Stiven Diaz Noguera - Profile on Academia.edu (original) (raw)

Papers by Stiven Diaz Noguera

The generalization of the monomiality principle for q-special polynomials has just been explained... more The generalization of the monomiality principle for q-special polynomials has just been explained and demonstrated. This extension is used to study the monomiality features of the number of q-special polynomials, such as q-Appell polynomials, q-Gould-Hopper polynomials, two variables q-Hermite, q-Laguerre and q-Legendre polynomials. Additionally, several kinds of hybrid q-special polynomials and their monomiality features are studied, such as two-variable q-Laguerre-Appell polynomials, two-variable based q-Hermite-Appell polynomials and q-Gould-Hopper-Appell polynomials. This study seeks to generate the q-Legendre-Gould-Hopper polynomials and then describe their attributes by extending the idea of monomiality for q-polynomials. Furthermore, we propose operational representations, expansion formulae and new families of these polynomials with the aid of q-operational methods and extension for monomiality principle of q-polynomials.

$Research paper thumbnail of <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi mathvariant="normal">Δ</mi><mi>h</mi></msub></mrow><annotation encoding="application/x-tex">\Delta_h</annotation></semantics></math>Δh-Appell versions of U-Bernoulli and U-Euler polynomials: properties, zero distribution patterns, and the monomiality principle.$ Deltah\Delta_hDeltah-Appell versions of U-Bernoulli and U-Euler polynomials: properties, zero distribution patterns, and the monomiality principle.

This paper explores the properties, generating functions, recurrence relations, and summation for... more This paper explores the properties, generating functions, recurrence relations, and summation formulas of a novel class of polynomials, referred to as Deltah\Delta_hDeltah-type U-Bernoulli and Deltah\Delta_hDeltah-type U-Euler polynomials. We delve into the characterization of these polynomials, including the monomiality principle, and derive the corresponding derivative and multiplicative operators. Additionally, we provide computational values in tables and visually appealing representations of the zeros of these polynomials in figures, offering a comprehensive understanding of their behavior.

In this paper, we introduce 2-variable truncated Tricomi functionsh n (x, y) and 2-parameter 2-va... more In this paper, we introduce 2-variable truncated Tricomi functionsh n (x, y) and 2-parameter 2-variable truncated Tricomi functions h (α) n,ν (x, y) employing integral forms and establish their characteristics, such as series definitions and generating functions. Also, we derive the higher-order truncated Tricomi functions and study their features.

This work presents the concept of weighted pseudo S-asymptotically (N, λ)-periodic sequences, whi... more This work presents the concept of weighted pseudo S-asymptotically (N, λ)-periodic sequences, which can be seen as a generalization of discrete weighted pseudo S-asymptotically λ-periodic and λ-antiperiodic sequences. We prove fundamental properties of such sequences such as completeness of the space, convolution and superposition theorems. These results lay the groundwork for investigating the existence and uniqueness of weighted pseudo S-asymptotically (N, λ)-periodic solutions to a specific class of abstract semilinear difference equations of convolution type, where the scalar kernels are given in terms of the Poisson transformation. Here we recall important properties of Poisson transformation and prove that it maps completely monotone functions in completely monotone sequences, maintaining the crucial feature of complete monotonicity across different domains. We present constructive examples to showcase the feasibility of the stated hypotheses, along with two numerical simulations that provide insight into the behavior of these functions as solutions to fractional-order difference equations.

Revista MATUA ISSN: 2389-7422, Jul 1, 2016

En este artículo presentamos los resultados de un estudio realizado con estudiantes de educación ... more En este artículo presentamos los resultados de un estudio realizado con estudiantes de educación secundaria para evaluar las actitudes hacia las matem áticas y el rendimiento académico. El an álisis de los resultados indica que las actitudes y el rendimiento correlacionan y se influyen mutuamente.

