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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.

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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.

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