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In this article we deal with a class of geometric inverse problem for bottom detection by one single measurement on the free surface in water--waves. We found upper and lower bounds for the size of the region enclosed between two different bottoms, in terms of Neumann and/or Dirichlet data on the free surface. Starting from the general water--waves system in bounded domains with side walls, we manage to formulate the problem in terms of the Dirichlet to Neumann operator and thus, as an elliptic problem in a bounded domain with Neumann homogeneous condition on the rigid boundary. Then we study the properties of the Dirichlet to Neumann map and analyze the called method of size estimation., Comment: version 2

In this work, we present an exploratory study of stability of an open pit mine in the north of Chile with the use of data mining. It is important to note that the study of slope stability is a subject of great interest to mining companies, this is due to the importance in the safety of workers and the protection of infrastructures, whether private or public, in those places susceptible to this kind of phenomena, as well as, for road slopes and close to communities or infrastructures, among others. It is also important to highlight that these phenomena can compromise important economic resources and can even cause human losses. In our case, this study seeks to increase the knowledge of these phenomena and thus, try to predict their occurrence, by means of risk indicators, potentially allowing the mining company supervision to consider predictive measures. It should be considered that there is no online test that ensures timely prediction. In previous studies conducted in other mines, it has been corroborated that the phenomena and factors associated with the movement of slopes and landslides are extremely complex and highly nonlinear, which is why the methods associated with the called "data mining", were found to be ideal for discovering new information in the data, which is recorded periodically in the continuous monitoring that mining companies have of their deposits, which allowed to find important correlations for the search of predictors of these phenomena. Some results, with data coming from different sources, are presented at the end of this work. We note that according to the information provided by the mining company, the results were favorable in the indicators of up to six months, giving as risk areas the correct sectors and predicting the April 2017 event.

In this paper we study the stability and deformation of structures, in particular the wall of an open pit mine is studied by using information obtained from a variety of remote sensors and some extra data, with a novelty approach considering the use of mathematical models and data mining techniques. In particular we present two models to help the study the slope stability of pit and the possible occurrence of movements. Primarily we present an static model for slow movements, which will help us identify areas of possible risks areas with time horizons of several months or years, depends on the available information, before the wall start moving, and secondly a dynamic short-term model, which help us to determine risks of collapse zones with several days in advance. We remark that this methodology can be a powerful tool to plain future actions in order to simulate possible scenarios considering the production plans.

In this work we are interested in estimating the size of a cavity D immersed in a bounded domain \Omega, contained in R^d, d=2,3, filled with a viscous fluid governed by the Stokes system, by means of velocity and Cauchy forces on the external boundary of \Omega. More precisely, we establish some lower and upper bounds in terms of the difference between the external measurements when the obstacle is present and without the object. The proof of the result is based on interior regularity results and quantitative estimates of unique continuation for the solution of the Stokes system.

In this paper we study a linear inverse problem with a biological interpretation, which is modeled by a Fredholm integral equation of the first kind. When the kernel in the Fredholm equation is represented by step func- tions, we obtain identifiability, stability and reconstruction results. Further- more, we provide a numerical reconstruction algorithm for the kernel, whose main feature is that a non-regular mesh has to be used to ensure the invert- ibility of the matrix representing the numerical discretization of the system. Finally, a second identifiability result for a polynomial approximation of degree less than nine of the kernel is also established.