Spectral Point Of View Research Articles

Second-Order Elliptic Equation of Divergence Form Having a Compactly Supported Solution

An equation of the form -div (g∇u) = λu has a solution u of class C 0 ∞ , where g is a real positive definite matrix-valued function belonging to the Holder classes with exponent less than 1. From the spectral point of view, this means that there exists a Schrodinger operator with periodic metric and the spectrum of this operator contains an eigenvalue of infinite multiplicity. Bibliography: 9 titles.

Spectra of Arithmetic Infinite Graphs and Their Application

We discuss some properties of certain finite volume infinite graphs defined arithmetically, from a spectral point of view. These graphs are constructed from principal congruence subgroups over function fields and known to be Ramanujan diagrams.

Many-body theory of pump-probe spectra for highly excited semiconductors

We present a unified theory for pump-probe spectra in highly excited semiconductors, which is applicable throughout the whole density regime including the high-density electron-hole BCS state and the low-density excitonic Bose-Einstein condensate (BEC). The analysis is based on the BCS-like pairing theory combined with the Bethe-Salpeter (BS) equation, which first enables us to incorporate the state-filling effect, the band-gap renormalization and the strong/weak electron-hole pair correlations in a unified manner. We show that the electron-hole BCS state is distinctly stabilized by the intense pump-light, and this result strongly suggests that the macroscopic quantum state can be observed under the strong photoexcitation. The calculated spectra considerably deviate from results given by the BCS-like mean field theory and the simple BS equation without electron-hole pair correlation especially in the intermediate density states between the electron-hole BCS state and the excitonic BEC state. In particular, we find the sharp stimulated emission and absorption lines which originate from the optical transition accompanied by the collective phase fluctuation mode in the electron-hole BCS state. From the pump-probe spectral viewpoint, we show that this fluctuation mode changes to the exciton mode with decreasing carrier density

Statistical distribution and spectral analysis of rainfallanomalies for Barcelona (NE Spain)

Rainfall anomaly patterns are obtained for the city of Barcelona from a statistical and a spectral point of view. The time series consists of monthly rainfall amounts recorded over 128 years without interruption. Monthly positive and negative anomalies, obtained as the difference between monthly amounts and monthly threshold values, are used for both types of analyses. The threshold levels are derived form the deciles of theoretical monthly rainfall distributions, which have been previously modelled by the gamma distribution. Positive and negative anomalies of the monthly rain amounts are investigated for these threshold levels. The statistical analysis is applied to each decile considered, yielding empirical exponential laws that can be used to forecast the cumulative number of episodes of consecutive months with either positive or negative anomalies equalling or exceeding a fixed length. A set of linear laws, relating the expected rainfall amount cumulated during an episode of a fixed length, is also deduced. It is worthy of mention that, independently of the decile considered, all the exponential and linear laws have satisfactory regression coefficients. At the same time, it has also been possible to establish the evolution of the coefficients of these laws with respect to the different deciles considered. The exponential laws for episodes of positive and negative anomalies are the starting point, together with two hypotheses, to model probabilities of repeated long episodes over an arbitrary number of years and their return periods in terms of the Poisson distribution model. Moreover, power spectra are derived for anomalies relative to the 50% decile at monthly and seasonal scale. The spectral estimates obtained are then compared with theoretical spectra deduced from possible Markovian or random behaviour of the time series of anomalies. Finally, the significant spectral peaks are discussed and compared with other significant spectral components deduced for some areas of the Mediterranean domain.

A simple interpolation formula for the spectraofpower-law and log potentials

Non-relativistic potential models are considered of the pure power V(r) = sgn(q) r q and logarithmic V(r) = ln (r) types. It is shown that, fromthe spectral viewpoint, these potentials are actually in a single family.The log spectra can be obtained from the power spectra by the limit q→0 taken in a smooth representation Pnℓ(q) for theeigenvalues Enℓ(q). A simple approximation formula is developedwhich yields the first 30 eigenvalues withan error less than0.04%.

Recent advances in mangrove studies using remote sensing data

This paper summarizes present capabilities in studying mangrove vegetation from space. There is no standard image processing method that can be applied for the identification and delineation of coastal ecosystems. From a spectral point of view, it is practically impossible to characterize each of the sixty species of trees and shrubs that constitute the mangroves of the world. Nevertheless, some possibilities exist to map at global and at local scales mangrove areas from satellite products, combining several space data sets, interpretation of aerial photographs and ground surveys. The monitoring of mangroves can be considered as operational at a local level using remote sensing techniques, whereas monitoring of these ecosystems at global or at regional levels has not yet been achieved.

Global Creepex Distribution and Its Relation to Earthquake-Source Geometry and Tectonic Origin

SUMMARY The Ms:mb ratio, conventionally used for the discrimination of earthquakes and underground nuclear explosions, has been studied for a pure earthquake catalogue in an attempt to classify earthquakes into two categories, one related to extremely lowfrequency events of creep and the other to relatively high-frequency explosions. Ms and mb measured at 20 s and 1 s respectively are considered as estimates of source spectra at two separate points, thus allowing one to compare large samples of earthquakes from the spectral point of view. Creepex, or the deviation of (Ms, mfc)-points from the orthogonal regression of Ms on mb, is by definition a parameter independent of the size of seismic events. It has been estimated from NEIC magnitudes and is studied in relation to parameters of central moment tensor solutions of the Harvard group. For this purpose, the parameters of central moment tensors have been factorized to make classes of equivalence of events with the same dip and rake and arbitrary strike and size. the resulting triangle representation of source mechanisms has been used to correct the global distribution of creepex for the type of source mechanism. Dip-slip events have consistently lower creepex than strike-slip ones. However, the global distribution of creepex, either corrected or uncorrected for source mechanism, has a clear tectonic pattern: negative values in most of the subduction zones and positive ones in mid-ocean ridges. the dependence of creepex on focal depth is negligible according to empirical data for events shallower than 40 km. Limitation of the sample by considering only events in this depth range does not diminish considerably the amount of data and does not change the tectonic pattern of the creepex.

