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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Journal of statistical physics 76 (1994), S. 1005-1043 
    ISSN: 1572-9613
    Keywords: Wave propagation ; spatiotemporal bifurcation theory ; biorthogonal decomposition ; Fourier analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract By using biorthogonal decompositions, we show how uniformly propagating waves, togehter with their velocity, shape, and amplitude, can be extracted from a spatiotemporal signal consisting of the superposition of various traveling waves. The interaction between the different waves manifests itself in space-time resonances in case of a discrete biorthogonal spectrum and in resonant wavepackets in case of a continuous biorthogonal spectrum. Resonances appear as invariant subspaces under the biorthogonal operator, which leads to closed sets of algebraic equations. The analysis is then extended to superpositions of dispersive waves for which the (Fourier) dispersion relation is no longer linear. We then show how a space-time bifurcation, namely a qualitative change in the spatiotemporal nature of the solution, occurs when the biorthogonal operator is a nonholomorphic function of a parameter. This takes place when two eigenvalues are degenerate in the biorthogonal spectrum and when the spatial and temporal eigenvectors rotate within each eigenspace. Such a scenario applied to the superposition of traveling waves leads to the generation of additional waves propagating at new velocities, which can be computed from the spatial and temporal eigenmodes involved in the process (namely the shape of the propagating waves slightly before the bifurcation). An eigenvalue degeneracy, however, does not necessarily lead to a bifurcation, a situation we refer to as being self-avoiding. We illustrate our theoretical predictions by giving examples of bifurcating and self-avoiding events in propagating phenomena.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    BIT 34 (1994), S. 177-204 
    ISSN: 1572-9125
    Keywords: 65F10 ; 15A06 ; 65F90 ; 65K10 ; Conjugate gradient method ; preconditioning ; incomplete factorization ; polynomial preconditioner ; matrix-free method ; Fourier analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Preconditioning strategies based on incomplete factorizations and polynomial approximations are studied through extensive numerical experiments. We are concerned with the question of the optimal rate of convergence that can be achieved for these classes of preconditioners. Our conclusion is that the well-known Modified Incomplete Cholesky factorization (MIC), cf. e.g., Gustafsson [20], and the polynomial preconditioning based on the Chebyshev polynomials, cf. Johnson, Micchelli and Paul [22], have optimal order of convergence as applied to matrix systems derived by discretization of the Poisson equation. Thus for the discrete two-dimensional Poisson equation withn unknowns,O(n 1/4) andO(n 1/2) seem to be the optimal rates of convergence for the Conjugate Gradient (CG) method using incomplete factorizations and polynomial preconditioners, respectively. The results obtained for polynomial preconditioners are in agreement with the basic theory of CG, which implies that such preconditioners can not lead to improvement of the asymptotic convergence rate. By optimizing the preconditioners with respect to certain criteria, we observe a reduction of the number of CG iterations, but the rates of convergence remain unchanged.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Journal of High Resolution Chromatography 17 (1994), S. 839-850 
    ISSN: 0935-6304
    Keywords: Capillary GC ; Chemometry ; Fourier analysis ; Multicomponent mixture chromatograms ; PCB analysis ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Aroclor and Aroclor mixture chromatograms obtained using temperature programmed high resolution capillary GC coupled with mass spectrometric selective detection have been investigated by Fourier analysis developed for the study of multicomponent chromatograms. The experimental autocorrelation function (EACF), i.e. peak shape and position correlation, showed a retention - structure pattern which could be associated with both the type of Aroclor and the ion used for selective ion monitoring (m/z value). In particular, o-m and m-m isomerization effects were singled out by EACF analysis. By fitting EACF with previously developed theoretical models, it was possible to characterize a specific Aroclor in terms of the number of PCB congeners present in it. The results obtained agreed closely with the typical Aroclor content. For the Aroclor mixture, the distribution of inter-distance between successive peaks was derived. The two first distribution moments obtained agreed with those derived from retention data reported in the literature. The consequences on the separation performance, i.e. the number of singlets, doublets, etc. in the chromatogram, are discussed.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
