Jafari Transformation for Solving a System of Ordinary Differential Equations with Medical Application

Integral transformations are essential for solving complex problems in business, engineering, natural sciences, computers, optical science, and modern mathematics. In this paper, we apply a general integral transform, called the Jafari transform, for solving a system of ordinary differential equations. After applying the Jafari transform, ordinary differential equations are converted to a simple system of algebraic equations that can be solved easily. Then, by using the inverse operator of the Jafari transform, we can solve the main system of ordinary differential equations. Jafari transform belongs to the class of Laplace transform and is considered a generalization to integral transforms such as Laplace, Elzaki, Sumudu, G\_transforms, Aboodh, Pourreza, etc. Jafari transform does not need a large computational work as the previous integral transforms. For the Jafari transform, we have studied some valuable properties and theories that have not been studied before. Such as the linearity property, scaling property, first and second shift properties, the transformation of periodic functions, Heaviside function, and the transformation of Dirac’s delta function, and so on. There is a mathematical model that describes the cell population dynamics in the colonic crypt and colorectal cancer. We have applied the Jafari transform for solving this model.

Dynamical collapse of cylindrical symmetric dipolar Bose–Einstein condensates

We study the formation of singularities for cylindrical symmetric solutions to the Gross–Pitaevskii equation describing a dipolar Bose–Einstein condensate. We prove that solutions arising from initial data with energy below the energy of the Ground State and that do not scatter collapse in finite time. The main tools to prove our result are the variational characterization of the Ground State energy, suitable localized virial identities for cylindrical symmetric functions, and general integral and pointwise estimates for operators involving powers of the Riesz transform.

New general integral transform via Atangana–Baleanu derivatives

The current paper is about the investigation of a new integral transform introduced recently by Jafari. Specifically, we explore the applicability of this integral transform on Atangana–Baleanu derivative and the associated fractional integral. It is shown that by applying specific conditions on this integral transform, other integral transforms are deduced. We provide examples to reinforce the applicability of this new integral transform.

Comparison of the Adomian Decomposition Method and Regular Perturbation Method on Nonlinear Equations Second Kind of Volterra

In this paper, we study convergence of Adomian decomposition method applied tosecond kind Volterra general integral and show that this method and regular perturbation method converges to the same solution.

DEFINITE INTEGRAL OF LOGARITHMIC FUNCTIONS AND POWERS IN TERMS OF THE LERCH FUNCTION

A family of generalized definite logarithmic integrals given by $$\int_{0}^{1}\frac{\left(x^{ i m} (\log (a)+i \log (x))^k+x^{-i m} (\log (a)-i \log (x))^k\right)}{(x+1)^2}dx$$built over the Lerch function has its analytic properties and special values listed in explicit detail. We use the general method as given in [6] to derive this integral. We then give a number of examples that can be derived from the general integral in terms of well known functions.

La motricidad en el triatlón: otra mirada desde la física hacia la biomecánica

Este artículo aborda aspectos de la motricidad, que se sustentan en los fundamentos de la biomecánica, en el razonamiento físico y el interdisciplinario. Estas ciencias en el preuniversitario revelan un acercamiento al estudio del hombre en la ejecución del movimiento. La comprensión acerca la motricidad incrementa el interés de los estudiantes-atletas de la escuela de iniciación deportiva escolar y, a su vez, son indispensables en la carrera de Cultura Física, como la estructura interna del cuerpo en el movimiento de articular y muscular. Se buscan propuestas didácticas para introducir estos contenidos y así lograr una cultura general integral y formarlos profesionalmente.

Sistema de talleres para la promoción cultural en la superación profesional del docente de la Educación Artística

La formación del profesional de la Educación Artística en Cuba se ha convertido en un factor esencial, el que con una cultura general integral debe convertirse en objeto imprescindible para la transformación de las instituciones educativas en centros culturales. Las insuficiencias detectadas en la práctica educativa de los docentes en cuanto a la promoción cultural, la dispersión de fundamentos teóricos sobre este particular y la significación que tiene este tema para el desarrollo intelectual del docente de la Educación Artística, meritó perfeccionar su desempeño profesional desde la Superación Profesional. Luego del empleo de métodos y técnicas de investigación se asume el taller como tipología de la Superación Profesional y se propone un sistema de talleres que está diseñado a través de cuatro acciones prácticas a partir de un objetivo general que guía su estructuración por etapas con los respectivos procedimientos para la implementación. El diagnóstico realizado a los docentes de la Educación Artística graduados en los cursos 2015, 2016, 2017 y 2018, que laboran en las instituciones educativas del municipio de Ciego de Ávila, reveló que, al promocionar la cultura, manifiestan insuficiencias que interfieren y limitan su realización al concebirla como acciones independientes, y no de forma integrada. En la investigación, se emplearon diferentes métodos y técnicas como el histórico-lógico, analítico-sintético, el sistémico estructural, la entrevista, la encuesta, la observación, que permitieron determinar tendencias y precisar insuficiencias en la práctica. El pre-experimento pedagógico permitió comprobar los resultados.

Classes of an univalent integral operator

"In this paper we introduce a new general integral operator for analytic functions in the open unit disk U and we obtain su cient conditions for univalence of this integral operator."

Univalence Criteria for some General Integral Operators

The main object of this paper is to extend the univalent condition for two general integral operators. A number of known univalent condition would follow upon specializing the parameters involved in our main results.

Models Of Forecasting Of Enterprise’s Behavior In Non-Stationary External Environment

In conditions of a high level of market economy instability, an enterprise's behavior is a complex phenomenon that depends on the impact of numerous external and internal factors. This determines the need to develop specific tools for modeling the behavior of the production system to support its competitiveness. The article is devoted to the construction of forecasting models of an enterprise's behavior, namely: 1) a predicting model of the production system's activities that combines the resource capabilities of the enterprise with the state and prospects of branch development; 2) a model of determining the sustainability of the enterprise's development trajectory. The first model contains the production component in the form of the Cobb-Douglas function; financial, labor, innovative and enterprise’s image components, represented by autoregressive functions. The specifically feature of the constructed model is to use capital and labor resources of the enterprise as factors that ensure the transfer and interaction of internal and external fluctuations of the production system. To using factors of the export volume and the gross value added of the branch in the enterprise’s image component allowed to have regard to the development opportunities of the enterprise in the national economy. To determine the stability of the enterprise's development trajectory, the study uses Lyapunov's theory of stability. The general integral factor proposes to use as a factor that reflects the trend of the enterprise’s behavior. Models tested on the data of two industrial enterprises in Morocco.