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Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas
Journal Prestige (SJR): 0.493

Citation Impact (citeScore): 1
Number of Followers: 0

Partially Free Journal
ISSN (Print) 1578-7303 - ISSN (Online) 1579-1505
Published by Springer-Verlag

[2468 journals]

The algebraic and geometric classification of nilpotent binary and mono
Leibniz algebras
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  Abstract: Abstract This paper is devoted to the complete algebraic and geometric classification of complex 5-dimensional nilpotent binary Leibniz and 4-dimensional nilpotent mono Leibniz algebras. As a corollary, we have the complete algebraic and geometric classification of complex 4-dimensional nilpotent algebras of nil-index 3.
  PubDate: 2023-12-06
Generalizations of the (F.2) supercongruence of Van Hamme
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  Abstract: Abstract In 2015, Swisher (Res Math Sci 2:18, 2015) verified Van Hamme’s (F.2) supercongruence conjecture, where $p\equiv 1 \pmod {4}$ is a prime. She also gave a similar formula, where $p\equiv 3 \pmod {4}$ is any prime, in the same paper. With the help of the creative microscoping method introduced by Guo and Zudilin, we obtain one-parameter generalizations of Van Hamme’s (F.2) supercongruence and Swisher’s result.
  PubDate: 2023-11-30
A simple Efimov space with sequentially-nice space of probability measures
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  Abstract: Abstract Under Jensen’s diamond principle $\diamondsuit $ , we construct a simple Efimov space K whose space of nonatomic probability measures $P_{na}(K)$ is first-countable and sequentially compact. These two properties of $P_{na}(K)$ imply that the space of probability measures P(K) on K is selectively sequentially pseudocompact. We show that any sequence of probability measures on K that converges to a purely atomic measure converges in norm, and any sequence of probability measures on K converging to zero in sup-norm has a subsequence converging to a nonatomic probability measure. We show also that the Banach space C(K) of continuous functions on K has the Gelfand–Phillips property but it does not have the Grothendieck property.
  PubDate: 2023-11-29
On some $$\Pi _{q}$$ -identities of Gosper
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  Abstract: Abstract In 2001 W. Gosper introduced a constant $\Pi _{q}$ and conjectured without proofs many intriguing identities on this constant. In this paper we establish some modular equations of degrees 3 and 5. From these modular equations we confirm two groups of $\Pi _{q}$ -identities in Gosper’s list. One group involves $\Pi _{q},\Pi _{q^{2}},\Pi _{q^{3}}$ or $\Pi _{q^{6}}$ while the other is related to $\Pi _{q},\Pi _{q^{2}},\Pi _{q^{5}}$ or $\Pi _{q^{10}}$ .
  PubDate: 2023-11-28
The interplay between recurrence and hypercyclicity in dissipative
contexts
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  Abstract: Abstract Motivated by recent investigations [9, 10] on the notion of recurrence in linear dynamics, we deepen into the notions of recurrence and frequent recurrence in the setting of dissipative composition operators with bounded distortion, a class of linear operators which includes backward shifts. Among other results, we show that these two notions are, actually, equivalent to those of hypercyclicity and frequent hypercyclicity, respectively. More particularly, we improve [9, Theorem 5.2] and, also, provide a partial answer to an open question posed in [9, Question 5.3].
  PubDate: 2023-11-20
On minimal Gorenstein Hilbert functions
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  Abstract: Abstract We conjecture that a class of Artinian Gorenstein Hilbert algebras called full Perazzo algebras always have minimal Hilbert function, fixing codimension and length. We prove the conjecture in length four and five, in low codimension. We also prove the conjecture for a particular subclass of algebras that occurs in every length and certain codimensions. As a consequence of our methods we give a new proof of part of a known result about the asymptotic behavior of the minimum entry of a Gorenstein Hilbert function.
  PubDate: 2023-11-15
Remarks on the paper “A characterization of weak proximal normal
structure and best proximity pairs”
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  Abstract: In this work we present an improved version of the recently introduced concept (Digar et al. in Rev Real Acad Cienc Exactas Fis Nat Ser A Mat 116:80, 2012) of pointwise cyclic contraction with respect to orbits. After this new concept, we prove new best proximity pair theorems. We also revisit the contents of the already referenced paper in this abstract. Examples are given to support the usability and improvements of our results.
