En este trabajo mostraremos una herramienta que nos permita transformar una foliación holomorfa singular a otra foliación holomorfa singular de tal forma que en ésta última tenemos más oportunidad a que las multiplicidades de las sigularidades disminuyan y así poder hacer un mejor análisis cualitativo de las órbitas de la foliación alrededor de una sigularidad...

In this research we will present the "Choice of optimal portfolios of assets with and without risk", where we propose an efficient portfolio optimization model based on the theory of Markowitz (Assets with Risks), who won the Nobel Prize in Economics in 1990 for their contributions to the analysis of investment portfolios and corporate financing methods. Markowitz based on his theory, defines that for a given performance the risk that they have is minimal, this model is the most efficient when it comes to reducing risks. On the other hand, if we opt for an optimal risk-free portfolio, we will rely on the Sharpe Model to establish a pricing of financial assets, in which an investor can choose a risk exposure through a combination of income values fixed and a variable income portfolio.

En este trabajo mostraremos una herramienta que nos permita transformar una foliación holomorfa singular a otra foliación holomorfa singular de tal forma que en ésta última tenemos más oportunidad a que las multiplicidades de las sigularidades disminuyan y así poder hacer un mejor análisis cualitativo de las órbitas de la foliación alrededor de una sigularidad...

En este trabajo de investigación presentaremos la "Elección de portafolios óptimos de activos con y sin riesgo", donde planteamos un modelo de optimización de portafolios eficientes basado en la teoría de Markowitz (Activos con Riesgos), quien ganó el Premio Nobel de Economía en 1990 por sus aportes al análisis de portafolios de inversión y a los métodos de financiación corporativa. Markowitz basándose en su teoría, define que para un rendimiento dado el riesgo que le deparan sea mínimo, éste modelo es el más eficiente a la hora de reducir riesgos. Por otro lado, si optamos por un portafolio óptimo de acivos sin riesgo nos apoyaremos en el Modelo de Sharpe, que establece una fijación de precios de activos financieros, en el cual un inversionista puede elegir una exposición al riesgo a través de una combinación de valores de renta fija y un portafolio de renta variabl...

En el presente trabajo, consideremos campos vectoriales holomorfos de dimensión compleja 3 deÖnidos en una vecindad de un punto p, donde p es una singularidad aislada, dicrÌtica o no. Es conocido que para campos holomorfos sobre un abierto de C2 que después de un número finito de blowing-up´s en los puntos singulares,la foliación asociada a dicho campo es transformada en una foliación que posee un número finito de singularidades, todas ellas irreducibles (Teorema de Seidenberg). En este trabajo se extiende el Teorema de Seidenberg para campos holomorfos sobre un abierto de C3, es decir, resolvemos el problema de desingularización sobre campos holomorfos 3-dimensiónales, restringiéndonos en el caso de que sea una singularidad absolutamente aislada. -- Palabras claves : Ecuaciones Diferenciales Ordinarias Complejas, Foliación Holomorfa Singular, Reducción de Singularidades, D...

In epidemiological mathematics, the SIR model is well known, as well as the diseases that can be simulated with this model. In the present work starting from a SIR model with vital dynamics, a host-vector model is elaborated, where the transmission of the disease is no longer given by interaction of individuals of the same species, but is carried out by interaction of the susceptible individuals with the infected individuals, of both populations. Two host-vector models (MVH) with vital dynamics are also developed, initially maintaining the population constant, then with variable population and death due to disease.

In epidemiological mathematics, the SIR model is well known, as well as the diseases that can be simulated with this model. In the present work starting from a SIR model with vital dynamics, a host-vector model is elaborated, where the transmission of the disease is no longer given by interaction of individuals of the same species, but is carried out by interaction of the susceptible individuals with the infected individuals, of both populations. Two host-vector models (MVH) with vital dynamics are also developed, initially maintaining the population constant, then with variable population and death due to disease.

In the present work, a perturbation of the model presented by Feng, Castillo-Chávez and Capurro (2000) will be carried out, where the dynamics of tuberculosis transmission will be described, where recovery from the disease will be incorporated. The model will include four epidemiological populations: Susceptible (S), Exposed (E), Infected (I) and Infected with treatment (T). This will allow to know how the interaction that exists with the infected can cause the permanence of the individuals with the disease. For which, its qualitative behavior will be analyzed as its evolution in time of the epidemiological populations for the model by the ordinary differential equations (ODE) and its perturbation to the dalay differential equations (DDE). In this way, it will allow us to know how the parameters influence the spread of the disease at the point free of infection and with a computational ...

In the present work, a perturbation of the model presented by Feng, Castillo-Chávez and Capurro (2000) will be carried out, where the dynamics of tuberculosis transmission will be described, where recovery from the disease will be incorporated. The model will include four epidemiological populations: Susceptible (S), Exposed (E), Infected (I) and Infected with treatment (T). This will allow to know how the interaction that exists with the infected can cause the permanence of the individuals with the disease. For which, its qualitative behavior will be analyzed as its evolution in time of the epidemiological populations for the model by the ordinary differential equations (ODE) and its perturbation to the dalay differential equations (DDE). In this way, it will allow us to know how the parameters influence the spread of the disease at the point free of infection and with a computational ...

In the present study, the computational modeling that describes the evolution and propagation of people susceptible to HIV-AIDS infection as well as Tuberculosis will be carried out. This additionally generates a coinfection in those infected that further complicates the epidemiological situation. Therefore, the presence of sanitary-epidemiological support personnel is important to consolidate prevention and control strategies. This epidemiological phenomenon could be modeled by differential equations, but we will focus on modeling by cellular automata to obtain computational simulations in time-space, and obtain possible scenarios and opt for the appropriate scenario to implement the most effective epidemiological strategies to obtain the results. better results and preserve the quality of life of society.