We are interested in the asymptotic behavior of the solution to the Cauchy problem for the linear evolution equation iε∂tψ = A(t)ψ, A(t) = A0 + V (t), ψ(0) = ψ0, in the limit ε → 0. A case of special interest is when the operator A(t) has continuous spectrum and the initial data ψ0 is, in particular, an improper eigenfunction of the continuous spectrum of A(0). Under suitable assumptions on A(t...

This paper presents a mathematical approach to properly account for uncertainty in wind resource assessment and wind energy production estimation. The evaluation of a wind resource and the subsequent estimation of the annual energy production (AEP) is a highly uncertain process. Uncertainty arises at all points in the process, from measuring the wind speed to the uncertainty in a power curve. A...

in this paper, we present a fractional mathematical model of a one-dimensional phase phase change problem (stefan problem) with latent heat a power function of position. this model includes space-time fractional derivatives in caputo sense and time dependent surface heat flux. an approximate solution of this model is obtained by optimal homotopy asymptotic method (oham) to find an approximate s...

in this paper we apply the homotopy perturbation method to derive the higher-order asymptotic distribution of the eigenvalues and eigenfunctions associated with the linear real second order equation of sturm-liouville type on $[0,pi]$ with neumann conditions $(y'(0)=y'(pi)=0)$ where $q$ is a real-valued sign-indefinite number of $c^{1}[0,pi]$ and $lambda$ is a real parameter.

the asymptotic behaviour of the sequence with general term $p_n=(varphi(1)+varphi(2)+cdots+varphi(n))/(1+2+cdots+n)$, is studied which appears in the studying of coprime integers, and an explicit bound for the difference $p_n-6/pi^2$ is found.

Prolate spheroidal wave functions have recently attracted much attention in applied harmonic analysis, signal processing, and mathematical physics. They are eigenvectors of the sinc-kernel operator Qc: time- band-limiting operator. The corresponding eigenvalues play a key role, aim this paper is to obtain precise non-asymptotic estimates with explicit constants related spectrum Qc. This issue r...

Integrate and fire oscillators are widely used to model the generation of action potentials in neurons. In this paper, we discuss small noise asymptotic results for a class of stochastic integrate and fire oscillators (SIFs) in which the buildup of membrane potential in the neuron is governed by a Gaussian diffusion process. To analyze this model, we study the asymptotic behavior of the spectru...