In Brazil, power supply safety criteria is established by the sector regulation, the power supply insufficiency risk must not exceed 5% limit. Thus, the tools that enable agents to model the rationing more accurately became necessary, estimating the impact caused by such kind of event and the future consequences. The official model used by Brazilian electric sector to carry out the expansion planning and medium/long-term operation is based on Stochastic Dual Dynamic Programming technique (SDDP). The main results that this model presents are the monthly evolution projection of Short Run Marginal Cost (SRMC) and hydrothermal dispatch, considering various hydrological scenarios. However, such model does not contain the representation of conjuncture changes occurred during a rationing, such as, for example, demand retraction and thermal dispatch out of merit order. This paper presents a new alternative to estimate rationing effects on power operation planning.
La diabetes, debido a sus complicaciones, es una de las enfermedades que m ás problemas plantean en la salud pública actual mundial. En este trabajo se parte de una población de diabéticos con y sin complicaciones y se asocia un problema de control optimal no lineal que describe la dinámica de la población. Para este modelo se prueba la existencia del estado de equilibrio y que es un punto de ensilladura. Además se obtuvo que no existen ciclos límite, lo que es un resultado importante, dado el problema que se describe. Se presentan ejemplos para los cuales el estado de equilibrio que se caracteriza no es necesariamente admisible.
In this paper, we develop a deterministic compartmental model for the obesity dynamics. Contrary to other contributions on this subject we explore the impact of the media on the spreading of this phenomenon in a constant population. Stability analysis shows that the disease-free equilibrium point is globally asymptotically stable when the number of reproduction is less than unity. We also show that the endemic equilibrium point when it exists is globally asymptotically stable under some conditions.
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