In this research paper, we present a class of polynomials referred to as Apostol-type Hermite-Ber... more In this research paper, we present a class of polynomials referred to as Apostol-type Hermite-Bernoulli/Euler polynomials U ν (x, y; ρ; µ), which can be given by the following generating function 2-µ + µ 2 ξ ρe ξ + (1-µ) e xξ+yξ 2 = ∞ ν=0 U ν (x, y; ρ; µ) ξ ν ν! , for some particular values of ρ and µ. Further, the summation formulae and determinant forms of these polynomials are derived. This novel family encompasses both the classical Appell-type polynomials and their noteworthy extensions. Our investigations heavily rely on generating function techniques, supported by illustrative examples to demonstrate the validity of our results. Furthermore, we introduce derivative and multiplicative operators, facilitating the definition of the Apostol-type Hermite-Bernoulli/Euler polynomials as a quasi-monomial set.

$Research paper thumbnail of The Appell sequences of fractional type$

In the article, we explore a form of generalization of Appell polynomials stemming from fractiona... more In the article, we explore a form of generalization of Appell polynomials stemming from fractional differential operators within the classical sense of Caputo and Riemann-Liuoville. To ascertain its generating function, we used the Mittag-Leffler function. Additionally, we propose a determinant form for this novel sequence family and derive general properties thereof.

Lp(Lq)-Maximal Regularity for Damped Equations in a Cylindrical Domain

We show maximal regularity estimates for the damped hyperbolic and strongly damped wave equations... more We show maximal regularity estimates for the damped hyperbolic and strongly damped wave equations with periodic initial conditions in a cylindrical domain. We prove that this property strongly depends on a critical combination on the parameters of the equation. Noteworthy, our results are still valid for fractional powers of the negative Laplacian operator. We base our methods on the theory of operator-valued Fourier multipliers on vector-valued Lebesgue spaces of periodic functions.

(N,λ)-periodic solutions to abstract difference equations of convolution type

This work primarily focuses on (N,λ)-periodic sequences and their applications. To begin, we prov... more This work primarily focuses on (N,λ)-periodic sequences and their applications. To begin, we provide a brief overview of (N,λ)-periodic sequences and introduce several results. Secondly, in terms of applications and main objective, we establish sufficient criteria for both the existence and uniqueness of (N,λ)-periodic mild solutions for abstract difference equations of convolution type. Furthermore, we present illustrative examples to highlight our key findings.

Axioms

In this paper, we introduce a class of new classes of degenerate unified polynomials and we show ... more In this paper, we introduce a class of new classes of degenerate unified polynomials and we show some algebraic and differential properties. This class includes the Appell-type classical polynomials and their most relevant generalizations. Most of the results are proved by using generating function methods and we illustrate our results with some examples.

This article presents a generalization of new classes of degenerated Apostol–Bernoulli, Apostol–... more This article presents a generalization of new classes of degenerated Apostol–Bernoulli, Apostol–Euler, and Apostol–Genocchi Hermite polynomials of level m. We establish some algebraic and differential properties for generalizations of new classes of degenerated Apostol–Bernoulli polynomials. These results are shown using generating function methods for Apostol–Euler and Apostol–Genocchi Hermite polynomials of level m.

In this paper, we investigate the existence and uniqueness of (ω,Q)-periodic mild solutions for t... more In this paper, we investigate the existence and uniqueness of (ω,Q)-periodic mild solutions for the following problem
x′(t)=Ax(t)+f(t,x(t)),t∈R,
on a Banach space X. Here, A is a closed linear operator which generates an exponentially stable C0-semigroup and the nonlinearity f satisfies suitable properties. The approaches are based on the well-known Banach contraction principle. In addition, a sufficient criterion is established for the existence and uniqueness of (ω,Q)-periodic mild solutions to the Hopfield-type neural network model.

This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY

WSEAS transactions on mathematics, Aug 5, 2022

The main objective of this work is to deduce some interesting algebraic relationships that connec... more The main objective of this work is to deduce some interesting algebraic relationships that connect the degenerated generalized Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials and other families of polynomials such as the generalized Bernoulli polynomials of level m and the Genocchi polynomials. Futher, find new recurrence formulas for these three families of polynomials to study.