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  • 4
    ISSN: 1615-2573
    Keywords: Source pressure ; Fourier analysis ; Contraction duration ; Shortening deactivation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Summary By fitting isovolumic phases of an ejecting beat with a model-wave function, one can predict source pressure of the ejecting beat (Sunagawa et al.Trans Biomed Eng 1980; 27:299–305), this being a major determinant of systolic performance. Prior applications of this principle have involved two assumptions: (1) that the isovolumic pressure wave is shaped like an inverted cosine wave, and (2) that duration of an isovolumic beat is the same as that of an ejecting beat. The first assumption might cause overestimation of source pressure, since an isovolumic pressure wave begins declining before the midpoint of the wave. The second assumption might cause underestimation of source pressure, since an ejecting beat is always shorter than an adjacent isovolumic beat at the ejecting beat's enddiastolic volume. Although the two errors tend to cancel, it would be more rational and accurate to use a realistic model wave shape and a realistic isovolumic beat duration. To acquire the information necessary for this, pressure and volume time courses were measured during ejecting beats and adjacent isovolumic beats in dogs under the following steady-state conditions: basal, atrial pacing at various rates, infusion of dobutamine, infusion of verapamil, coronary ligation(s), and ventricular pacing at various sites. These conditions affected the amplitude and duration of isovolumic pressure waves substantially but did not affect the shape of the waves significantly. The duration of each isovolumic beat exceeded that of the previous ejecting beat to a degree which corresponded approximately to the ejecting beat's normalized pressure reserve (source pressure minus peak ejection pressure)/(source pressure). A more accurate source-pressure prediction should be possible by use of a realistic isovolumic pressure-wave shape and by taking account of the effect of pressure reserve on contraction duration.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Annals of the Institute of Statistical Mathematics 44 (1992), S. 13-25 
    ISSN: 1572-9052
    Keywords: Fourier analysis ; array estimation ; velocity estimation ; space-time spectral analysis ; random media ; random arrays ; frequency wavenumber processing
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Consider the situation where a plane wave signal is received by a spatial arrangement of recorders. Information derived from observations on such a process can be used to determine the speed and direction of the signal together with properties of the medium through which the signal is being propagated. Certain models for the case where the signal velocity can be regarded as stochastic and where the array is irregular are investigated and estimation procedures proposed. A major practical property of these models is that, unlike their deterministic counterparts, coherence decays to zero as distance between recorders increases.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Hydrobiologia 247 (1992), S. 109-117 
    ISSN: 1573-5117
    Keywords: Crassostrea cucullata ; Fourier analysis ; shell form ; shell length ; regression analysis ; environmental factors
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract Variations of shell form and shell length were studied for oysters growing in the mangroves of Gazi Creek, Kenya, and related to different environmental factors. For the study of the form, Fourier analysis was performed on the circumference of 85 oysters. The resulting coefficients were compared among specimens using cluster analysis. The correspondence between this classification and substrate diameter is virtually perfect (only one misclassification out of 85 oysters). For the clusters based on height above chart datum, 9 specimens, all on intermediate height levels, were misclassified. Orientation with respect to tidal current had 13 misclassifications. Mangrove species seemed to influence form only marginally, if at all. In the study of the size ofCrassostrea cucullata, the length of 956 oysters, growing along two transects were measured, and correlated with several environmental factors. Oyster length was not related to substrate diameter or its orientation with respect to the main current. Length was not influenced by density up to a cover of 70%. For densities higher than 70%, there was a fairly strong negative correlation (r 2 = 0.634,n = 217). Length was not correlated with height above bottom (base of the tree) for heights lower than 20 cm, while oysters growing closer to the bottom were smaller. The correlation with height above chart datum was negative but very low (r 2 = 0.060,n = 957). However, if all measurements of oysters closer than 20 cm to the bottom, and all from a density of more than 70% cover are deleted from the data set, the correlation with height increased dramatically, the slope still being negative (r 2 = 0.859,n = 543).