  PubDate: 2023-11-14
Nonexistence of extremals for an improved Adimurthi-Druet inequality
involving $$L^p$$ -norm on a closed Riemann surface
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  Abstract: Abstract It is well known that the Adimurthi-Druet inequality admits extremal function, when the perturbation parameter is sufficiently small. As for the question of when extremal function does not exist, Mancini-Thizy first solved this problem by the method of energy estimate in (J. Differential Equations). After that Yang extended the work to a closed Riemann surface in (Sci. China Math.). In this paper, we generalize Yang’s result to a version involving $L^{p}$ -norms for any $p>1$ . Moreover, this work complements our result in (Acta Math. Sin.) and extends Wang’s result (Commun. Pure Appl. Anal.) in Euclidean space.
  PubDate: 2023-11-11
Infinite pointwise lineability: general criteria and applications
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  Abstract: Abstract In this paper we introduce the concept of infinite pointwise dense lineability (spaceability), and provide a criterion to obtain density from mere lineability. As an application, we study the linear and topological structures within the set of infinite differentiable and integrable functions, for any order $p \ge 1$ , on $\mathbb R^N$ which are unbounded in a pre-fixed set.
  PubDate: 2023-11-11
On spaces with a $$\pi $$ -base with elements with compact closure
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  Abstract: Abstract In this paper we show that if X is a $T_1$ -space with a $\pi $ -base whose elements have compact closure, then $d(X)\le c(X)\cdot 2^{\psi (X)}$ and therefore, for such spaces we have $d(X)^{\psi (X)} = c(X)^{\psi (X)}$ . This result allows us to restate several known upper bounds of the cardinality of a Hausdorff space X by replacing in them d(X) with c(X). In addition, we show that for such spaces X Šapirovskiĭ’s inequality $d(X)\le \pi \chi (X)^{c(X)}$ , which is known to be true for regular Hausdorff spaces, is also valid. In the case when the space X is in addition sequential or radial, we show that $ X \le 2^{c(X)}$ . This result extends two theorems of Arhangel $'$ skiĭ to the class of Hausdorff spaces with a $\pi $ -base whose elements have compact closures. We also show that spaces with a $\pi $ -base with elements with compact closures are $\alpha $ -favorable in the Banach–Mazur game, which implies such spaces are Baire. It was shown in Bella et al. (Quaest Math 46(4):745–760, 2023) that if a Hausdorff space X has a $\pi $ -base consisting of elements with compact closure, then $ X \le 2^{wL(X)t(X)\psi _c(X)}$ . We give a variation of this result by showing $ X \le \pi \chi (X)^{wL(X)\textrm{ot}(X)\psi _c(X)}$ for such a space X. Note that since $wL(X)\textrm{ot}(X)\le c(X)$ , this result is at least as good as that given by Sun (Proc Am Math Soc 104:313–316, 1988). We also give a possible improvement of the bound in Bella et al. (2023) by showing that $ X \le 2^{wL(X)wt(X)\psi _c(X)}$ for a Hausdorff space X with a $\pi $ -base consisting of elements with compact closure. This uses the weak tightness wt(X) defined in Carlson (Topol Appl 249:103–111, 2018), which has the property $\textrm{ot}(X)\le wt(X)\le t(X)$ . We also show that if X is a Hausdorff homogeneous space with a $\pi $ -base consisting of elements with compact closure (such spaces are locally compact), then $ X \le wL(X)^{wt(X)\pi \chi (X)}$ . This generalizes the result in Bella and Carlson (Monatsh Math 192(1):39–48, 2020) that if X is a homogeneous compactum, then $ X \le 2^{wt(X)\pi \chi (X)}$ .
  PubDate: 2023-11-11
On invariant operations of Fedosov structures
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  Abstract: Abstract This paper describes the spaces of natural tensors associated to Fedosov structures by an identification with some linear representations of the symplectic Lie group $\textrm{Sp}(2n, \mathbb {R})$ . This is accomplished with no restrictions on the order of the natural tensors involved and through use of the language of sheaves and ringed spaces.
