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Cofiniteness of top local cohomology modules RACSAM (IF 2.9) Pub Date : 2024-03-14
Abstract Let R be a commutative Noetherian ring with non-zero identity, \(\mathfrak {a}\) an ideal of R, M a finitely generated R-module with finite Krull dimension d, and n a non-negative integer. In this paper, we prove that the top local cohomology module \({\text {H}}^{d-n}_{\mathfrak {a}}(M)\) is an \(({\text {FD}}_{
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Ellis enveloping semigroups in real closed fields RACSAM (IF 2.9) Pub Date : 2024-03-13 Elías Baro, Daniel Palacín
We introduce the Boolean algebra of d-semialgebraic (more generally, d-definable) sets and prove that its Stone space is naturally isomorphic to the Ellis enveloping semigroup of the Stone space of the Boolean algebra of semialgebraic (definable) sets. For definably connected o-minimal groups, we prove that this family agrees with the one of externally definable sets in the one-dimensional case. Nonetheless
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A geometric Jordan decomposition theorem RACSAM (IF 2.9) Pub Date : 2024-03-11
Abstract For a compact convex set K, let A(K) denote the space of real-valued affine continuous functions, equipped with the supremum norm. For a closed subspace \(X \subset A(K)\) we give sufficient conditions, so that the weak \(^*\) closure of the set of extreme points of the dual unit ball has a decomposition in terms of ‘positive’ and ‘negative’ parts. We give several applications of these ideas
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New bounds for a generalized logarithmic mean and Heinz mean RACSAM (IF 2.9) Pub Date : 2024-03-10 Jiahua Ding, Ling Zhu
In this paper, by using the monotone form of L’Hospital’s rule and a criterion for the monotonicity of quotient of two power series we present some sharp bounds for a generalized logarithmic mean and Heinz mean by weighted means of harmonic mean, geometric mean, arithmetic mean, two power means \(M_{1/2}(a,b)\) and \(M_{2}(a,b)\). Operator versions of these inequalities are obtained except for those
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$$L^\infty $$ a-priori estimates for subcritical p-laplacian equations with a Carathéodory non-linearity RACSAM (IF 2.9) Pub Date : 2024-03-10
Abstract Let us consider a quasi-linear boundary value problem \( -\Delta _p u= f(x,u),\) in \(\Omega ,\) with Dirichlet boundary conditions, where \(\Omega \subset \mathbb {R}^N \) , with \(p0\) there exists a constant \(C_\varepsilon >0\) such that for any solution \(u\in H^1_0(\Omega )\) , the following holds $$\begin{aligned} \Big [\log \big (e+\Vert u\Vert _{\infty }\big )\Big ]^\alpha \le C_\varepsilon
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A Reilly type integral inequality for the p-Laplacian and applications to submanifolds of the unit sphere RACSAM (IF 2.9) Pub Date : 2024-03-08 Fábio R. dos Santos, Matheus N. Soares
An integral inequality for the compact (with or without boundary) submanifolds in the unit sphere with constant scalar curvature is established. Through this result, a characterization of totally geodesic spheres is obtained.
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Modes of convergence of random variables and algebraic genericity RACSAM (IF 2.9) Pub Date : 2024-02-24 G. Araújo, M. Fenoy, J. Fernández-Sánchez, J. López-Salazar, J. B. Seoane-Sepúlveda, J. M. Vecina
Important probabilistic problems require to find the limit of a sequence of random variables. However, this limit can be understood in different ways and various kinds of convergence can be defined. Among the many types of convergence of sequences of random variables, we can highlight, for example, that convergence in \(L^p\)-sense implies convergence in probability, which, in turn, implies convergence
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Some variations of the Banach-Mazur game RACSAM (IF 2.9) Pub Date : 2024-02-23
Abstract The classical Banach-Mazur game is directly related to the Baire property and the property of being a productively Baire space. In this paper, we discuss two variations of this classic game that are even more related to these properties.