    Type of Medium: Electronic Resource
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  • 7
    ISSN: 1619-7089
    Keywords: Technetium-99m methoxyisobutylisonitrile single photon emission tomography (SPET) ; Amplitude images ; Fourier analysis ; Thallium-201 SPET
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Abstract To determine the role of rest and stress gated technetium-99m methoxyisobutylisonitrile (sestamibi), in the detection of coronary artery disease, routine Fourier analysis of these images was performed with the best septal left anterior oblique (LAO) position of 20 patients (17 men, 3 women; aged 40–75 years) who also underwent rest or redistribution/stress single photon emission tomography (SPET) (99mTc-sestamibi and Thallium-201), gated blood pool imaging and coronary angiogram. There were 6 patients with single-vessel disease, 6 with two-vessel disease, 4 with three-vessel disease, 2 with coronary spasms, 1 with a patent graft and 1 with anginal episodes but a normal angiogram result. Three normal volunteers (2 women, 1 man; aged 24–26 years) also had rest and stress gated blood pool as well as rest and stress gated 99mTc-sestamibi imaging. Rest and stress 99mTc-ses-tamibi amplitude and phase images depicted regional myocardial wall shortening from the outer layer of the myocardium to the center of the left ventricle as follows a high amplitude halo of maximal negative count rate variaton; a circular thinner halo of negligible amplitude; a central region of maximal positive count rate variation, as the images evolved from end-diastole to end-systole. Similar patterns with regional differences represented abnormal myocardial wall shortening. (99mTc-sestamibi and 201T1 SPET) images were in agreement in 90% of the patients and 92% of myocardial regions. 201T1 SPET detected 83% of angiographically proven lesions, as compared with 80% for 99mTc-setamibi SPET and 80% for the amplitude images. The amplitude images demonstrated a larger number of other abnormalities not predicted on the angiogram, probably because they were able to detect regions with a potential for flow improvement and transient regional wall shortening abnormalities. Amplitude and phase analyses of gated rest and stress 99mTc-ses-tamibi images are easy to perform and may become an important adjunct to (99mTc-sestamibi SPET) images for a complete evaluation of both regional myocardial perfusion and regional contractile function using a single tracer.
    Type of Medium: Electronic Resource
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  • 8
    ISSN: 1573-6792
    Keywords: Obsessive-compulsive disorder ; EEG ; Theta rhythm ; Fourier analysis ; Coefficient of variations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Summary Spectral EEG characteristics of thirteen patients with severe Obsessive-Compulsive Disorder (OCD) were investigated topographically. The finding of predominantly left posterior frontal to mid-temporal theta-2 is discussed in light of previous EEG studies and recent neuroradiologic findings.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    Springer
    Brain topography 4 (1992), S. 309-319 
    ISSN: 1573-6792
    Keywords: Principal components ; Isotropicity ; Complex statistics ; Electroencephalography ; Equivalent dipoles ; Fourier analysis ; Brain mapping
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Summary The structure of the normal resting EEG crosspectrum Svv(ω) is analyzed using complex multivariate statistics. Exploratory data analysis with Principal Component Analysis (PCA) is followed by hypothesis testing and computer simulations related to possible neural generators. The Svv(ω) of 211 normal individuals (ages 5 to 97) may be decomposed into two types of processes: the ξ process with spatial isotropicity reflecting diffuse, correlated cortical generators with radial symmetry, and processes that seem to be generated by more spatially concentrated, correlated sources. The latter are reflected as spectral peaks such as the process. The eigenvectors of the ξ process are the Spherical Harmonic Functions which explains the recurring pattern of maps characteristic of the spatial PCA of qEEG data. A new method for estimating sources in the frequency domain which fits dipoles to the whole crosspectrum is applied to explain the characteristics of the localized sources.
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    Springer
    European journal of applied physiology 63 (1991), S. 300-307 
    ISSN: 1439-6327
    Keywords: Oxygen uptake ; Carbon dioxide output ; Ventilation ; Pseudorandom binary sequence ; Fourier analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Summary The dynamics of ventilation (VE), oxygen uptake (VO2), carbon dioxide output (VCO2), and heart rate (f c) were studied in 12 healthy young men during upright and supine exercise. Responses to maximal and to two different types of submaximal exercise tests were contrasted. During incremental exercise to exhaustion, the maximal work rate, VO2max, VEmax, f c,max, and ventilatory threshold were all significantly reduced in supine compared to upright exercise (P〈0.01–0.001). Following step increases or decreases in work rate between 25 W and 105 W, both VO2 and VCO2 responded more slowly in supine than upright exericse. Dynamics were also studied in two different pseudorandom binary-sequence (PRBS) exercise tests, with the work rate varying between 25 W and 105 W with either 5-s or 30-s durations of each PRBS unit. In both of these tests, there were no differences caused by body position in the amplitude or phase shifts obtained from Fourier analysis for any observed variable. These data show that the body position alters the dynamic response to the more traditional step increase in work rate, but not during PRBS exercise. It is speculated that the elevation of cardiac output observed with supine exercise in combination with the continuously varying work-rate pattern of the PRBS exercise allowed adequate, perhaps near steady-state, perfusion of the working muscles in these tests, whereas at the onset of a step increase in work rate, greater demands were placed on the mechanisms of blood flow redistribution.
