In this paper we study the existence of Lelong numbers of m−subharmonic currents of bidimension (p, p) on an open subset of C n , when m+p ≥ n. In the special case of m−subharmonic function ϕ, we give a relationship between the Lelong numbers of dd c ϕ and the mean values of ϕ on spheres or balls. As an application we study the integrability exponent of ϕ. We express the integrability exponent of ϕ in terms of volume of sub-level sets of ϕ and we give a link between this exponent and its Lelong number.2010 Mathematics Subject Classification. 32U25; 32U40; 32U05.
Abstract. This paper presents an application of two advanced approaches, Artificial Neural Networks (ANN) and Principal Component Analysis (PCA) in predicting the axial pile capacity. The combination of these two approaches allowed the development of an ANN model that provides more accurate axial capacity predictions. The model makes use of Back-Propagation Multi-Layer Perceptron (BPMLP) with Bayesian Regularization (BR), and it is established through the incorporation of approximately 415 data sets obtained from data published in the literature for a wide range of uncemented soils and pile configurations. The compiled database includes, respectively 247 and 168 loading tests on largeand low-displacement driven piles. The contributions of the soil above and below pile toe to the pile base resistance are pre-evaluated using separate finite element (FE) analyses. The assessment of the predictive performance of the new method against a number of traditional SPT-based approaches indicates that the developed model has attractive capabilities and advantages that render it a promising tool. To facilitate its use, the developed model is translated into simple design equations based on statistical approaches.
A neural network is, in essence, an attempt to simulate the brain. Neural network theory revolves around the idea that certain key properties of biological neurons can be extracted and applied to simulations, thus creating a simulated (and very much simplified) brain. The first important thing to understand then is that the components of an artificial neural network are an attempt to recreate the computing potential of the brain. This famous network memorizes information by a process of training, to this effect the theory of artificial neural network is developed and is applied in several fields of sciences. The geotechnical domain is among them and in particular the resolution of problems of which parameters that govern them have an uncertain character, as the case of the prediction of the pile capacity. For it we collected 120 cases of the literature, sweeping a variety of sites through the world. The model conceived by an iterative process that is, the retropropagation was validated by experimental tests and was compared with the values predicted by four of the most commonly used traditional methods. In this paper, the developed neural network model is based on the principal component analysis approach (PCA) for data analysis in the aim to improve the generalization process. The results indicate that the ANN model is able to accurately predict the capacity in several cases, including the experiments on model piles. The PCA technique shows the efficiency in the variable analysis in order to determine their relative contribution on the pile capacity and improve the generalization capacity. This study is limited for the driven piles.
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