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Trigonometric background multivariate smooth trigonometric singular integrals approximations RACSAM (IF 2.9) Pub Date : 2024-02-22 George A. Anastassiou
In this article we apply the uniform and \(L_{p}\), \(1\le p<\infty \) approximation properties of general smooth multivariate singular integral operators over \({\mathbb {R}}^{N}\), \(N\ge 1\). It is a trigonometric based approach with detailed applications to the corresponding smooth multivariate trigonometric singular integral operators. The results are quantitative via Jackson type inequalities
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Solution theory to semilinear stochastic equations of Schrödinger type on curved spaces I: operators with uniformly bounded coefficients RACSAM (IF 2.9) Pub Date : 2024-02-16
Abstract We study the Cauchy problem for Schrödinger type stochastic semilinear partial differential equations with uniformly bounded variable coefficients, depending on the space variables. We give conditions on the coefficients, on the drift and diffusion terms, on the Cauchy data, and on the spectral measure associated with the noise, such that the Cauchy problem admits a unique function-valued
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Sufficiency of weighted jets using Paunescu’s singular metric RACSAM (IF 2.9) Pub Date : 2024-02-05
Abstract In this work we consider the Paunescu’s singular metric in the source to investigate the bi-Lipschitz and differential sufficiency in the set of weighted jets of map germs with a fixed weighted degree. This approach was motivated by the works of Paunescu, who investigated the V-sufficiency from the weighted point of view considering this metric in the source. Here we show a criterion for the
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On the determination of p-Frobenius and related numbers using the p-Apéry set RACSAM (IF 2.9) Pub Date : 2024-02-03 Takao Komatsu
In this paper, we give convenient formulas in order to obtain explicit expressions of a generalized Frobenius number called the p-Frobenius number as well as its related values. Here, for a non-negative integer p, the p-Frobenius number is the largest integer whose number of solutions of the linear diophantine equation in terms of positive integers \(a_1,a_2,\ldots ,a_k\) with \(\gcd (a_1,a_2,\ldots
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Generating functions for polynomials derived from central moments involving bernstein basis functions and their applications RACSAM (IF 2.9) Pub Date : 2024-02-02 Ayse Yilmaz Ceylan, Yilmaz Simsek
The main objective of this article is to construct generating functions for central moments involving Bernstein basis functions. We give some alternating generating functions of these functions. We also give derivative formulas and a recurrence relation of central moments with the help of their generating functions. We also establish new relations between combinatorial numbers and polynomials, and
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Monotonicity and convexity (concavity) properties for zero-balanced hypergeometric function RACSAM (IF 2.9) Pub Date : 2024-01-31 Tie-Hong Zhao, Miao-Kun Wang
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Densifiability in hyperspaces RACSAM (IF 2.9) Pub Date : 2024-01-31 E. López-Pezoa, G. Mora, D. A. Redtwitz
The densifiability of a metric space (X, d) is the susceptibility of being filled by Peano continua. In the present paper we introduce the notion of densifiability on the hyperspace obtained from a determined collection of subsets of a metric space (X, d) endowed with a metric structure. Concretely, by using two theorems of Borsuk-Mazurkiewicz and Michael, we show that if the space (X, d) is a continuum
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Seiberg–Witten differentials on the Hitchin base RACSAM (IF 2.9) Pub Date : 2024-01-29 Ugo Bruzzo, Peter Dalakov
In this note we describe explicitly, in terms of Lie theory and cameral data, the covariant (Gauss–Manin) derivative of the Seiberg–Witten differential defined on the weight-one variation of Hodge structures that exists on a Zariski open subset of the base of the Hitchin fibration.
