Scientia Series A: Mathematical Sciences
type: channel
description: SCIENTIA. Series A: Mathematical Science is an open access official journal of theUniversidad Técnica Federico Santa María, one of the leader Chilean institutions in science and education. It publishes original research papers in any branch of pure and applied mathematics. An international journal, its policy is to feature a wide variety of research areas, which in recent issues have included Complex Geometry, Complex and Real Analysis, Differential Equations, Dynamical Systems.
publisher: Departamento de Matemáticas. Universidad Técnica Federico Santa María
language: en
publication name: Scientia Series A: Mathematical Sciences
issn: 0716-8446
copyright: Copyright © {$copyrightYear} by the author(s). Published by Universidad Técnica Federico Santa María. This work is licensed under a Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
items: Generalization of the Laplace Transform of Powers of the sinc function
items: A note on the Hurwitz-Lerch zeta function
items: Derivation of some definite integrals
items: Symmetric tensor powers of graphs
items: A four parameter integral identity and a few consequences
items: On some improper integrals containing products between the tails of Maclaurin series for the sine and cosine functions
items: Gain of regularity for a nonlinear dispersive equation
items: Abel summability and angular convergence
items: Long-pin perturbations of the trivial solution for Hele-Shawcorner flows
items: Fourth coefficient estimate in the class of univalent functions with quasiconformal extensions
items: Some open problems related to 16b Hilbert problem.
items: On I-almost continuity and new descomposition of continuity
items: Uniqueness Theorem for Hilbert Transform for Boehmians
items: Some remarks, generalizations and misprints in the integrals in Gradshteyn and Ryzhik
items: DIG-Semigroups
items: Some Inequalities for Power Series with nonnegative coefficients via a divided difference reverse of Jensen inequality
items: A table of definite integrals from the marriage of power and Fourier series
items: One modulo \(N\) gracefulness of H-class of graphs
items: The integrals in Gradshteyn and Ryzhik Part 28: The confluent hypergeometric function and Whittaker functions
items: The integrals in Gradshteyn and Ryzhik Part 27: More logarithmic examples
items: The integrals in Gradshteyn and Ryzhik Part 26: The exponential integral
items: On \(\aleph_0\)-\(sn\)-networks
items: Some integrals related to the Basel problem
items: On two families of stochastic predation models with Allee effect
items: On \(g\)-scattered spaces
items: Evaluation of entries in Gradshteyn and Ryzhik employing the method of brackets
items: Certain Inequalities Related to the Chebyshev’s Functional Involving Erdélyi-Kober Operators
items: Coexistence of limit cycles and invariant curves for Extended Kukles systems
items: Poisson’s formula with principal value integrals and some special Gradshteyn and Ryzhik integrals
items: Companions of Hermite-Hadamard Inequality for Convex Functions (I)

Generalization of the Laplace Transform of Powers of the sinc function
type: item
description: In this work, general expressions are found for the Laplace transform of \[L\left(\frac{\sin^m(at)}{t^n}\right) \quad \text{or} \quad L\left(\frac{\sin^n(t)\,\sin^m(at)}{t^p}\right).\] The results are expressed in terms of usual functions such as logarithms, arctangent, and rational functions. Thus, these expressions can be incorporated into the general literature to facilitate the calculation of Laplace transforms. In addition, the results of the article can be implemented in different mathematical software for a direct calculation of such transforms or to study the analytical properties of these transforms more directly.
subject: Articles
  topic: section
subject: Laplace Transform
  topic: keywords
subject: powers of the cardinal sine function
  topic: keywords
subject: powers of the sine function
  topic: keywords
creator: Rimer Zurita
rights: Copyright (c) 2025 Scientia Series A: Mathematical Sciences https://creativecommons.org/licenses/by-nc/4.0
date: 2025-09-02
publication date: 2025-09-02
starting page: 171
ending page: 188
doi: 10.71712/p5cn-sn64

