Identifying the sources of oscillatory activity in the human brain is a challenging problem in current magnetoencephalography (MEG) and electroencephalography (EEG) research. The fluctuations in phase and amplitude of cortical oscillations preclude signal averaging over successive sections of the data without a priori assumptions. In addition, several sources at different locations often produc...

We present a numerically stable way to compute oscillatory integrals of the form ∫ 1 −1 f(x)e iωg(x) dx. For each additional frequency, only a small, well-conditioned linear system with a Hessenberg matrix must be solved, and the amount of work needed decreases as the frequency increases. Moreover, we can modify the method for computing oscillatory integrals with stationary points. This is the ...

In a recent publication [4] the author developed an extrapolation method, the ^-transformation, for the accurate computation of convergent oscillatory infinite integrals. In yet another publication [6] this method was shown to be applicable to divergent oscillatory infinite integrals that are defined in the sense of summability. The application of the VK-transformation involves some asymptotic ...

This paper will focus on identifying the interacting dynamic phenomena in power systems by using continuation of invariant subspaces (CIS). With this approach one can trace the trajectory of different oscillatory modes as system parameter changes. Many power system dynamic phenomena, such as strong resonance, subsynchronous resonance (SSR) et al., are related to the interaction of oscillatory m...

The integrable focusing nonlinear Schrödinger equation admits soliton solutions whose associated spectral data consist of a single pair conjugate poles arbitrary order. We study families such multiple-pole solitons generated by Darboux transformations as the pole order tends to infinity. show that in an appropriate scaling, there are four regions space-time plane where display qualitatively dis...

Objectives: To examine the characteristics of evoked and induced gamma band oscillatory responses occurring during P300 development in an auditory oddball paradigm. Methods: A time-frequency analysis method was applied to an auditory oddball paradigm in 7 healthy subjects. This method combines a multiresolution wavelet algorithm for signal extraction and the Gabor transform to represent the tem...

The essentially non-oscillatory (ENO) method is an efficient high order numerical method for solving hyperbolic conservation laws designed to reduce the Gibbs oscillations, if existent, by adaptively choosing the local stencil for the interpolation. The original ENO method is constructed based on the polynomial interpolation and the overall rate of convergence provided by the method is uniquely...

|Reaction-diiusion systems whose kinetics contain a stable limit cycle are an established class of models for a range of oscillatory biological and chemical phenomena. In this paper, the author compares two numerical methods for calculating the oscillatory wake solutions generated by spatially localized perturbations for one particular reaction-diiusion system, of-! type. The two methods are a ...

The previous studies of authors on passive micromixers indicated that the micromixers dividing the flow to several layers, such as rhombus micromixers and micromixers with obstacles in the middle of the mixing channel, have higher mixing degree than other types. Also, using of oscillatory inlet velocities is an active method to enhance the mixing efficiency of micromixers. Therefore, in this st...

We introduce a new numerical strategy to solve a class of oscillatory transport PDE models which is able to capture accurately the solutions without numerically resolving the high frequency oscillations in both space and time. Such PDE models arise in semiclassical modeling of quantum dynamics with band-crossings, and other highly oscillatory waves. Our first main idea is to use the nonlinear g...