Geometry from the spectral point of view

In this Letter, we develop geometry from a spectral point of view, the geometric data being encoded by a triple (A. H. D.) of an algebraA represented in a Hilbert spaceH with selfadjoint operatorD. This point of view is dictated by the general framework of noncommutative geometry and allows us to use geometric ideas in many situations beyond Riemannian geometry.

Frequency analysis and synthesis of a class of nonlinear filters

Nonlinear filters are analyzed from a spectral point of view. The equivalent frequency behavior of a filter is described by its linear part, which represents the linear nonrecursive filter, that best matches, in the mean-square sense, the behavior of the filter. The class considered includes all the order statistic filters (L-filters) such as median, midrange, alpha-trim, and some new order statistic filters (Ll-filters) defined by the authors to generalize L-filters and FIR filters. The formulation leads to a technique for imposing on the nonlinear filters a given spectral behavior. A simulation of the design for a low-pass Ll-filter is given. >

Electromagnetic pulse propagation in dispersive planar dielectrics.

The responses of a plane-wave pulse train irradiating a lossy dispersive dielectric half-space are investigated. The incident pulse train is expressed as a Fourier series with summing done by the inverse fast Fourier transform. The Fourier series technique is adopted to avoid the many difficulties often encountered in finding the inverse Fourier transform when transform analyses are used. Calculations are made for propagation in pure water, and typical waveforms inside the dielectric half-space are presented. Higher harmonics are strongly attenuated, resulting in a single continuous sinusoidal waveform at the frequency of the fundamental depth in the material. The time-averaged specific absorption rate (SAR) for pulse-train propagation is shown to be the sum of the time-averaged SARs of the individual harmonic components of the pulse train. For the same average power, calculated SARs reveal that pulse trains generally penetrate deeper than carrier-frequency continuous waves but not deeper than continuous waves at frequencies approaching the fundamental of the pulse train. The effects of rise time on the propagating pulse train in the dielectrics are shown and explained. Since most practical pulsed systems are very limited in bandwidth, no pronounced differences between their response and continuous wave (CW) response would be expected. Typical results for pulse-train propagation in arrays of dispersive planar dielectric slabs are presented. Expressing the pulse train as a Fourier series provides a practical way of interpreting the dispersion characteristics from the spectral point of view.

Spectral aspects of the Gaussian beam method: reflection from a homogeneous half-space

Summary. Use of paraxially approximated Gaussian beams continues to be actively pursued for construction of synthetic seismograms in complicated environments. How to select the beams in the stack remains a source of difficulty which has primarily been addressed by semi-heuristic considerations. In this paper, the classical example of line-source field reflection from a homogeneous half-space that can sustain a head wave is examined from a plane-wave spectral point of view. The individual beam fields are modelled exactly by the complex source point technique, which emphasizes the complex spectral content of these wave objects. The quality of the paraxial approximation of a typical reflected (Gaussian) beam characterized by different parameters is examined from this perspective, and is compared with uniform and non-uniform asymptotics generated from the exact beam field spectral integral. With this information as background, the reflected field for a real line-source is synthesized by beam superposition. Except for the immediate vicinity of the critical reflection angle, the well-known failure of narrow paraxial beams, no matter how densely stacked, to reproduce the head wave effects is shown to be due to the inadequate spectral content of these beams and not to the failure of beam stacking per se. When the rigorous solutions are used for the narrow-waist beams, even relatively few suffice to yield agreement with the exact solution. This circumstance emphasizes the importance of fully understanding the spectral implications of various beam stacking schemes.

Spectral relationships between velocity and temperature fluctuations in turbulent shear flows

The frequency dependence of a turbulent Prandtl number, defined using the Reynolds shear stress and normal heat flux co-spectra, in various turbulent shear flows accentuates the inadequacy of the Reynolds analogy from a spectral point of view. For the same flows, the analogy between spectral distributions of the kinetic energy and the temperature variance is validated over a significant frequency domain. This analogy suggests a spectral parameter which is very close to unity in this frequency range for all the flows considered.

Effects of laser linewidth on coherent antiStokes Raman spectroscopy

Expressions for the generated antiStokes spectral density in coherent antiStokes Raman spectroscopy (CARS) are obtained, which take into account the finite linewidths of laser sources and which may be used to analyse observed spectra. Lorentzian and gaussian laser lineshapes are taken as special cases, which enable further analytic results for single and multiline CARS spectra to be derived. Emphasis is placed on scanning and broadband (multiplex) CARS techniques, and the choice of laser sources discussed from the spectral point of view. As examples of multiline spectra an analytical account of a periodic spectrum is presented and temperature measurement from Q-branch spectra is treated.

C-Mode Scan and Resolution Improvement Techniques for Ultrasonic Diagnosis

This paper presents a new method for obtaining plane images perpendicular to the axis of the transducer and discusses some resolution improvement techniques utilizing a computer. The method, called C-mode scan, is carried out by successive application of a conventional B-mode scan, and supplies more information such as the outline, size, and extent of a lesion such as a breast tumor. To improve the resolution of a transducer, a deconvolution technique together with non-linear filtering are employed from a spectral point of view. Several clinical images produced by C-mode and the computer improvement of resolution are demonstrated.