A note on the Hurwitz-Lerch zeta function
type: item
description: In this work we derive a functional equation in terms of the Hurwitz-Lerch zeta function along with de nite integrals in terms of the incomplete gamma and Hurwitz-Lerch zeta functions. The method used in these derivations is contour integration. Special cases in terms of fundamental constants are produced.
subject: Articles
  topic: section
subject: Lerch zeta function
  topic: keywords
subject: Cauchy integral
  topic: keywords
subject: denite integral
  topic: keywords
subject: loggamma
  topic: keywords
creator: Robert Reynolds
rights: Copyright (c) 2025 Scientia Series A: Mathematical Sciences https://creativecommons.org/licenses/by-nc/4.0
date: 2025-02-09
publication date: 2025-02-09
starting page: 139
ending page: 170
doi: 10.71712/mryc-b928

Derivation of some definite integrals
type: item
description: In this work derivations of de nite integrals listed in Prudnikov volume I, Gradshteyn and Ryzhik and a few other tables are produced along with errata. Special cases of these integrals in terms of fundamental constants are also evaluated. The method used in these derivations is contour integration.
subject: Articles
  topic: section
subject: Prudnikov
  topic: keywords
subject: Gradshteyn and Ryzhik
  topic: keywords
subject: denite integral
  topic: keywords
subject: Catalan's constant
  topic: keywords
subject: contour integration
  topic: keywords
subject: elliptic functions
  topic: keywords
subject: special functions
  topic: keywords
creator: Robert Reynolds
rights: Copyright (c) 2025 https://creativecommons.org/licenses/by/4.0
date: 2025-02-09
publication date: 2025-02-09
starting page: 37
ending page: 137
doi: 10.71712/6k7n-5750

Symmetric tensor powers of graphs
type: item
description: We introduce the symmetric tensor power of graphs and explore the fundamental properties of this operation. A wide range of intriguing phenomena occur when one considers symmetric tensor powers of familiar graphs. We conclude with a host of open questions that we hope will spur future research.
subject: Articles
  topic: section
subject: Graph
  topic: keywords
subject: Kronecker product
  topic: keywords
subject: tensor product
  topic: keywords
subject: symmetric tensor product
  topic: keywords
creator: Weymar Astaiza
creator: Alexander J. Barrios
creator: Henry Chimal-Dzul
creator: Stephan Ramon García
creator: Jaaziel Lopez de la Luz
creator: Victor H. Moll
creator: Diego Villamizar
creator: Yunied Puig
rights: Copyright (c) 2025 https://creativecommons.org/licenses/by-nc/4.0
date: 2025-02-09
publication date: 2025-02-09
starting page: 13
ending page: 35
doi: 10.71712/vtk1-mg46

A four parameter integral identity and a few consequences
type: item
description: The identity \[ \int_0^\infty \frac{e^{-ax} \, e^{-b\sqrt{x^2 + 2cx + a^2}}}{\sqrt{x^2 + 2cx + b^2}} \, dx = \int_0^\infty \frac{e^{-bx} \, e^{-a\sqrt{x^2 + 2cx + b^2}}}{\sqrt{x^2 + 2cx + a^2}} \, dx \] is derived, applied to the Struve function $H_0$, and used to deduce the reduction formula \[ \int_0^\infty \frac{F(\sqrt{x^2 + 2cx + b^2} + x)}{\sqrt{x^2 + 2cx + b^2}} \, dx = \int_0^\infty f(t)e^{-t} E_1[(c+b)t] \, dt, \] where $F$ is arbitrary.
subject: Articles
  topic: section
subject: Integral Identities
  topic: keywords
subject: Bessel Function
  topic: keywords
subject: Struve functions
  topic: keywords
subject: Elliptic Integral
  topic: keywords
creator: M.L. Glasser
rights: Copyright (c) 2025 https://creativecommons.org/licenses/by/4.0/
date: 2025-02-09
publication date: 2025-02-09
starting page: 9
ending page: 12
doi: 10.71712/f1ya-ec51

