This paper presents the calibration study of a two - dimensional mathematical model for the problem of urban air pollution. It is mainly assumed that air pollution is aected by wind convection, difusion and chemical reactions of pollutants. Consequently, a convection-diusion-reaction equation is obtained as a direct problem. In the inverse problem, the determination of the diusion is analyzed,assuming that one has an observation of the pollutants in a nite time. To solve it numerically the nite volume method is used, the least squares function is considered as cost function and the gradient is calculated with the sensitivity method.

This paper presents the calibration study of a two - dimensional mathematical model for the problem of urban air pollution. It is mainly assumed that air pollution is aected by wind convection, difusion and chemical reactions of pollutants. Consequently, a convection-diusion-reaction equation is obtained as a direct problem. In the inverse problem, the determination of the diusion is analyzed,assuming that one has an observation of the pollutants in a nite time. To solve it numerically the nite volume method is used, the least squares function is considered as cost function and the gradient is calculated with the sensitivity method.

This article deals with the asymptotic behavior of nonoscillatory solutions of fourth order linear differential equation where the coefficients are perturbations of linear constant coefficient equation. We define a change of variable and deduce that the new variable satisfies a third order nonlinear differential equation. We assume three hypotheses. The first hypothesis is related to the constant coefficients and set up that the characteristic polynomial associated with the fourth order linear equation has simple and real roots. The other two hypotheses are related to the behavior of theperturbation functions and establish asymptotic integral smallness conditions of the perturbations. Under these general hypotheses, we obtain four main results. The first two results are related to the application of a fixed point argument to prove that the nonlinear third order equation has a unique solu...

This article deals with the asymptotic behavior of nonoscillatory solutions of fourth order linear differential equation where the coefficients are perturbations of linear constant coefficient equation. We define a change of variable and deduce that the new variable satisfies a third order nonlinear differential equation. We assume three hypotheses. The first hypothesis is related to the constant coefficients and set up that the characteristic polynomial associated with the fourth order linear equation has simple and real roots. The other two hypotheses are related to the behavior of theperturbation functions and establish asymptotic integral smallness conditions of the perturbations. Under these general hypotheses, we obtain four main results. The first two results are related to the application of a fixed point argument to prove that the nonlinear third order equation has a unique solu...

The main objective of this research work is to determine the vector autoregressive _x000D_ models (VAR) that best predicts the unemployment rate, GDP and CPI in Peru. With the help _x000D_ of the R programming language applied in RStudio. The methodology of VAR models was used, _x000D_ where the analysis was consolidated in graphs, tests such as Dickey Fuller, Phillips Perron and _x000D_ the Kwiatkowski-Phillips-Schmidt-Shin (KPSS) test to determine if a time series is stationary _x000D_ around a trend, for the validation of the model it was incurred to apply the three basic tests _x000D_ through which a model must pass (VAR), the Jarque-Bera normality test, No Autocorrelation _x000D_ and the Heteroskedasticity test.In the process of searching for a VAR model, a residual _x000D_ normality problem was incurred since the Jarque-Bera test showed a p – value = 0.00, _x000D_ consequently, i...

En este documento se analiza la elección del rezago (truncación) que se utiliza en la aplicación de estadísticos de raíz unitaria tales como el ADFGLS y los tests MGLS propuestos por Elliott et al. (1996) y Ng y Perron (2001) y extendidos al contexto de cambio estructural por Perron y Rodríguez (2003). Dos modelos son considerados: uno que admite un cambio estructural en la pendiente y el otro que admite un cambio estructural en pendiente e intercepto, Se usan simulaciones de Monte Carlo usando varios métodos para seleccionar el largo del rezago: AIC, BIC, MAIC, MBIC. También se incluye y analiza la performance de la propuesta híbrida sugerida por Perron y Qu (2007) la cual usa MCO en lugar de MCG para eliminar los componentes determinísticos cuando se construyen los criterios de información. Todos estos métodos se comparan con el método secuencial t-sig que está basado en ...

En el año 1917 el matemático japonés Soichi Kakeya propuso el siguiente problema conocido mundialmente como el Problema de la aguja de Kakeya: ¿Cuál es el área mínima que se requiere para rotar continuamente un segmento de línea de longitud 1 en el plano, de manera que después del giro vuelva a ocupar su posición original pero con los extremos invertidos? De la pregunta anterior se ve claramente que el giro es de 180° e implícitamente se pide que tal conjunto con área mínima, conocido como conjunto de Kakeya, sea convexo. Este problema tendría una solución trivial a no ser por una restricción: EL ÁREA DEBE SER MÍNIMA ... pero si no fuera por esto dejaría de ser interesante pues fácilmente giraríamos este segmento de línea unitario(al que llamaremos aguja) por su punto medio y así se barreña un área ¡ (que corresponde al círculo de radio ~)- Esta solución triv...