional non-Archimedean normed spaces
type: item
description: In this paper, we are interested in the study of certain operators in non-Archimedean normed spaces of finite dimension. We introduce the notion of p-delta function, then we characterize the simple operators, the similarities and the expansions. We show if E has an orthogonal basis, then each injective operator on E is the composition of an isometry and an expansion.
subject: Non-Archimedean Functional Analysis
  topic: section
subject: Non-Archimedean normed space
  topic: keywords
subject: t-Orthogonal basis
  topic: keywords
subject: p-delta function
  topic: keywords
subject: Simple operator
  topic: keywords
subject: Similarity
  topic: keywords
subject: Isometry
  topic: keywords
subject: Expansion
  topic: keywords
creator: M Babahmed
rights: Copyright (c) 2024 The author https://creativecommons.org/licenses/by-nc/4.0/
date: 2025-01-03
publication date: 2025-01-03
starting page: 255
ending page: 271
doi: 10.17398/2605-5686.39.2.255

Some applications of Q-points and Lebesgue filters to Banach spaces
type: item
description: We present a new characterization of Q-point ultrafilters and use it to optimize the result of Avilés, Martı́nez-Cervantes, and Rueda Zoca linking the existence of L-orthogonal sequences and L-orthogonal elements in Banach spaces via ultrafilter limits.
subject: Banach Space Theory
  topic: section
subject: Q-point
  topic: keywords
subject: Katětov order
  topic: keywords
subject: L-sequence
  topic: keywords
subject: L-element
  topic: keywords
creator: M. Hrušák
creator: L. Sáenz
rights: Copyright (c) 2024 The authors https://creativecommons.org/licenses/by-nc/4.0/
date: 2025-01-03
publication date: 2025-01-03
starting page: 173
ending page: 187
doi: 10.17398/2605-5686.39.2.173

A spectral theorem for a non-Archimedean valued field whose residue field is formally real
type: item
description: In this paper, we will prove a spectral theorem for self-adjoint compactoid operators. Also, we will study the condition on which the coefficient field must be imposed. In order to get the theorems, we will use the Fredholm theory for compactoid operators. Moreover, the property of maximal complete field is important for our study. These facts will allow us to find that the spectral theorem depends only on the residue class field, and is independent of the valuation group of the coefficient field. As a result, we can settle the problem of the spectral theorem in the case where the residue class field is formally real.
subject: Non-Archimedean Functional Analysis
  topic: section
subject: self-adjoint operators
  topic: keywords
subject: spectral theorem
  topic: keywords
creator: K. Ishizuka
rights: Copyright (c) 2024 The author https://creativecommons.org/licenses/by-nc/4.0/
date: 2025-01-03
publication date: 2025-01-03
starting page: 235
ending page: 254
doi: 10.17398/2605-5686.39.2.235

The Arens-Calderon theorem for commutative topological algebras
type: item
description: A theorem of Arens and Calderon states that if A is a commutative Banach algebra with Jacobson radical Rad(A), and if a0 , . . . , an∈ A with a0 ∈ Rad(A) and a1 an invertible element of k A, then there exists y ∈ Rad(A) such that Σ ak yk = 0. In this paper, we give extensions of this result to commutative non-normed topological algebras, as this is vital for extending an embedding theorem of Allan in [2] regarding the embedding of the formal power series algebra CX into a commutative Banach algebra.
subject: Functional Analysis and Operator Theory
  topic: section
subject: Formal power series
  topic: keywords
subject: theorem of Arens and Calderon
  topic: keywords
subject: commutative topological algebra
  topic: keywords
subject: functional calculus
  topic: keywords
creator: M. Weigt
creator: I. Zarakas
rights: Copyright (c) 2024 The authors https://creativecommons.org/licenses/by-nc/4.0/
date: 2024-05-31
publication date: 2024-05-31
starting page: 19
ending page: 35
doi: 10.17398/2605-5686.39.1.19