This paper investigates the commonly overlooked “sensitivity” of sensitivity analysis (SA) to what we refer to as parameter “perturbation scale”, which can be defined as a prescribed size of the sensitivityrelated neighbourhood around any point in the parameter space (analogous to step size Dx for numerical estimation of derivatives). We discuss that perturbation scale is inherent to any (local...

the current paper focuses on some analytical techniques to solve the non-linear duffing oscillator with large nonlinearity. four different methods have been applied for solution of the equation of motion; the variational iteration method, he’s parameter expanding method, parameterized perturbation method, and the homotopy perturbation method. the results reveal that approximation obtained by th...

We introduce a method of observer design for systems described by a linear part with a nonlinear perturbation, where the perturbation is parameterized by a vector of unknown, constant parameters. The design is modular, and consists of a modified high-gain observer that estimates the states of the system together with the full perturbation, and a parameter estimator. The parameter estimator is c...

We prove nonlinear stability in L 1 of planar shock front solutions to a viscous conservation law in two spatial dimensions, and obtain an expression for the asymptotic form of small perturbations. The leading-order behavior is shown rigorously to be governed by an eeective diiusion coeecient depending on forces transverse to the shock front. The proof is based on a spectral analysis of the lin...

Provided the velocity of the medium is known and the the medium does not allow different reflectors to have identical surface seismic measurements that persist under small perturbations of the medium, map migration achieves a one-to-one mapping from surface seismic data to the subsurface seismic image by using the slopes in addition to the location (and time) of the events in the data. In this ...

The supergenerator of superparamagnetic system quantum evolution is investigated in discrete orientation model (DOM). It is shown that the generator is J-self-adjoint one at the case of potential drift field agreed upon magnetic anisotropy of the sample investigated. Perturbation theory is used for spectral analysis. The qualitative dependence of resonance absorption spectrum on the relation be...

A rigorous accuracy analysis is given to various techniques for estimating parameters of geometric models from noisy data. It is first pointed out that parameter estimation for computer vision applications is very different in nature from traditional statistical analysis and that a different mathematical framework is necessary in such a domain. After general theories on estimation and accuracy ...

The age-old problem of the quark mass function in QCD is examined afresh with special reference to the infrared behavour of the gluon propagator with small mass (m g). Linear confinement in the instantaneous limit is ensured by a non-perturbative term proportional to k −4 , obtained via two differentiations: µ 2 ∂ 2 m (m 2 g + k 2) −1 , µ being another scale (to be determined). With this input,...

The quark mass problem is revisited, regarding the infrared behaviour of the gluon propagator with small mass (m g). Linear confinement in the instantaneous limit is ensured by a non-perturbative term 2µ 2 /(k 2 + m 2 g) −2 , µ being another scale (to be determined). Now, we propose a new (differential) form of the Dyson-Schwinger Equation (DSE) for solving the mass function Σ(p), based on a su...