This article investigates the properties and monomiality principle within Bell-based Apostol-Bernoulli-type polynomials. Beginning with the establishment of a generating function, the study proceeds to derive explicit expressions for these polynomials, providing insight into their structural characteristics. Summation formulae are then derived, facilitating efficient computation and manipulation. Implicit formulae are also examined, revealing underlying patterns and relationships. Through the lens of the monomiality principle, connections between various polynomial aspects are elucidated, uncovering hidden symmetries and algebraic properties. Moreover, connection formulae are derived, enabling seamless transitions between different polynomial representations. This analysis contributes to a comprehensive understanding of Bell-based Apostol-Bernoulli-type polynomials, offering valuable insights into their mathematical nature and applications.

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.

The main purpose of this paper is to investigate the Fourier series representation of the generalized Apostol-type Frobenius–Euler polynomials, and using the above-mentioned series we find its integral representation. At the same time applying the Fourier series representation of the Apostol Frobenius–Genocchi and Apostol Genocchi polynomials, we obtain its integral representation. Furthermore, using the Hurwitz–Lerch zeta function we introduce the formula in rational arguments of the generalized Apostol-type Frobenius–Euler polynomials in terms of the Hurwitz zeta function. Finally, we show the representation of rational arguments of the Apostol Frobenius Euler polynomials and the Apostol Frobenius–Genocchi polynomials.

In this paper, we introduce the $U$-Bernoulli, $U$-Euler, and $U$-Genocchi polynomials, their numbers, and their relationship with the Riemann zeta function. We also derive the Apostol-type generalizations to obtain some of their algebraic and differential properties. We introduce generalized $U$-Bernoulli, $U$-Euler and $U$-Genocchi polynomial Pascal-type matrix. We deduce some product formulas related to this matrix. Furthermore, we establish some explicit expressions for the $U$-Bernoulli, $U$-Euler, and $U$-Genocchi polynomial matrices, which involves the generalized Pascal matrix.

We introduce two biparametric families of Apostol-Frobenius-Euler polynomials of level-$m$. We give some algebraic properties, as well as some other identities which connect these polynomial class with the generalized $\lambda$-Stirling type numbers of the second kind, the generalized Apostol--Bernoulli polynomials, the generalized Apostol--Genocchi polynomials, the generalized Apostol--Euler polynomials and Jacobi polynomials. Finally, we will show the differential properties of this new family of polynomials.

Con el fin de establecer la percepción de estrés en estudiantes de primer semestre de la Universidad Metropolitana-Barranquilla, se utilizó un cuestionario Likert como instrumento de recolección de datos, estructurado con 27 interrogantes sobre estresores relacionados con las clases virtuales, donde el estudiante, según su percepción, debía responder a niveles de estrés: Normal, Leve, Moderado y Severo. Obteniéndose que los estresores con mayores niveles de percepción fueron el exceso de actividades académicas, la red inestable de internet y la interrupción en el fluido eléctrico; también, se observó que el nivel de percepción estrés severo fue ligeramente mayor en las mujeres, comparado con los hombres; se encontró, además, que algunos programas académicos presentan mayor nivel de percepción de estrés, lo cual se explicaría por la cantidad de mujeres matriculadas en los programas, y como se dijo anteriormente, los niveles de percepción de estrés en las mujeres son más altos, comparados con los hombres. Por otra parte, el nivel de estrés percibido no mostró dependencia de la edad (p: 0,1471). Por último, se proponen estrategias para reducir los niveles de estrés, que pueden ser implementadas en la Universidad Metropolitana y en otras instituciones educativas.