the rock masses in a construction site of underground cavern are generally not continuous, due to the presence of discontinuities, such as bedding, joints, faults, and fractures. the performance of an underground cavern is principally ruled by the mechanical behaviors of the discontinuities in the vicinity of the cavern. during underground excavation, many surrounding rock failures have close r...

Neural continuum networks are an important aspect of the modeling of macroscopic parts of the cortex. Two classes of such networks are considered: voltage and activity based. In both cases, our networks contain an arbitrary number, n, of interacting neuron populations. Spatial nonsymmetric connectivity functions represent cortico-cortical, local connections, and external inputs represent nonloc...

As follows from the Schwartz Impossibility Theorem, multiplication of two distributions is in general impossible. Nevertheless, often one needs to multiply a distribution by a discontinuous function, not by an arbitrary distribution. In the present paper we construct a space of distributions where the general operation of multiplication by a discontinuous function is defined, continuous, commut...

We examine the e ect of constraining the number of hidden units For one hidden layer networks with fairly general type of units including perceptrons with any bounded activation function and radial basis function units we show that when also the size of parameters is bounded the best approximation property is satis ed which means that there always exists a parameterization achieving the global ...

A new method for constructing Clifford algebra-valued orthogonal polynomials in the open unit ball of Euclidean space is presented. In earlier research, we only dealt with scalar-valued weight functions. Now the class of weight functions involved is enlarged to encompass Clifford algebra-valued functions. The method consists in transforming the orthogonality relation on the open unit ball into ...

The theory of distributions in non-Riemannian spaces is used to obtain exact static thin domain wall solutions of Einstein-Cartan equations of gravity. Curvature δ-singularities are found while Cartan torsion is given by Heaviside functions. Weitzenböck planar walls are caracterized by torsion δ-singularities and zero curvature. It is shown that Weitzenböck static thin domain walls do not exist...

This paper is devoted to the study of inhomogeneous wave equation with singular (less than continuous) time dependent coefficients. Particular attention given role lower order terms and suitable Levi conditions are formulated in obtain a very weak solution as introduced [15]. Very solutions for this kind equations also investigated from numerical point view two toy models: Heaviside function de...

A methodology for solving three-dimensional crack problems with geometries that are independent of the mesh is described. The method is based on the extended 5nite element method, in which the crack discontinuity is introduced as a Heaviside step function via a partition of unity. In addition, branch functions are introduced for all elements containing the crack front. The branch functions incl...