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Differential gradient estimates for nonlinear parabolic equations under integral Ricci curvature bounds RACSAM (IF 2.9) Pub Date : 2024-01-29 Shahroud Azami
Let \((M^{n},g)\) be a complete Riemannian manifold. We prove a space-time gradient estimates for positive solutions of nonlinear parabolic equations $$\begin{aligned} \partial _{t}u(x,t)=\Delta u(x,t)-p(x,t)A(u(x,t))-q(x,t) ( u(x,t))^{a+1}, \end{aligned}$$ on geodesic balls B(o, r) in M with \(0\frac{n}{2}\) when integral Ricci curvature k(p, 1) is small enough. By integrating the gradient estimates
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Helix surfaces for Berger-like metrics on the anti-de Sitter space RACSAM (IF 2.9) Pub Date : 2024-01-29 Giovanni Calvaruso, Irene I. Onnis, Lorenzo Pellegrino, Daria Uccheddu
We consider the Anti-de Sitter space \(\mathbb {H}^3_1\) equipped with Berger-like metrics, that deform the standard metric of \(\mathbb {H}^3_1\) in the direction of the hyperbolic Hopf vector field. Helix surfaces are the ones forming a constant angle with such vector field. After proving that these surfaces have (any) constant Gaussian curvature, we achieve their explicit local description in terms
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On polynomial representation by U-numbers RACSAM (IF 2.9) Pub Date : 2024-01-29
Abstract Let n be a positive integer and let \(P(x,y)\in \mathbb {Z}[x,y]\) be a non-constant polynomial. In this paper, we prove that every S- and T-number (under some technical conditions) can be written in the form \(P(\sigma , \tau )\) for uncountable many pairs \((\sigma , \tau )\) of \(U_n\) -numbers.
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Hall classes of groups RACSAM (IF 2.9) Pub Date : 2024-01-18
Abstract In 1958, Philip Hall (Ill J Math 2:787–801, 1958) proved that if a group G has a nilpotent normal subgroup N such that \(G/N'\) is nilpotent, then G is nilpotent. The scope of Hall’s nilpotency criterion is not restricted to group theory, and in fact similar statements hold for Lie algebras and more generally for algebraically coherent semiabelian categories (see Chao in Math Z 103:40–42,
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The isomorphism problem for basic modules and the divisibility profile of the algebra of polynomials RACSAM (IF 2.9) Pub Date : 2024-01-16 P. Aydoğdu, C. A. Arellano, S. R. López-Permouth, R. Muhammad, M. Zailaee
While mutual congeniality of bases is known to guarantee that basic modules from so-related bases are isomorphic, the question of what can be said about isomorphism of basic modules in general has remained open. We show that, for some algebras, basic modules may be non-isomorphic. We also show that it is possible, for some algebras, for all basic modules to be isomorphic, regardless of congeniality
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On structures of normal forms of complex points of small $${\mathcal {C}}^{2}$$ -perturbations of real 4-manifolds embedded in a complex 3-manifold RACSAM (IF 2.9) Pub Date : 2024-01-16 Tadej Starčič
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On zeros of the regular power series of a quaternionic variable RACSAM (IF 2.9) Pub Date : 2024-01-11 Gradimir V. Milovanović, Abdullah Mir
Using tools from the newly developed theory of regular functions and polynomials with quaternionic coefficients located on only one side of the variable, we derive zero-free regions for the related subclass of regular power series and obtain discs that are not centered at the origin, containing all the zeros of these polynomials. The results obtained for this particular subclass of regular functions
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Short $$(\textbf{SL}_2\times \textbf{SL}_2)$$ -structures on Lie algebras RACSAM (IF 2.9) Pub Date : 2024-01-06 Patricia D. Beites, Alejandra S. Córdova-Martínez, Isabel Cunha, Alberto Elduque
\(\textbf{S}\)-structures on Lie algebras, introduced by Vinberg, represent a broad generalization of the notion of gradings by abelian groups. Gradings by, not necessarily reduced, root systems provide many examples of natural \(\textbf{S}\)-structures. Here we deal with a situation not covered by these gradings: the short \((\textbf{SL}_2\times \textbf{SL}_2)\)-structures, where the reductive group
