We introduce and analyse the so-called Fourier extension method for the approximation of oscillatory phenomena in bounded intervals. As we show, this method possesses good resolution properties for such problems. In particular, the resolution constant, the number of degrees of freedom per wavelength required to resolve an oscillation at a given frequency, can be varied between 2 and π by a user...

We present a multiscale finite element method (MFEM) for solving partial differential equations with highly oscillatory coefficients. MFEM provides a general and systematic framework for effectively capturing the large scale solutions without directly resolving the small scale details. This is accomplished by constructing the multiscale finite element base functions that are adaptive to the loc...

Abstract—In this work, we use the numerical steepest descent path (numerical SDP) method in complex analysis theory to calculate the highly oscillatory physical optics (PO) integral with quadratic phase and amplitude variations on the triangular patch. The Stokes’ phenomenon will occur due to various asymptotic behaviors on different domains. The stationary phase point contributions are careful...

Texture segmentation is a typical difficult problem in image processing. This paper presents a new textural oscillatory feature based on image decomposition. The oscillatory feature together with other textural features based on the structure tensor and nonlinear diffusion constructs a 5 dimensional textural feature space. The last result can be obtained by segmenting the feature space using le...

Based on locally excitatory globally inhibitory oscillator networks (LEGION), an object extraction method was proposed. The oscillation network can segment image and extracted objects by the scene and object feature. In this paper, the normalized difference water index (NDWI) was used as the feature of water body to segment remote sensing image. Because of the good coherence of spectrum propert...

The main purpose of this paper is to describe and analyse techniques for the numerical solution of highily oscillatory ordinary differential equations by exploying a Neumann expansion. Once the variables in the differential system are changed with respect to a rapidly rotating frame of reference, the Neumann method becomes very effective indeed. However, this effectiveness rests upon suitable q...

Let (un) be a sequence of real numbers and let L be an additive limitable method with some property. We prove that if the classical control modulo of the oscillatory behavior of (un) belonging to some class of sequences is a Tauberian condition for L, then convergence or subsequential convergence of (un) out of L is recovered depending on the conditions on the general control modulo of the osci...

Enhancement of heat and mass transfer and decrease of energy dissipation are great necessities of the evolution of fluid flow devices. Utilizing oscillatory or pulsatile fluid flow for periodic disturbing of velocity and thermal boundary layers is one of the methods with exciting results. Passive methods of generating oscillatory flow are preferred to active methods because of simplicity, no ne...

Oscillatory activity is a principal mode of operation in the brain. Despite an intense resurgence of interest in the mechanisms and functions of brain rhythms, methods for the detection and analysis of oscillatory activity in neurophysiological recordings are still highly variable across studies. We recently proposed a method for detecting oscillatory activity from time series data, which we ca...

BACKGROUND Gamma (γ) oscillations (30-50 Hz) have been shown to be excessive in patients with schizophrenia (SCZ) during working memory (WM). WM is a cognitive process that involves the online maintenance and manipulation of information that is mediated largely by the dorsolateral prefrontal cortex (DLPFC). Repetitive transcranial magnetic stimulation (rTMS) represents a non-invasive method to ...