We analyze the spatiotemporal dynamics of a system of integro-differential equations that describes a one-dimensional excitatory neuronal network with synaptic depression and spike frequency adaptation. Physiologically suggestive forms are used for both types of negative feedback. We also consider the effects of employing two different types of firing rate function, a Heaviside step function an...

In this paper, one of the simplest and most regular members of the family of the Meshless Local Petrov-Galerkin (MLPG) methods; namely MLPG5, is applied to analyze the thick-walled isotropic laminated cylinders under elasto-static pressure. A novel simple technique is proposed to eliminate a very important difficulty of the meshless methods to deal with material discontinuities regarding to the...

A truly Meshless Local Petrov-Galerkin (MLPG) method is developed for solving 3D elasto-static problems. Using the general MLPG concept, this method is derived through the local weak forms of the equilibrium equations, by using a test function, namely, the Heaviside step function. The Moving Least Squares (MLS) are chosen to construct the shape functions. The penalty approach is used to impose ...

Abstract We rigorously investigate the rapidly oscillating contributions in sinc-function representation of Dirac delta function and Fourier transform Coulomb potential. Beginning with a derivation standard integral Heaviside step function, we examine that contains sinc function. By contour integration, prove satisfies properties although it is divergent at nonzero points. This good pedagogical...

This paper introduces a new approach to the recursive propagation of probability density functions through discrete-time stochastic nonlinear dynamic systems. An efficient recursive procedure is proposed that is based on the optimal approximation of the posterior densities after each prediction step by means of Dirac mixtures. The parameters of the individual components are selected by systemat...

We propose a geometrically nonlinear extended isogeometric analysis approach for cohesive fracture. A shifting technique is used to enforce compatibility in the direction perpendicular crack path, while blending has been adopted remove effect of discontinuity extension crack. Bézier extraction employed cast formulation finite element datastructure. The use sign function instead Heaviside step r...

An inconsistent boundary condition in eq 2 was corrected. This change does not in any way alter the results or the conclusions of the paper. Page1549, column1, line11. The text reads as follows: “In Laplace space, each transition is modeled with a Heaviside step function, Rp(s) =ΔRp/s, whereΔRp is the instantaneous change in pore resistance, per unit time. We can obtain an expression for the na...

of mathematical symbols used Symbol Description Units λ 0,X Emission/observation wavelength m r Range from instrument m z Vertical height above the instrument m c Speed of light in vacuum m s −1 H[x] Heaviside step function, which equals unity for x > 0 and zero otherwise — P (λ, r) Number of photons observed at wavelength λ from range r counts η(λ) Instrument detection efficiency at λ — σ(λ) S...

A time-domain adaptive algorithm was developed for solving elasto-dynamics problems through a mixed meshless local Petrov-Galerkin finite volume method (MLPG5). In this time-adaptive algorithm, each time-dependent variable is interpolated by time series function of n-order, which determined criterion in step. The high-order expanded variables bring high accuracy the domain, especially elasto-dy...