  PubDate: 2023-11-10
Absolutely closed semigroups
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  Abstract: Abstract Let ${\mathcal {C}}$ be a class of topological semigroups. A semigroup X is called absolutely ${\mathcal {C}}$ -closed if for any homomorphism $h:X\rightarrow Y$ to a topological semigroup $Y\in {\mathcal {C}}$ , the image h[X] is closed in Y. Let $\textsf {T}_{\!\textsf {1}}\textsf {S}$ , $\textsf {T}_{\!\textsf {2}}\textsf {S}$ , and $\textsf {T}_{\!\textsf {z}}\textsf {S}$ be the classes of $T_1$ , Hausdorff, and Tychonoff zero-dimensional topological semigroups, respectively. We prove that a commutative semigroup X is absolutely $\textsf {T}_{\!\textsf {z}}\textsf {S}$ -closed if and only if X is absolutely $\textsf {T}_{\!\textsf {2}}\textsf {S}$ -closed if and only if X is chain-finite, bounded, group-finite and Clifford + finite. On the other hand, a commutative semigroup X is absolutely $\textsf {T}_{\!\textsf {1}}\textsf {S}$ -closed if and only if X is finite. Also, for a given absolutely ${\mathcal {C}}$ -closed semigroup X we detect absolutely ${\mathcal {C}}$ -closed subsemigroups in the center of X.
  PubDate: 2023-11-09
A note on the hit problem for the polynomial algebra in the case of odd
primes and its application
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  Abstract: Abstract Denote by $\mathbb {F}_p[t_1,t_2,\ldots ,t_h]$ the polynomial algebra on h variables over the field of p elements, $\mathbb F_p$ (p being a prime), and by $GL(h, \mathbb F_p)$ the general linear group of rank h on $\mathbb F_p.$ We are interested in the hit problem, set up by Franklin Peterson, of finding a minimal system of generators for $\mathbb {F}_p[t_1,t_2,\ldots ,t_h]$ as a module over the mod p Steenrod algebra, $\mathscr {A}_p.$ Equivalently, we need to determine a monomial basis for the $\mathbb Z$ -graded space $\mathbb F_p\otimes _{\mathscr {A}_p}\mathbb {F}_p[t_1,t_2,\ldots ,t_h].$ Let V be an elementary abelian p-group of rank h on $\mathbb F_p.$ As well known, the $\mathbb F_p$ -cohomology $H^{*}(V; \mathbb F_p)$ is isomorphic to the tensor product $\Lambda (V^{\sharp })\otimes _{\mathbb F_p}\mathbb {F}_p[t_1,t_2,\ldots ,t_h],$ where $V^{\sharp }$ denotes the dual of V and $\Lambda (V^{\sharp })$ is the exterior algebra on h generators of degree 1. As information about $H^{*}(V; \mathbb F_p)$ can usuallly be obtained from similar information about $\mathbb {F}_p[t_1,t_2,\ldots ,t_h],$ we have the hit problem for $H^{*}(V; \mathbb F_p)$ as a module on $\mathscr {A}_p.$ This problem has been utilized to investigate the Singer algebraic transfer, defined as a homomorphism from the $GL(h, \mathbb F_p)$ -coinvariants of $H^{*}(V; \mathbb F_p)$ to the $\mathbb F_p$ -cohomology of the Steenrod algebra $\textrm{Ext}_{\mathscr {A}_p}^{h,h+*}(\mathbb F_p, \mathbb F_p).$ This homomorphism constitutes a valuable instrument for analyzing the intricate structure of complex Ext groups. The aim of this short Note is to study $\mathscr {A}_p$ -generators for $\mathbb {F}_p[t_1,t_2,\ldots ,t_h]$ with p odd. As an application, we investigate the behavior of the third algebraic transfer for the cases of odd primes p in some general degrees. The outcome shows that this algebraic transfer is an isomorphism in the cases under consideration.
  PubDate: 2023-11-07
One dimensional equisymmetric strata in moduli space with genus 1 quotient
surfaces
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  Abstract: Abstract The complex orbifold structure of the moduli space of Riemann surfaces of genus g ( $g\ge 2$ ) produces a stratification into complex subvarieties named equisymmetric strata. Each equisymmetric stratum is formed by the surfaces where the group of automorphisms acts in a topologically equivalent way. The Riemann surfaces in the equisymmetric strata of dimension one are of two structurally different types. Type 1 equisymmetric strata correspond to Riemann surfaces where the group of automorphisms produces a quotient surface of genus zero, while those of Type 2 appear when such a quotient is a surface of genus one. Type 1 equisymmetric strata have been extensively studied by the authors of the present work in a previous recent paper, we now focus on Type 2 strata. We first establish the existence of such strata and their frequency of occurrence in moduli spaces. As a main result we obtain a complete description of Type 2 strata as coverings of the sphere branched over three points (Belyi curves) and where certain isolated points (punctures) have to be eliminated. Finally, we study in detail the doubly infinite family of Type 2 strata whose automorphism groups have order the product of two primes.