On some improper integrals containing products between the tails of Maclaurin series for the sine and cosine functions
type: item
description: The values of twenty-six improper integrals containing products between the tails of Maclaurin series for the sine and cosine functions are evaluated using elementary methods. The values found extend work where the values for six improper integrals containing the squares of the tails of the Maclaurin series for the sine and cosine functions were recently reported.
subject: Articles
  topic: section
subject: Improper integral
  topic: keywords
subject: Maclaurin series
  topic: keywords
subject: tails of series
  topic: keywords
creator: Seán M. Stewart
rights: Copyright (c) 2025 Scientia https://creativecommons.org/licenses/by/4.0/
date: 2025-09-02
publication date: 2025-09-02
starting page: 1
ending page: 7
doi: 10.71712/42f7-cb32

Gain of regularity for a nonlinear dispersive equation
type: item
description: In this paper we study the gain of regularity of solutions of a dispersive evolution nonlinear equation. We consider the equation \[(1) =\begin{cases}\dfrac{\partial u}{\partial t} + \dfrac{\partial}{\partial x} \left[ f(u) \right] = \epsilon \, \dfrac{\partial}{\partial x} \left[ g\left( \dfrac{\partial u}{\partial x} \right) \right] - \delta \, \dfrac{\partial^3 u}{\partial x^3}, \\[6pt] u(x,0) = \varphi(x)\end{cases}\] where \( x \in \mathbb{R} \), \( t \in [0,T] \) and \( T \) is an arbitrary positive time. The flux \( f = f(u) \) and the (degenerate) viscosity \( g = g(\lambda) \) are smooth functions satisfying certain assumptions to be listed below. It is shown under certain additional conditions on \( f \) that \( C^\infty \)-solutions \( u(x,t) \) are obtained for all \( t > 0 \) if the initial data \( u(x,0) = \varphi(x) \) decays faster than polynomially on \( \mathbb{R}^+ = \{ x \in \mathbb{R} ; x > 0 \} \) and it has certain initial Sobolev regularity.
subject: Articles
  topic: section
subject: Evolution equations
  topic: keywords
subject: Weighted Sobolev Space
  topic: keywords
creator: Octavio Paulo Vera Villagrán
rights: Copyright (c) 2025 Scientia Series A: Mathematical Sciences https://creativecommons.org/licenses/by-nc/4.0
date: 2025-08-11
publication date: 2025-08-11
starting page: 53
ending page: 62
doi: 10.71712/

Abel summability and angular convergence
type: item
description: We construct an example of a series that is Abel summable but whose associated power series does not converge on angular sectors. We also give some related results.
subject: Articles
  topic: section
subject: Abel summability
  topic: keywords
subject: angular limit
  topic: keywords
creator: Ricardo Estrada
rights: Copyright (c) 2025 Scientia Series A: Mathematical Sciences https://creativecommons.org/licenses/by-nc/4.0
date: 2025-08-11
publication date: 2025-08-11
starting page: 45
ending page: 51
doi: 10.71712/

Long-pin perturbations of the trivial solution for Hele-Shawcorner flows
type: item
description: We consider two-dimensional Hele-Shaw corner flows without effect of the surface tension and with an interface extending to the infinity along one of the walls. Explicit solutions that present a ”long-pin” deformations of the trivial solution are got. Making use of the Polubarinova-Galin approach we derive parametric equations for the moving interface in terms of univalent mappings of a canonical domain. For the right angle we repeat a result by Leo P. Kadanoff.
subject: Articles
  topic: section
subject: free boundary problem
  topic: keywords
subject: conformal map
  topic: keywords
subject: complex analysis
  topic: keywords
subject: univalent function
  topic: keywords
subject: hypergeometric function
  topic: keywords
creator: Irina Markina
creator: Alexander Vasiliev
rights: Copyright (c) 2025 Scientia Series A: Mathematical Sciences https://creativecommons.org/licenses/by-nc/4.0
date: 2025-08-11
publication date: 2025-08-11
starting page: 33
ending page: 43
doi: 10.71712/

