Best L1 approximations of the Heaviside function in Chebyshev and weak-Chebyshev spaces has a Gibbs phenomenon. It has been shown in the nineties for the trigonometric polynomial [1] and polygonal line cases [2]. By mean of recent results of characterization of best L1 approximation in Chebyshev and weak-Chebyshev spaces [3] that we recall, this Gibbs phenomenon can also be evidenced in the pol...

The Strukov model was the phenomenological model that accompanied the announcement of the first recognised physical instantiation of the memristor and, as such, it has been widely used. This model described the motion of a boundary, w, between two types of inter-converting material, Roff and Ron, seemingly under a uniform field across the entire device. In fact, what was intended was a field wi...

and His the Heaviside function, and C is the wave velocity in free space. The Green function has a long tail which means that we had to integrate the time of the whole history of the current [7] as shown in eqn. 4. However, in TDMEI, J(T,,, t ) need not be the true current distribution, and can be chosen arbitrarily to obtain the measuring functions. Thus currents with special waveforms in time...

We study the nonlinear elliptic problem with discontinuous nonlinearity −∆u = f(u)H(u− μ) in Ω, u = h on ∂Ω, where H is the Heaviside unit function, f, h are given functions and μ is a positive real parameter. The domain Ω is the unit ball in Rn with n ≥ 3. We show the existence of a positive solution u and a hypersurface separating the region where −∆u = 0 from the region where −∆u = f(u). Our...

We consider the existence and stability of traveling front solutions of a neural network consisting of a single–layer of neurons synaptically connected by lateral inhibition. For a specific ‘Mexican Hat’ coupling function, the existence condition for traveling fronts can be reduced to the solution of an algebraic system. Our work extends the existence of traveling fronts of the classic Amari mo...

We study the asymptotic behavior of the wave function in a simple one dimensional model of ionization by pulses, in which the time-dependent potential is of the form V (x, t) = −2δ(x)(1 − e cosωt), where δ is the Dirac distribution. We find the ionization probability in the limit t → ∞ for all λ and ω. The long pulse limit is very singular, and, for ω = 0, the survival probability is const λ, m...

a new approach for analyzing cracked problems in 2d orthotropic materials using the well-known element free galerkin method and orthotropic enrichment functions is proposed. the element free galerkin method is a meshfree method which enables discontinuous problems to be modeled efficiently. in this study, element free galerkin is extrinsically enriched by the recently developed crack-tip orthot...