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Directed sets of topology: Tukey representation and rejection RACSAM (IF 2.9) Pub Date : 2024-01-05 Ziqin Feng, Paul Gartside
Every directed set is Tukey equivalent to (a) the family of all compact subsets, ordered by inclusion, of a (locally compact) space, to (b) a neighborhood filter, ordered by reverse inclusion, of a point (of a compact space, and of a topological group), and to (c) the universal uniformity, ordered by reverse inclusion, of a space. Two directed sets are Tukey equivalent if they are cofinally equivalent
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Existence and stability of invariant/periodic measures of lattice reversible Selkov systems driven by locally Lipschitz noise RACSAM (IF 2.9) Pub Date : 2024-01-04 Yan Wang, Chunxiao Guo, Yunshun Wu, Renhai Wang
This article is concerned with the existence and stability of invariant or periodic probability measures for a wide class of lattice reversible Selkov systems with coupled nonlinear terms of polynomial growth of arbitrary order defined on the entire integer set \(\mathbb {Z}\) driven by locally Lipschitz noise. We first formulate the stochastic lattice equations to an abstract system defined in the
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Hamiltonian systems involving exponential growth in $${\mathbb {R}}^{2}$$ with general nonlinearities RACSAM (IF 2.9) Pub Date : 2024-01-04 Uberlandio B. Severo, Manassés de Souza, Marta Menezes
In this work, we establish the existence of ground state solution for Hamiltonian systems of the form $$\begin{aligned} \left\{ \begin{aligned} -\Delta u + V(x)u = H_v(x,u,v), \quad x \in {\mathbb {R}}^2, \\ -\Delta v + V(x)v = H_u(x,u,v), \quad x \in {\mathbb {R}}^2, \end{aligned} \right. \end{aligned}$$ where \(V \in C({\mathbb {R}}^2, (0, \infty ))\) and \(H \in C^1({\mathbb {R}}^2 \times {\mathbb
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The m-weak core inverse RACSAM (IF 2.9) Pub Date : 2023-12-23 D. E. Ferreyra, Saroj B. Malik
Since the day the core inverse was known in a paper of Bakasarly and Trenkler, it has been widely researched. So far, there are four generalizations of this inverse for the case of matrices of an arbitrary index, namely, the BT inverse, the DMP inverse, the core-EP inverse and the WC inverse. In this paper we introduce a new type of generalized inverse for a matrix of an arbitrary index to be called
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Sharp sufficient conditions for mean convergence of the maximal partial sums of dependent random variables with general norming sequences RACSAM (IF 2.9) Pub Date : 2023-12-22 Lê Vǎn Thành
This paper provides sharp sufficient conditions for mean convergence of the maximal partial sums from triangular arrays of dependent random variables with general norming sequences. As an application, we use this result to give a positive answer to an open question in [Test 32(1):74–106, 2023] concerning mean convergence for the maximal partial sums under regularly varying moment conditions. The techniques
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Strongly Einstein real hypersurfaces in $${\mathbb {C}}P^2$$ and $${\mathbb {C}}H^2$$ RACSAM (IF 2.9) Pub Date : 2023-12-14 Yaning Wang, Yingdong Zhang
In this paper, we prove that a real hypersurface in \({\mathbb {C}}P^2(c)\) and \({\mathbb {C}}H^2(c)\) is strongly Einstein if and only if it is locally congruent to a geodesic sphere with radius \(d=2\ln (\sqrt{2}+1)/\sqrt{-c}\) in \({\mathbb {C}}H^2(c)\). This improves a resent paper by the present authors Wang and Zhang (Weakly Einstein real hypersurfaces in \({\mathbb {C}}P^2\) and \({\mathbb
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Some q-supercongruences from squares of basic hypergeometric series RACSAM (IF 2.9) Pub Date : 2023-12-08 Hanfei Song, Chun Wang
Inspired by the recent work of El Bachraoui and Guo-Li, we establish several q-supercongruences on the truncated forms of squares of basic hypergeometric series modulo the cube and the fourth power of a cyclotomic polynomial. Our proofs heavily rely on the creative microscoping method devised by Guo and Zudilin, a lemma due to El Bachraoui and the Chinese remainder theorem for coprime polynomials.