    Type of Medium: Electronic Resource
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  • 11
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 13 (1991), S. 579-597 
    ISSN: 0271-2091
    Keywords: Diffusion-convection ; Fourier analysis ; Stability ; Artificial viscosity ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper develops a stability analysis of second-order, two- and three-time-level difference schemes for the 2D linear diffusion-convection model problem. The corresponding 1D schemes have been extensively analysed in two previous papers by the same author. Most of these 2D schemes obviously generalize 1D schemes, i.e. their stencil only uses the nearest points and defines ‘product difference schemes’; however, the stability results are not always the exact generalization of the 1D stability properties. Moreover, the 1D nonviscous MFTCS scheme may only be generalized if one uses a nine-point scheme. Numerical experiments for different values of the cell Reynolds number allow a comparison to be made between the theoretical and numerical stability limits.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
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  • 12
    Electronic Resource
    Electronic Resource
    Springer
    Documenta ophthalmologica 76 (1990), S. 65-71 
    ISSN: 1573-2622
    Keywords: Coefficient of variation ; domain of frequency ; domain of time ; Fourier analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Abstract The dark-adapted and light-adaped electroretinograms of 13 subjects with 23 normal eyes were analyzed by means of Fourier spectrum. The oscillatory potentials in the time domain were filtered out from the electroretinogram after a corresponding bandpass was given in the frequency domain. The coefficient of variation of total power, dominant power and dominant frequency of the isolated oscillatory potentials in the frequency domain, summed amplitudes and area of the isolated oscillatory potentials, each amplitude and implicit time of the first four major oscillatory potential wavelets in the time domain were compared. The implicit time showed the smallest coefficient of variation; summed amplitudes of OP1 to OP4 showed smaller coefficients of variation than those of the area, the amplitude of each oscillatory potential wavelet, dominant frequency and dominant and total power. The coefficient of variation of these measurement parameters in light-adapted electroretinograms was smaller than those in dark-adapted electroretinograms.
    Type of Medium: Electronic Resource
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  • 13
    ISSN: 1741-0444
    Keywords: Aortic regurgitation ; Arterial compliance ; Fourier analysis ; Impedance ; Mean aortic pressure ; Peripheral resistance ; Windkessel model
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Chemistry and Pharmacology , Medicine
    Notes: Abstract Three methods for measuring arterial compliance when aortic regurgitation is present are examined. The first two methods are based on a Windkessel model composed of two elements, compliance C and resistance R. Arterial compliance was estimated from diastolic pressure waveforms and diastolic regurgitant flow for one method, and from systolic aortic pressure waveforms and systolic flow for the other method. The third method was based on a three-element Windkessel model, composed of characteristic resistance r, compliance C and resistance R. In this method arterial compliance was calculated by adjusting the model to the modulus and phase of the first harmonic term of the aortic input impedance. The three methods were compared and validated in six anaesthetised pigs over a broad range of aortic pressures. The three methods were found to give quantitatively similar estimates of arterial compliance at mean aortic pressures above 60 mm Hg. Below 60 mm Hg, estimates of arterial compliance varied widely, probably because of poor validity of the Windkessel models in the low pressure range.
    Type of Medium: Electronic Resource
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  • 14
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 11 (1990), S. 427-444 
    ISSN: 0271-2091
    Keywords: Fourier analysis ; Eulerian-Lagrangian ; Least squares ; Transport ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A Fourier analysis was performed in order to study the numerical characteristics of the effective Eulerian-Lagrangian least squares collocation (ELLESCO) method. As applied to the transport equation, ELLESCO requires a C1-continuous trial space and has two degrees of freedom per node. Two coupled discrete equations are generated for a typical interior node for a one-dimensional problem. Each degree of freedom is expanded separately in a Fourier series and is substituted into the discrete equations to form a homogeneous matrix equation. The required singularity of the system matrix leads to a ‘physical’ amplification factor that characterizes the numerical propagation of the initial conditions and a ‘computational’ one that can affect stability.Unconditional stability for time-stepping weights greater than or equal to 0-5 is demonstrated. With advection only, ELLESCO accurately propagates spatial wavelengths down to 2Δx. As the dimensionless dispersion number becomes large, implicit formulations accurately propagate the phase, but the higher-wave-number components are underdamped. At large dispersion numbers, phase errors combined with underdamping cause oscillations in Crank-Nicolson solutions. These effects lead to limits on the temporal discretization when dispersion is present. Increases in the number of collocation points per element improve the spectral behaviour of ELLESCO.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
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