Fourth coefficient estimate in the class of univalent functions with quasiconformal extensions
type: item
description: We denote by \( S(k) \) the class of all univalent conformal maps \( f \) defined in the unit disk \( \Delta \) normalized by \[f(z) = z + \sum_{n=2}^{\infty} a_n z^n, \] such that all \( f \) admit \( k \)-quasiconformal homeomorphic extension to the whole Riemann sphere \( \hat{\mathbb{C}} \), and \( f(\infty) = \infty \). In our note we give a new estimate for \( |a_4| \) in \( S(k) \) making use of the Area Principle.
subject: Articles
  topic: section
subject: univalent function
  topic: keywords
subject: quasiconformal extension
  topic: keywords
subject: coefficient
  topic: keywords
creator: Larisa L. Gromova
rights: Copyright (c) 2025 Scientia Series A: Mathematical Sciences https://creativecommons.org/licenses/by-nc/4.0
date: 2025-08-11
publication date: 2025-08-11
starting page: 27
ending page: 31
doi: 10.71712/

Some open problems related to 16b Hilbert problem.
type: item
description: This article contains a brief summary of the topics and concepts related to 16b Hilbert problem which refers to the existence of a bound on the number of limit cycles of a polynomial system in function of its degree. Both algebraic and analytic perspectives are described. Moreover, collateral open questions related to the mentioned problem are given. Finally, the bibliography, which does not intend to be exhaustive, contains more than one hundred of references.
subject: Articles
  topic: section
subject: Limit cycles
  topic: keywords
subject: integrability
  topic: keywords
subject: algebraic invariant curves
  topic: keywords
subject: centers
  topic: keywords
creator: Javier Chavarriga
creator: Maite Grau
rights: Copyright (c) 2025 Scientia Series A: Mathematical Sciences https://creativecommons.org/licenses/by-nc/4.0
date: 2025-08-11
publication date: 2025-08-11
starting page: 1
ending page: 26
doi: 10.71712/

On I-almost continuity and new descomposition of continuity
type: item
description: In this paper, I-almost continuous functions are introduced and their characterizations and properties are given. Relationships between I-almost continuity and other forms of continuity are discussed. Moreover, new decomposition of continuity with I-almost continuity as a factor is obtained.
subject: Articles
  topic: section
subject: I-almost continuity
  topic: keywords
subject: R-I-open sets
  topic: keywords
subject: Almost continuity
  topic: keywords
subject: Weakly I-continuity
  topic: keywords
subject: Decompositions of continuity
  topic: keywords
creator: Xiaomin Li
rights: Copyright (c) 2025 Scientia Series A: Mathematical Sciences https://creativecommons.org/licenses/by-nc/4.0
date: 2025-08-08
publication date: 2025-08-08
starting page: 141
ending page: 153
doi: 10.71712/

Uniqueness Theorem for Hilbert Transform for Boehmians
type: item
description: In this paper a uniqueness theorem is proved for the Hilbert transform for the Boehmians of analytic function by using a relation between the Hilbert transform and the Fourier transform. Hilbert transform of Boehmians of analytic type is also discussed.
subject: Articles
  topic: section
subject: Generalized functions
  topic: keywords
subject: Boehmians
  topic: keywords
subject: Fourier transform
  topic: keywords
subject: Hilbert transform
  topic: keywords
subject: uniqueness theorem.
  topic: keywords
creator: Abhishek Singh
rights: Copyright (c) 2025 Scientia Series A: Mathematical Sciences https://creativecommons.org/licenses/by-nc/4.0
date: 2025-08-08
publication date: 2025-08-08
starting page: 133
ending page: 140
doi: 10.71712/

Some remarks, generalizations and misprints in the integrals in Gradshteyn and Ryzhik
type: item
description: This paper presents some remarks, generalizations and misprints to the classic table of integrals of Gradshteyn and Ryzhik. It is noted that the conditions for convergence in a number of integrals, that in the original source were obtained via Bessel transforms, are too restrictive. Also, a property of the parabolic cylinder function is used to simplify one of the integrals in Gradshteyn and Ryzhik into a result that enables the calculation of integrals for squares and higher powers of the error function. Subsequently, an indefinite integral for the normal distribution is specialized into several expressions that are reported in Gradshteyn and Ryzhik. The paper ends by listing integrals for which the aforementioned overly restrictive conditions emerge and/or for which generalizations or misprints are found
subject: Articles
  topic: section
subject: Bessel function
  topic: keywords
subject: Bessel transform
  topic: keywords
subject: error function
  topic: keywords
subject: hypergeometric function
  topic: keywords
subject: integrals
  topic: keywords
subject: Owen’s T function
  topic: keywords
subject: parabolic cylinder function
  topic: keywords
subject: Whittaker function
  topic: keywords
creator: Dirk Veestraeten
rights: Copyright (c) 2025 Scientia Series A: Mathematical Sciences https://creativecommons.org/licenses/by-nc/4.0
date: 2025-08-08
publication date: 2025-08-08
starting page: 115
ending page: 131
doi: 10.71712/