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Bivariate generalized Kantorovich-type exponential sampling series RACSAM (IF 2.9) Pub Date : 2023-12-08 Tuncer Acar, Abdulkadir Eke, Sadettin Kursun
In this paper, we introduce a family generalized Kantorovich-type exponential sampling operators of bivariate functions by using the bivariate Mellin-Gauss-Weierstrass operator. Approximation behaviour of the series is established at continuity points of log-uniformly continuous functions. A rate of convergence of the family of operators is presented by means of logarithmic modulus of continuity and
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Discrete approximation of complete p-elliptic integral of the second kind and its application RACSAM (IF 2.9) Pub Date : 2023-12-11 Tiehong Zhao, Miaokun Wang
By virtue of the generalized trigonometric function \(\sin _p(\theta )\) and the generalized \(\pi _p\), Legendre’s complete elliptic integrals are generalized to the complete p-elliptic integral by Takeuchi. In this article, it was shown, for \(p=3,4\), that complete p-elliptic integrals of the second kind can be obtained efficiently by the decreasing and increasing recursive sequences. As an application
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Submultiplicative norms in $$\mathcal C_{\mathbb C}(\mathcal K)$$ spaces with applications to uniform algebras RACSAM (IF 2.9) Pub Date : 2023-12-12 F. Albiac, O. Blasco, E. Briem
Certain algebra norms on the algebra of functions on a two-point set are defined and used to construct a new family of parametric algebra norms on the space \(\mathcal C_{\mathbb C}(\mathcal K)\) of continuous complex-valued functions on a compact Hausdorff space. As a by-product of our work we transfer our construction to uniform algebras to obtain a new collection of norms with special properties
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The algebraic and geometric classification of nilpotent binary and mono Leibniz algebras RACSAM (IF 2.9) Pub Date : 2023-12-06 Kobiljon Abdurasulov, Ivan Kaygorodov, Abror Khudoyberdiyev
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.
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A simple Efimov space with sequentially-nice space of probability measures RACSAM (IF 2.9) Pub Date : 2023-11-29 T. Banakh, S. Gabriyelyan
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
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Generalizations of the (F.2) supercongruence of Van Hamme RACSAM (IF 2.9) Pub Date : 2023-11-30 Chuanan Wei
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
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On some $$\Pi _{q}$$ -identities of Gosper RACSAM (IF 2.9) Pub Date : 2023-11-28 Bing He
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
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The interplay between recurrence and hypercyclicity in dissipative contexts RACSAM (IF 2.9) Pub Date : 2023-11-20 E. D’Aniello, M. Maiuriello, J. B. Seoane–Sepúlveda
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
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Remarks on the paper “A characterization of weak proximal normal structure and best proximity pairs” RACSAM (IF 2.9) Pub Date : 2023-11-14 Moosa Gabeleh
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
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On minimal Gorenstein Hilbert functions RACSAM (IF 2.9) Pub Date : 2023-11-15 Lenin Bezerra, Rodrigo Gondim, Giovanna Ilardi, Giuseppe Zappalà
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Infinite pointwise lineability: general criteria and applications RACSAM (IF 2.9) Pub Date : 2023-11-11 M. C. Calderón-Moreno, P. J. Gerlach-Mena, J. A. Prado-Bassas
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.
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On invariant operations of Fedosov structures RACSAM (IF 2.9) Pub Date : 2023-11-10 Adrián Gordillo-Merino, Raúl Martínez-Bohórquez, José Navarro-Garmendia
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.
