The space of solutions to the Hessian one equation in the finitely punctured plane

We construct the space of solutions to the elliptic Monge-Ampere equation det(D^2 u)=1 in the plane R^2 with n points removed. We show that, modulo equiaffine transformations and for n>1, this space can be seen as an open subset of R^{3n-4}, where the coordinates are described by the conformal equivalence classes of once punctured bounded domains in the complex plane of connectivity n-1. This approach actually provides a constructive procedure that recovers all such solutions to the Monge-Ampere equation, and generalizes a theorem by K. Jorgens.Comment: 14 pages, 3 figure

MODEL ORDER REDUCTION OF NONLINEAR DYNAMIC SYSTEMS USING MULTIPLE PROJECTION BASES AND OPTIMIZED STATE-SPACE SAMPLING

Model order reduction (MOR) is a very powerful technique that is used to deal with the increasing complexity of dynamic systems. It is a mature and well understood field of study that has been applied to large linear dynamic systems with great success. However, the continued scaling of integrated micro-systems, the use of new technologies, and aggressive mixed-signal design has forced designers to consider nonlinear effects for more accurate model representations. This has created the need for a methodology to generate compact models from nonlinear systems of high dimensionality, since only such a solution will give an accurate description for current and future complex systems.The goal of this research is to develop a methodology for the model order reduction of large multidimensional nonlinear systems. To address a broad range of nonlinear systems, which makes the task of generalizing a reduction technique difficult, we use the concept of transforming the nonlinear representation into a composite structure of well defined basic functions from multiple projection bases.We build upon the concept of a training phase from the trajectory piecewise-linear (TPWL) methodology as a practical strategy to reduce the state exploration required for a large nonlinear system. We improve upon this methodology in two important ways: First, with a new strategy for the use of multiple projection bases in the reduction process and their coalescence into a unified base that better captures the behavior of the overall system; and second, with a novel strategy for the optimization of the state locations chosen during training. This optimization technique is based on using the Hessian of the system as an error bound metric.Finally, in order to treat the overall linear/nonlinear reduction task, we introduce a hierarchical approach using a block projection base. These three strategies together offer us a new perspective to the problem of model order reduction of nonlinear systems and the tracking or preservation of physical parameters in the final compact model

Analysis of heavy rainfall in two contrasted Mediterranean watersheds from 1993 to 2017

"Despite the proximity of the watersheds there are strong" "environmental contrasts between both." "• The current rainfall dynamics follows a trend towards concentration in fewer days." "• A rainfall cataloged as torrential by the AEMET (≥ 100 / 24h, ≥60 mmh-1) is not necessary to activate erosion and degradation processes, especially when the system conditions are vulnerable. There are downpours hidden in the hourly precipitation data that get at very high intensities." "• It is considered the need to analyze exhaustively the characteristics of a given system, in order to establish what capacity of response has a specific area in an event of extreme precipitation.

The geomorphological rainfall in the Mediterranean landscape modeling

The kinetic energy derived from the heavy rainfall constitutes one of the main factors of the geomorphological processes in Mediterranean environments, as well as in the landscape and the ecosystem modeling, resulting from its extraordinary spatial and temporal variability. When the rainfall is analyzed, particularly in Mediterranean climate and in the context of Climate Change, it is not only necessary to consider the total rainfall collected annually, but also it is essential to take into account other variables as intensity, duration, and frequency. A series of extreme rainfall databases have been analyzed for the last 25 years (1993-2017), with daily, horary and 10-minutes registers. These have been obtained from different weather stations belonging to the Agencia Estatal de Meteorología –AEMET- and the S.A.I.H. Hydrosur Network, spatially distributed in two regions of the province of Malaga. (Guadalhorce and Axarquía). The results show the limited frequency of the events considered as torrential rainfall according to the Agencia Estatal de Meteorología criteria ( 100mm/24h; 60mm/60’) and a high occurrence of shorts heavy downpours ( 10mm/10’), especially in recent years. These downpours have been classified as “geomorphological rainfall”, short events capable of activating hydro-soil processes, owing to its high intensity and the vulnerable conditions of the eco-geomorphological system in the study areas

Study of the return-on-investment surface of a small chemical plant

A study of the return-on-investment (ROI) surfaces for a single reactor chemical plant (Westbrook (8)) with a discontinuous investment function confirms its unimodality in the valid region. In both cases studied, the return-on-investment surfaces rise smoothly to the adiabatic boundary from a singular flow rate below which two of the component flow are not physically realizable. The optimum is located on the adiabatic boundary. Comparison with these surfaces shows that using linear regression to obtain the parameters for an algebraic simulation of investment does not yield ROI values acceptably near the optimal. However, an heuristic approach, which assumes that minimizing the recycle heat exchanger area requires the optimal design to lie on the adiabatic boundary, was correct --Abstract, page ii