DIG-Semigroups
type: item
description: In this paper, we introduce a new class of algebras that related to distributive implication groupoids(DIG) and semigroups, call it a DIG-semigroup. We also define the concept of left(resp. right) deductive systems(LDS (resp. RDS) for short) of a DIG-semigroup and of unit divisors in DIG-semigroups. The notion of DIG-homomorphisms between DIG semigroups is introduced and investigate some of their properties and the quotient of DIG-semigroup via deductive systems is constructed.
subject: Articles
  topic: section
subject: Distributive Implication Groupoid(DIG)
  topic: keywords
subject: DIG-semigroup
  topic: keywords
subject: homomorphism.
  topic: keywords
subject: Deductive System(DS)
  topic: keywords
creator: Ravi Kumar Bandaru
creator: Arsham Borumand Saeid
rights: Copyright (c) 2025 Scientia Series A: Mathematical Sciences https://creativecommons.org/licenses/by-nc/4.0
date: 2025-08-08
publication date: 2025-08-08
starting page: 101
ending page: 114
doi: 10.71712/

Some Inequalities for Power Series with nonnegative coefficients via a divided difference reverse of Jensen inequality
type: item
description: Some inequalities for power series with nonnegative coefficients via a divided difference reverse of Jensen inequality are given. Applications for some fundamental functions defined by power series are also provided.
subject: Articles
  topic: section
subject: Power series
  topic: keywords
subject: Jensen’s inequality
  topic: keywords
subject: Reverse of Jensen’s inequality
  topic: keywords
creator: S. S. Dragomir
rights: Copyright (c) 2025 Scientia Series A: Mathematical Sciences https://creativecommons.org/licenses/by-nc/4.0
date: 2025-08-08
publication date: 2025-08-08
starting page: 83
ending page: 99
doi: 10.71712/

A table of definite integrals from the marriage of power and Fourier series
type: item
description: In this paper we show an unusual way to obtain values for definite integrals of the forms \(\int_{-\pi}^{\pi} f(x)dx\), \(\int_{-\pi}^{\pi} f(x)\cos(nx)dx\) and \(\int_{-\pi}^{\pi} f(x)\sin(nx)dx\) where \(n\) is a positive integer. Our method is indirect in that we do not start with the integral. The integral is obtained as the end result of a process that did not visualize the integral at the start. We begin with an analytic function, and obtain our integrals by comparing the coefficients of related power series and Fourier series. A table of 36 definite integrals results. Eleven of these can be reproduced by Mathematica or found in familiar tables, while 25 others cannot. These may be new integral evaluations.
subject: Articles
  topic: section
subject: Definite integrals
  topic: keywords
subject: Taylors series
  topic: keywords
subject: Fourier series
  topic: keywords
creator: James Rosado
creator: Thomas J. Osler
rights: Copyright (c) 2025 Scientia Series A: Mathematical Sciences https://creativecommons.org/licenses/by-nc/4.0
date: 2025-08-08
publication date: 2025-08-08
starting page: 77
ending page: 82
doi: 10.71712/

