In the present work it is indicated that the entropy of the information is the most appropriate tool to analyze the behavior of the flow of prices in the financial market. For this, the following points are mentioned: general concepts of chaos theory applied to the financial market, concept of dynamic systems applied to the flow of prices, time series of prices and the entropy of information applied to the flow of prices in the financial market.

Transfer of energy from large to small scales in turbulent flows is described as a flux of energy from small wave numbers to large wave numbers in the spectral representation of the Navier-Stokes equation. The problem of resolving the relevant scales in the flow corresponds in the spectral representation to determining the spectral truncation at large wave numbers. The effective number of degrees of freedom in the flow depends on the Reynolds number and a numerical simulation of the Navier Stokes equation for high Reynolds numbers is impractical without some sort of reduction of the number of degrees of freedom. The shell models are constructed to obey the same conservation laws and symmetries as the Navier Stokes equation as an alternative. In this work we present the Sabra shell model for the study of the energy cascade of turbulence and we will show numerically that the energy dissipation is approximately -1/3 which is in agreement with the theory K41.

In this research work, shell deformations generated by surface forces acting on the shell are described and simulated. The Naghdi and Koiter models are used to describe shell deformations. A weak formulation for the model is obtained, and some results on the existence of solutions are presented. The finite element method is then used to obtain the deformations. In addition, simulations of shell deformations are shown for the case of sectional curvature k = 0.

This study investigates conditions under which information dimension provides an upper bound for Hausdorff dimension using Shannon entropy and box occupancy. We establish a sufficient entropic condition and introduce the asymptotic entropic quotient, which measures the proportion of maximal entropy retained across scales. Its complement quantifies entropy loss, while its reciprocal defines an entropic correction factor. Cantor-type examples show that the quotient distinguishes distributions sharing the same geometric support. For finite samples, we justify a constrained least-squares estimator and develop a multi-criteria procedure for selecting the principal scaling window. The framework is applied to the Hénon, Lorenz, Ikeda, Rössler, and Chua double-scroll attractors, with sensitivity analyses for sample size and window selection. Estimated entropy losses range from 3.69% to 8.35%, and the entropic quotients remain stable across the tested conditions. The correction improves agreement with the reported Hausdorff dimension for Lorenz. For Hénon, it does not improve that agreement, although both estimates remain compatible with reported fractal dimensions. Results for Ikeda, Rössler, and Chua are consistent in scale with reported dimensions. Overall, the quotient provides distributional information beyond box occupancy and supports a finite-scale interpretation of entropy loss and its associated dimensional correction.

In the present work, necessary and sufficient optimality conditions are presented for the solution to a mínimum time problem. These conditions are established by the principle of the Pontryagin maximum, as a necessary and sufficient condition. In addition, the principle of the Pontryagin maximum is used in the search for the solution to an optimal control problem of mechanical origin. En el presente trabajo se presentan condiciones necesarias y suficientes de optimalidad para la solución a un problema de tiempo mínimo. Estas condiciones son establecidas por el principio del máximo de Pontryagin, como condición necesaria y suficiente. Además, se utiliza el principio del máximo de Pontryagin en la búsqueda de la solución a un problema de control óptimo de origen mecánico.

This paper presents an improved approach to measuring monetary poverty using a fuzzy methodology, specifically the recent model proposed by Belhadj and Bounani (2023). Using data from the National Household Survey for the province of Trujillo, La Libertad, Peru, the study demonstrates that this method provides a more detailed and continuous assessment of monetary poverty levels than traditional binary classifications. The fuzzy framework captures the intensity of deprivation experienced by individuals or households by assigning different degrees of membership to each poverty indicator, allowing the identification of intermediate situations that conventional methods typically ignore. The results reveal the existence of individuals or households that are not officially categorized as poor but exhibit deprivation patterns similar to those of the poor population. Identifying these vulnerable groups is essential for designing more inclusive and effective public policies, as it helps populations at risk of falling into poverty and supports a more precise targeting of social programs. Overall, the fuzzy approach offers a more sensitive and realistic representation of poverty dynamics in the study area, providing valuable information for decision-makers seeking to improve poverty-reduction strategies.