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Nonexistence of extremals for an improved Adimurthi-Druet inequality involving $$L^p$$ -norm on a closed Riemann surface RACSAM (IF 2.9) Pub Date : 2023-11-11 Mengjie Zhang
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,
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On spaces with a $$\pi $$ -base with elements with compact closure RACSAM (IF 2.9) Pub Date : 2023-11-11 Angelo Bella, Nathan Carlson, Ivan S. Gotchev
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
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Absolutely closed semigroups RACSAM (IF 2.9) Pub Date : 2023-11-09 Taras Banakh, Serhii Bardyla
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
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A note on the hit problem for the polynomial algebra in the case of odd primes and its application RACSAM (IF 2.9) Pub Date : 2023-11-07 Đặng Võ Phúc
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
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One dimensional equisymmetric strata in moduli space with genus 1 quotient surfaces RACSAM (IF 2.9) Pub Date : 2023-11-06 S. Allen Broughton, Antonio F. Costa, Milagros Izquierdo
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
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S-injective modules RACSAM (IF 2.9) Pub Date : 2023-11-02 Jongwook Baeck
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
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New operators based on Laguerre polynomials RACSAM (IF 2.9) Pub Date : 2023-11-02 Vijay Gupta
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
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Duality and stable compactness in Orlicz-type modules RACSAM (IF 2.9) Pub Date : 2023-10-30 José Orihuela, José M. Zapata
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
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Proofs of some conjectures of Sun on representations by linear combinations of triangular numbers RACSAM (IF 2.9) Pub Date : 2023-10-29 Liping Cao, Bernard L. S. Lin
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
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Boole-Dunkl polynomials and generalizations RACSAM (IF 2.9) Pub Date : 2023-10-26 Alejandro Gil Asensi, Edgar Labarga, Judit Mínguez Ceniceros, Juan Luis Varona
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
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Jacobi–Piñeiro Markov chains RACSAM (IF 2.9) Pub Date : 2023-10-25 Amílcar Branquinho, Juan E. F. Díaz, Ana Foulquié-Moreno, Manuel Mañas, Carlos Álvarez-Fernández
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
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Brownian motion approximation by parametrized and deformed neural networks RACSAM (IF 2.9) Pub Date : 2023-10-24 George A. Anastassiou, Dimitra Kouloumpou
The first author recently derived several approximation results by neural network operators see the new monograph (Anastassiou GA, Parametrized, deformed and general neural networks, accepted. Springer, Heidelberg, 2023). There, the approximation methods derived from the parametrized and deformed neural networks induced by the \(q-\)deformed and \(\lambda -\)parametrized logistic and hyperbolic tangent
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Application of m-weak group inverse in solving optimization problems RACSAM (IF 2.9) Pub Date : 2023-10-18 Dijana Mosić, Predrag S. Stanimirović, Lev A. Kazakovtsev
Several new expressions are proved for the m-weak group inverse. An effective algorithm for computing m-weak group inverse in terms of the QR decomposition is proposed. Applying the m-weak group inverse, we present the uniquely determined solution to the restricted minimization problem in the Frobenius norm: \(\min \Vert A^{m+1}X-A^mB\Vert _F\) provided that \(\mathcal{R}(X)\subseteq \mathcal{R}(A^k)\)
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Fractional Hamiltonian type system on $$\mathbb R$$ with critical growth nonlinearity RACSAM (IF 2.9) Pub Date : 2023-10-05 G. C. Anthal, J. M. Do Ó, J. Giacomoni, K. Sreenadh
This article investigates the existence and properties of ground state solutions to the following nonlocal Hamiltonian elliptic system: $$\begin{aligned} {\left\{ \begin{array}{ll} (-\Delta )^\frac{1}{2} u +V_0 u =g(v),~x\in \mathbb R\\ (-\Delta )^\frac{1}{2} v +V_0 v =f(u),~x\in \mathbb R, \end{array}\right. } \end{aligned}$$ where \((-\Delta )^\frac{1}{2}\) is the square root Laplacian operator,
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Supercongruences involving Domb numbers and binary quadratic forms RACSAM (IF 2.9) Pub Date : 2023-10-03 Guo-Shuai Mao, Michael J. Schlosser
In this paper, we prove two recently conjectured supercongruences (modulo \(p^3\), where p is any prime greater than 3) of Zhi-Hong Sun on truncated sums involving the Domb numbers. Our proofs involve a number of ingredients such as congruences involving specialized Bernoulli polynomials, harmonic numbers, binomial coefficients, and hypergeometric summations and transformations.
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Comparison of orders generated by Ky Fan type inequalities for bivariate means RACSAM (IF 2.9) Pub Date : 2023-09-30 Monika Nowicka, Alfred Witkowski
In this paper, we deal with seven types of Ky Fan type relations between bivariate, symmetric and homogeneous means. For each relation we determine necessary and sufficient conditions for means to be in this relation. Additionally, we investigate the dependencies between these relations.