One modulo \(N\) gracefulness of H-class of graphs
type: item
description: A function \(f\) is called a graceful labelling of a graph \(G\) with \(q\) edges if \(f\) is an injection from the vertices of \(G\) to the set \(\{0, 1, 2, \ldots, q\}\) such that, when each edge \(xy\) is assigned the label \(|f(x) - f(y)|\), the resulting edge labels are distinct. A graph \(G\) is said to be one modulo \(N\) graceful (where \(N\) is a positive integer) if there is a function \(\phi\) from the vertex set of \(G\) to \(\{0, 1, N, (N + 1), 2N, (2N + 1), \ldots, N(q - 1), N(q - 1) + 1\}\) in such a way that \( (i)\) \( \phi\) is \(1 - 1\) \( (ii) (\phi\) induces a bijection \(\phi^*\) from the edge set of \(G\) to \(\{1, N + 1, 2N + 1, \ldots, N(q - 1) + 1\}\) where \(\phi^*(uv)=|\phi(u) - \phi(v)|\). In this paper we prove that the H-graph, \(H \odot mK_1\) and \(H_{(n)}^{(a)}\) are one modulo \(N\) graceful for all positive integers \(N\).
subject: Articles
  topic: section
subject: Graceful
  topic: keywords
subject: one modulo \(N\) graceful
  topic: keywords
subject: H-graph
  topic: keywords
subject: Paths
  topic: keywords
creator: V. Ramachandran
creator: C. Sekar
rights: Copyright (c) 2025 Scientia Series A: Mathematical Sciences https://creativecommons.org/licenses/by-nc/4.0
date: 2025-08-08
publication date: 2025-08-08
starting page: 63
ending page: 76
doi: 10.71712/

The integrals in Gradshteyn and Ryzhik Part 28: The confluent hypergeometric function and Whittaker functions
type: item
description: The table of Gradshteyn and Ryzhik contains many entries where the integrand contains the confluent hypergeometric function \(_{1}F_{1}(a;c;z)\) and a closely associated function studied by Whittaker. A selection of these entries are evaluated.
subject: Articles
  topic: section
subject: Integrals
  topic: keywords
subject: Whittaker function
  topic: keywords
subject: hypergeometric functions
  topic: keywords
creator: A. Dixit
creator: V. H. Moll
rights: Copyright (c) 2025 Scientia Series A: Mathematical Sciences https://creativecommons.org/licenses/by-nc/4.0
date: 2025-08-08
publication date: 2025-08-08
starting page: 49
ending page: 61
doi: 10.71712/

The integrals in Gradshteyn and Ryzhik Part 27: More logarithmic examples
type: item
description: The table of Gradshteyn and Ryzhik contains many entries where the integrand is a combination of an elementary function and the logarithmic of another function of the same type. This paper presents proofs of some of these. A sample of examples where the elementary function is replaced by an algebraic function is also discussed.
subject: Articles
  topic: section
subject: Integrals.
  topic: keywords
creator: Luis A. Medina
creator: V. H. Moll
rights: Copyright (c) 2025 Scientia Series A: Mathematical Sciences https://creativecommons.org/licenses/by-nc/4.0
date: 2025-08-08
publication date: 2025-08-08
starting page: 31
ending page: 47
doi: 10.71712/

The integrals in Gradshteyn and Ryzhik Part 26: The exponential integral
type: item
description: The table of Gradshteyn and Ryzhik contains many entries where the evaluation is given in terms of the exponential integral. A selection of these formulas are established.
subject: Articles
  topic: section
subject: Integrals.
  topic: keywords
creator: K. Boyadzhiev
creator: Victor H. Moll
rights: Copyright (c) 2025 Scientia Series A: Mathematical Sciences https://creativecommons.org/licenses/by-nc/4.0
date: 2025-08-08
publication date: 2025-08-08
starting page: 19
ending page: 30
doi: 10.71712/

On \(\aleph_0\)-\(sn\)-networks
type: item
description: In this paper, we discuss spaces with \(\aleph_0\)-\(sn\)-networks and give some characterizations of \(\aleph_0\)-\(sn\)-metric spaces. For a space \(X\) we prove that \(X\) has a point-countable \(\aleph_0\)-\(sn\)-network if and only if \(X\) is an sequentially quotient, countable-to-one image of a metric space. and \(X\) is an \(\aleph_0\)-\(sn\)-metric space if and only if \(X\) is a sequentially quotient, \(\sigma\), countable-to-one image of a metric space
subject: Articles
  topic: section
subject: \(\aleph_0\)-\(sn\)-networks
  topic: keywords
subject: \(\aleph\)-space
  topic: keywords
subject: \(\aleph_0\)-space
  topic: keywords
subject: \(\aleph_0\)-\(sn\)-weakly first-countable
  topic: keywords
subject: cs∗- network.
  topic: keywords
creator: Pei Wang
creator: Xun Ge
rights: Copyright (c) 2025 Scientia Series A: Mathematical Sciences https://creativecommons.org/licenses/by-nc/4.0
date: 2025-08-08
publication date: 2025-08-08
starting page: 13
ending page: 17
doi: 10.71712/