$Research paper thumbnail of Existence of <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow></mrow><annotation encoding="application/x-tex"></annotation></semantics></math>(N,\lambda )$$-Periodic Solutions for Abstract Fractional Difference Equations$

Mediterranean Journal of Mathematics, 2022

We establish sufficient conditions for the existence and uniqueness of (N, λ)-periodic solutions ... more We establish sufficient conditions for the existence and uniqueness of (N, λ)-periodic solutions for the following abstract model: where 0 < α ≤ 1, A is a closed linear operator defined in a Banach space X, Δ α denotes the fractional difference operator in the Weyl-like sense, and f satisfies appropriate conditions.

$Research paper thumbnail of Subordination principle, Wright functions and large-time behavior for the discrete in time fractional diffusion equation$

Journal of Mathematical Analysis and Applications, 2022

The main goal in this paper is to study asymptotic behaviour in L p (R N) for the solutions of th... more The main goal in this paper is to study asymptotic behaviour in L p (R N) for the solutions of the fractional version of the discrete in time N-dimensional diffusion equation, which involves the Caputo fractional h-difference operator. The techniques to prove the results are based in new subordination formulas involving the discrete in time Gaussian kernel, and which are defined via an analogue in discrete time setting of the scaled Wright functions. Moreover, we get an equivalent representation of that subordination formula by Fox H-functions.

C-Semigroups, subordination principle and the Lévy α-stable distribution on discrete time

Communications in Contemporary Mathematics, 2020

In this paper, we introduce the notion of Lévy [Formula: see text]-stable distribution within the... more In this paper, we introduce the notion of Lévy [Formula: see text]-stable distribution within the discrete setting. Using this notion, a subordination principle is proved, which relates a sequence of solution operators — given by a discrete [Formula: see text]-semigroup — for the abstract Cauchy problem of first order in discrete-time, with a sequence of solution operators for the abstract Cauchy problem of fractional order [Formula: see text] in discrete-time. As an application, we establish the explicit solution of the abstract Cauchy problem in discrete-time that involves the Hilfer fractional difference operator and prove that, in some cases, such solution converges to zero. Our findings give new insights on the theory, provide original concepts and extend as well as improve recent results of relevant references on the subject.

$Research paper thumbnail of On the existence and uniqueness of ( N , λ ) <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mi>N</mi><mo separator="true">,</mo><mi>λ</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(N,\lambda )</annotation></semantics></math>(N,λ) -periodic solutions to a class of Volterra difference equations$

Advances in Difference Equations, 2019

In this paper we introduce the class of (N, λ)-periodic vector-valued sequences and show several ... more In this paper we introduce the class of (N, λ)-periodic vector-valued sequences and show several notable properties of this new class. This class includes periodic, anti-periodic, Bloch and unbounded sequences. Furthermore, we show the existence and uniqueness of (N, λ)-periodic solutions to the following class of Volterra difference equations with infinite delay: u(n + 1) = α n j=-∞ a(n-j)u(j) + f (n, u(n)), n ∈ Z, α ∈ C, where the kernel a and the nonlinear term f satisfy suitable conditions.

Numerical Methods for Partial Differential Equations, 2018

In this article, we conduct an a posteriori error analysis of the two-dimensional time-dependent ... more In this article, we conduct an a posteriori error analysis of the two-dimensional time-dependent Stokes problem with homogeneous Dirichlet boundary conditions, which can be extended to mixed boundary conditions. We present a full time-space discretization using the discontinuous Galerkin method with polynomials of any degree in time and the P 2 -P 1 Taylor-Hood finite elements in space, and propose an a posteriori residual-type error estimator. The upper bounds involve residuals, which are global in space and local in time, and an L 2 -error term evaluated on the left-end point of time step. From the error estimate, we compute local error indicators to develop an adaptive space/time mesh refinement strategy. Numerical experiments verify our theoretical results and the proposed adaptive strategy. a posteriori error estimate, adaptive algorithm, discontinuous Galerkin method, time-dependent Stokes equations 1

Un método adaptativo para elementos finitos de un problema de Stokes dependiente del tiempo