  PubDate: 2023-11-06
S-injective modules
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  Abstract: Abstract Let S be a multiplicative subset of a ring R with unity. A unitary right R-module M is referred to as S-injective if there exist an element $s \in S$ and an injective R-submodule Q of M such that $Ms \subseteq Q \subseteq M$ . In this paper, we study the structure of S-injective modules which extend the notion of injective modules. Some characterizations and various examples of S-injective modules are provided, and the S-variants of Baer’s criterion, the Bass-Papp theorem, and the Eakin-Nagata-Eisenbud theorem are proven.
  PubDate: 2023-11-02
New operators based on Laguerre polynomials
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  Abstract: Abstract A discrete operators based on the modified Laguerre polynomials is studied here. As per our knowledge approximation of these operators have not been studied earlier. We find the moments by using the moment generating function and give some direct convergence results for such operators. It is observed here that composition of these operators with some integral operators provide us a discrete operator. We introduce here four new operators obtained from composition of operators, which can be a new source of study for further research.
  PubDate: 2023-11-02
Duality and stable compactness in Orlicz-type modules
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  Abstract: Abstract Orlicz-type modules are module analogues of classical Orlicz spaces. We study duality and stable compactness in Orlicz-type modules. We characterize the conditional Köthe dual of an Orlicz-type module as the space of all $\sigma $ -order continuous module homomorphisms. We find an order continuity criterion for stable compactness in Orlicz-type modules. As an application, we obtain a robust representation result for conditional risk measures on Orlicz spaces.
  PubDate: 2023-10-30
Proofs of some conjectures of Sun on representations by linear
combinations of triangular numbers
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  Abstract: Abstract For positive integers a, b, c and d, let N(a, b, c, d; n) be the number of representations of n as $ax^2+by^2+cz^2+dw^2$ and T(a, b, c, d; n) be the number of representations of n as $a\frac{X(X+1)}{2}+b\frac{Y(Y+1)}{2}+c\frac{Z(Z+1)}{2}+d\frac{W(W+1)}{2}$ , where x, y, z, w are integers, and n, X, Y, Z, W are nonnegative integers. Recently, Sun (J. Ramanujan Math. Soc., 35 (2020), 373–389) established a number of relations between T(a, b, c, d; n) and N(a, b, c, d; n), and posed some conjectures on such relations. In this paper, we confirm several Sun’s conjectures by employing Ramanujan’s theta function identities.
  PubDate: 2023-10-29
Boole-Dunkl polynomials and generalizations
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  Abstract: Abstract Appell sequences of polynomials can be extended to the Dunkl context replacing the ordinary derivative by the Dunkl operator on the real line, and the exponential function by the Dunkl kernel. In a similar way, discrete Appell sequences can be extended to the Dunkl context; here, the role of the ordinary translation is played by the Dunkl translation, which is a much more intricate operator. Some sequences as the falling factorials or the Bernoulli polynomials of the second kind have already been extended and investigated in the mathematical literature. In this paper, we study the discrete Appell version of the Euler polynomials, usually known as Euler polynomials of the second kind or Boole polynomials. We show how to define the Dunkl extension of these polynomials (and some of their generalizations), and prove some relevant properties and relations with other polynomials and with Stirling-Dunkl numbers.
  PubDate: 2023-10-26
Jacobi–Piñeiro Markov chains
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  Abstract: Abstract Given a non-negative recursion matrix describing higher order recurrence relations for multiple orthogonal polynomials of type II and corresponding linear forms of type I, a general strategy for constructing a pair of stochastic matrices, dual to each other, is provided. The Karlin–McGregor representation formula is extended to both dual Markov chains and applied to the discussion of the corresponding generating functions and first-passage distributions. Recurrent or transient character of the Markov chain is discussed. The Jacobi–Piñeiro multiple orthogonal polynomials are taken as a case study of the described results. The region of parameters where the recursion matrix is non-negative is given. Moreover, two stochastic matrices, describing two dual Markov chains are given in terms of the recursion matrix and the values of the multiple orthogonal polynomials of type II and corresponding linear forms of type I at the point $x=1.$ The region of parameters where the Markov chains are recurrent or transient is given, and the connection between both dual Markov chains is discussed at the light of the Poincaré’s theorem.
  PubDate: 2023-10-25