Some integrals related to the Basel problem
type: item
description: We evaluate several arctangent and logarithmic integrals depending on a parameter. This provides a closed form summation of certain series and also integral and series representation of some classical constants.
subject: Articles
  topic: section
subject: Basel problem
  topic: keywords
subject: integrals
  topic: keywords
subject: dilogarithm
  topic: keywords
subject: trilogarithm
  topic: keywords
subject: Catalan constant
  topic: keywords
creator: Khristo N. Boyadzhiev
rights: Copyright (c) 2025 Scientia Series A: Mathematical Sciences https://creativecommons.org/licenses/by-nc/4.0
date: 2025-08-08
publication date: 2025-08-08
starting page: 1
ending page: 11
doi: 10.71712/

On two families of stochastic predation models with Allee effect
type: item
description: Two classes of stochastic models of predator-prey interaction with Allee effect on prey are presented in this paper. Both families are introduced as generalizations of Leslie type predation models with Holling type functional response. The stochastic perturbations are considered of polynomial kind in order to model environmental random noise affecting both species. The only difference between both families of models is the way the Allee effect is modeled, namely, by means of a generic term whose conveniently chosen properties give rise to a behavior that is representative of either additive or multiplicative Allee effect, respectively. We show that both classes of models are well-posed in the sense that any positive solution starting in the open first quadrant remains in that region and, hence, it never becomes negative. In the particular case when the random noise is absent, we find that all the solutions are bounded for both sets of models. We also prove that the stochastic solutions exist, are unique in pathwise sense and have bounded moments. Moreover, we find that, as a consequence of our modeling approach, for sufficiently low population densities, the solutions of the random systems behave like the associated deterministic trajectories and, in doing so, the overall dynamics is determined by the features of the Allee effect.
subject: Articles
  topic: section
subject: Population dynamics
  topic: keywords
subject: Equations and systems with randomness
  topic: keywords
subject: Allee effect.
  topic: keywords
creator: Pablo Aguirre
rights: Copyright (c) 2025 Scientia Series A: Mathematical Sciences https://creativecommons.org/licenses/by-nc/4.0
date: 2025-08-08
publication date: 2025-08-08
starting page: 95
ending page: 107
doi: 10.71712/

On \(g\)-scattered spaces
type: item
description: This paper is devoted to investigate scatteredness on generalized topological spaces. The concept of \(g\)-scattered spaces is introduced. Their characterizations, properties and mapping theorems are obtained.
subject: Articles
  topic: section
subject: GTS’s
  topic: keywords
subject: g-scattered spaces
  topic: keywords
subject: g-dense sets
  topic: keywords
subject: g-isolated points
  topic: keywords
subject: g-limit points
  topic: keywords
subject: g-derived sets
  topic: keywords
subject: GT-sums
  topic: keywords
creator: Xiaomin Li
rights: Copyright (c) 2025 Scientia Series A: Mathematical Sciences https://creativecommons.org/licenses/by-nc/4.0
date: 2025-08-08
publication date: 2025-08-08
starting page: 85
ending page: 94
doi: 10.71712/

Evaluation of entries in Gradshteyn and Ryzhik employing the method of brackets
type: item
description: The method of brackets was created for the evaluation of definite integrals appearing in the resolution of Feynman diagrams. This method consists of a small number of heuristic rules and it is quite easy to apply. The first of these is Ramanujan’s Master Theorem, one of his favorite tools to evaluate integrals. The current work illustrates its applicability by evaluating a variety of entries from the classical table of integrals by I. S. Gradshteyn and I. M. Ryzhik.
subject: Articles
  topic: section
subject: Definite integrals
  topic: keywords
subject: method of brackets
  topic: keywords
subject: tables of integrals.
  topic: keywords
creator: Ivan Gonzalez
creator: Karen T. Kohl
creator: V. H. Moll
rights: Copyright (c) 2025 Scientia Series A: Mathematical Sciences https://creativecommons.org/licenses/by-nc/4.0
date: 2025-08-08
publication date: 2025-08-08
starting page: 65
ending page: 84
doi: 10.71712/

