Approximation of certain functions given by integrals with highlyoscillatory integrands

There is often a need to approximate integrals of highly oscillatory functions when studying scattering and diffraction of electromagnetic waves. This paper presents a method of estimating certain types of these integrals by evaluating one interpolating function and performing one or two relatively easy numerical integrations. The method is demonstrated for the case of a Fresnel integral     

Radar target discrimination using the extinction-pulse technique

An aspect independent radar target discrimination scheme based on the natural frequencies of the target is considered. An extinction-pulse waveform upon excitation of a particular conducting target results in the elimination of specified natural modal content of the scattered field. Excitation of a dissimilar target produces a noticeably different late-time response. Construction of appropriate extinction-pulse waveforms is discussed, as well as the effects of random noise on their application to thin cylinder targets. Also presented is experimental verification of this discrimination concept using simplified aircraft models.     

Accurate evaluation of Sommerfeld integrals using the fast Fouriertransform

It is shown that the fast Fourier transform (FFT) combines naturally with Simpson's rule for Sommerfeld-type integral computation. The principal advantage of using the FFT is that a single subroutine call yields a set of sample values of an integral (i.e. the integral for various values of an integrand parameter). Such samples could be useful in themselves. In other applications Sommerfeld integrals represent Green's functions nested within other spatial integrals, so samples from the FFT might be useful in approximating the outernested integral. Several examples are provided to illustrate the process     

Solid state NMR characterisation of the thermal transformation of Fuller's Earth

Fuller's Earth, a dioctahedral calcium montmorillonite clay mineral of the smectite group, undergoes thermal transformation via a series of complex intermediate states that are highly structurally disordered. Fuller's Earth is a commercially significant material with considerable levels of paramagnetic iron (Fe3+) substitution into octahedrally coordinated metal sites. Despite the high iron-content (approximately 10% of the occupied octahedral metal sites) in these samples 29Si and 27Al magic angle spinning (MAS) NMR spectra of sufficient quality are obtained to reveal structural changes in samples that have been heated from room temperature to 1400 degrees C. Two major structural changes are clearly observed, initial dehydroxylation and then collapse of the layer structure into more highly connected silica-rich domains and an alumina-rich phase.     

A continuation method for identification of the natural frequencies of an object using a measured response

The identification of the natural frequencies of an object using measured data is an ill-conditioned problem. A method and algorithm to solve the problem based on regularization by a continuation method is presented. The algorithm is applied to the measured response of a model aircraft, and the superiority of this method to Prony's method in the presence of noise is demonstrated.     

Two methods to deconvolve: L1-method using simplex algorithm and L2-method using least squares and parameter

Ifr(t)is the linear scattering response of an object to an excitation waveforme(t), thenr(t) = (e ast h) (t). One would like to deconvolve and solve forh(t), the impulse response. It is well-known that this is often an ill-conditioned problem. Two methods are discussed. The first method replaces the discretized matrix formE cdot H = Rby the following problem. Minimize|h_{1}|+ ldots + |h_{n}|subject toR - lambda leq E cdot H leq R + lambdawherelambdais a column vector chosen sufficiently small to yield acceptable residuals, yet large enough to make the problem well-conditioned. This problem is converted to a linear programming problem so that the simplex algorithm can be used. The second method is to minimizeparallel E cdot H - R parallel^{2} +lambda parallel H parallel^{2}where againlambdais chosen small enough to yield acceptable residuals and large enough to make the problem well-conditioned. The method will be demonstrated with a Hilbert matrix inversion problem, and also by the deconvolution of the impulse response of a simple target from measured data.     

Are muscle fibers denervated in myotonic dystrophy?

An underlying neurogenic abnormality has recently been postulated in the muscular dystrophies. To test this hypothesis, we applied a widely accepted criterion of denervation-ie, and increase in extrajunctional acetyicholine (ACh) receptor sites--to muscles biopsy specimens from nine patients with myotonic dystrophy and three with amyotrophic lateral scierosis (ALS). The ACh receptor sites were determined by means of iodine 125-labeled alpha-bungarotoxin binding, measured by scintillation counting and autoradiography. None of the myotonic dystrophy muscles showed increased extrajunctiona ACh receptor sites, even in the smallest fibers. By contrast, muscle biopsy specimens from patients with ALS showed notably increased extrajunctional ACh receptor sites, especially in the small fibers. Our findings do not support the hypothesis of a neurogenic defect in myotonic dystrophy.