Certain Inequalities Related to the Chebyshev’s Functional Involving Erdélyi-Kober Operators
type: item
description: The object of the present investigation is to obtain certain Chebyshev type integral inequalities involving the Erd´elyi-Kober fractional integral operators. Some consequent results and special cases of the main results are also pointed out.
subject: Articles
  topic: section
subject: Integral inequalities
  topic: keywords
subject: fractional integral operators
  topic: keywords
subject: Erd´elyi-Kober operator
  topic: keywords
creator: S.D. Purohit
creator: S.L. Kalla
rights: Copyright (c) 2025 Scientia Series A: Mathematical Sciences https://creativecommons.org/licenses/by-nc/4.0
date: 2025-08-08
publication date: 2025-08-08
starting page: 55
ending page: 63
doi: 10.71712/

Coexistence of limit cycles and invariant curves for Extended Kukles systems
type: item
description: We work with a certain class of extended Kukles system of arbitrary degree n with at least three invariant straight lines. We show that for a certain values of the parameters, the system has an lower bound of limit cycles. By writing the system as a perturbation of a Hamiltonian system, we show that the first Poincar´e-Melnikov integral of the system is a polynomial whose coefficients are the Lyapunov quantities. The maximum number of simples zero of this polynomial gives the maximum number of the global limit cycles; the multiplicity of the origin as a root the polynomial gives the maximum weakness that the weak focus at the origin. On the other hand, we also work with a certain extended Kukles system of order four with a invariant circumference. We show that for certain values of the parameters the system has an lower bound of limit cycles at the origin.
subject: Articles
  topic: section
subject: Polynomial differential system
  topic: keywords
subject: limit cycles
  topic: keywords
subject: invariant curves
  topic: keywords
subject: Hamiltonian system
  topic: keywords
creator: Ricardo Reyes Carocca
rights: Copyright (c) 2025 Scientia Series A: Mathematical Sciences https://creativecommons.org/licenses/by-nc/4.0
date: 2025-08-08
publication date: 2025-08-08
starting page: 37
ending page: 45
doi: 10.71712/

Poisson’s formula with principal value integrals and some special Gradshteyn and Ryzhik integrals
type: item
description: Poisson’s integral formula for holomorphic functions on the right half plane can be used to quickly evaluate certain integrals from Gradshteyn and Ryzhik’s table. In addition we prove a version of Poisson’s formula for principal value integrals and use it in several interesting cases.
subject: Articles
  topic: section
subject: principal value integrals
  topic: keywords
subject: Poisson’s integral formula
  topic: keywords
creator: Khristo N. Boyadzhiev
rights: Copyright (c) 2025 Scientia Series A: Mathematical Sciences https://creativecommons.org/licenses/by-nc/4.0
date: 2025-08-08
publication date: 2025-08-08
starting page: 27
ending page: 35
doi: 10.71712/

Companions of Hermite-Hadamard Inequality for Convex Functions (I)
type: item
description: Companions of Hermite-Hadamard inequalities for convex functions defined on the positive axis in the case when the integral has the weight \(\frac{1}{t^3}\), \(t > 0\) are given. Applications for special means are provided as well.
subject: Articles
  topic: section
subject: Convex functions
  topic: keywords
subject: Hermite-Hadamard inequality
  topic: keywords
subject: Special means
  topic: keywords
creator: S. S. Dragomir
creator: I. Gomm
rights: Copyright (c) 2025 Scientia Series A: Mathematical Sciences https://creativecommons.org/licenses/by-nc/4.0
date: 2025-08-08
publication date: 2025-08-08
starting page: 17
ending page: 25
doi: 10.71712/