Tafeln zur harmonischen Analyse periodischer Kurven,

"Berichtigung" slip inserted following p. [2]

Statistical theory of communication.

Mode of access: Internet.

Winding patterns for biplanar MRI shim coils with rectangular and circular target-field regions

A method is presented for calculating the winding patterns required to design independent zonal and tesseral biplanar shim coils for magnetic resonance imaging. Streamline, target-field, Fourier integral and Fourier series methods are utilized. For both Fourier-based methods, the desired target field is specified on the surface of the conducting plates. For the Fourier series method it is possible to specify the target field at additional depths interior to the two conducting plates. The conducting plates are confined symmetrically in the xy plane with dimensions 2a x 2b, and are separated by 2d in the z direction. The specification of the target field is symmetric for the Fourier integral method, but can be over some asymmetric portion pa < x < qa and sb < y < tb of the coil dimensions (-1 < p < q < 1 and -1 < s < t < 1) for the Fourier series method. Arbitrary functions are used in the outer sections to ensure continuity of the magnetic field across the entire coil face. For the Fourier series case, the entire field is periodically extended as double half-range sine or cosine series. The resultant Fourier coefficients are substituted into the Fourier series and integral expressions for the internal and external magnetic fields, and stream functions on both the conducting surfaces. A contour plot of the stream function directly gives the required coil winding patterns. Spherical harmonic analysis of field calculations from a ZX shim coil indicates that example designs and theory are well matched.

Probabilistic Approach to the Neumann Problem for a Symmetric Operator

2000 Mathematics Subject Classification: Primary 60J45, 60J50, 35Cxx; Secondary 31Cxx.

Pseudo-Reimannian metrics with parallel spinor fields and vanishing Ricci tensor

I discuss geometry and normal forms for pseudo-Riemannian metrics with parallel spinor fields in some interesting dimensions. I also discuss the interaction of these conditions for parallel spinor fields with the condition that the Ricci tensor vanish (which, for pseudo-Riemannian manifolds, is not an automatic consequence of the existence of a nontrivial parallel spinor field).

Is the Russell Cycle a true cycle? Multidecadal zooplankton and climate trends in the western English Channel

The Russell Cycle is one of the classical examples of climate influence on biological oceanography, represented as shifts in the marine plankton over several decades with warm and cool conditions. While the time-series data associated with the phenomenon indicate cyclical patterns, the question remains whether or not the Russell Cycle should be considered a “true cycle”. Zooplankton time-series data from 1924 to 2011 from the western English Channel were analysed with principal component (PC), correlation and spectral analyses to determine the dominant trends, and cyclic frequencies of the Russell Cycle indicators in relation to long-term hydroclimatic indices. PC1 accounted for 37.4% of the variability in the zooplankton data with the main contributions from non-clupeid fish larvae, southwestern zooplankton, and overall zooplankton biovolume. For PC2 (14.6% of data variance), the dominant groups were northern fish larvae, non-sardine eggs, and southern fish larvae. Sardine eggs were the major contributors to PC3 (representing 12.1% of data variance). No significant correlations were observed between the above three components and climate indices: Atlantic Multidecadal Oscillation, North Atlantic Oscillation, and local seawater temperature. Significant 44- and 29-year frequencies were observed for PC3, but the physical mechanisms driving the cycles are unclear. Harmonic analysis did not reveal any significant frequencies in the physical variables or in PCs 1 and 2. To a large extent, this is due to the dominant cycles in all datasets generally being long term (>50 years or so) and not readily resolved in the examined time frame of 88 years, hence restricting the ability to draw firm conclusions on the multidecadal relationship between zooplankton community dynamics in the western English Channel and environmental indices. Thus, the zooplankton time-series often associated and represented as the Russell Cycle cannot be concluded as being truly cyclical.

Is the Russell Cycle a true cycle? Multidecadal zooplankton and climate trends in the western English Channel

The Russell Cycle is one of the classical examples of climate influence on biological oceanography, represented as shifts in the marine plankton over several decades with warm and cool conditions. While the time-series data associated with the phenomenon indicate cyclical patterns, the question remains whether or not the Russell Cycle should be considered a “true cycle”. Zooplankton time-series data from 1924 to 2011 from the western English Channel were analysed with principal component (PC), correlation and spectral analyses to determine the dominant trends, and cyclic frequencies of the Russell Cycle indicators in relation to long-term hydroclimatic indices. PC1 accounted for 37.4% of the variability in the zooplankton data with the main contributions from non-clupeid fish larvae, southwestern zooplankton, and overall zooplankton biovolume. For PC2 (14.6% of data variance), the dominant groups were northern fish larvae, non-sardine eggs, and southern fish larvae. Sardine eggs were the major contributors to PC3 (representing 12.1% of data variance). No significant correlations were observed between the above three components and climate indices: Atlantic Multidecadal Oscillation, North Atlantic Oscillation, and local seawater temperature. Significant 44- and 29-year frequencies were observed for PC3, but the physical mechanisms driving the cycles are unclear. Harmonic analysis did not reveal any significant frequencies in the physical variables or in PCs 1 and 2. To a large extent, this is due to the dominant cycles in all datasets generally being long term (>50 years or so) and not readily resolved in the examined time frame of 88 years, hence restricting the ability to draw firm conclusions on the multidecadal relationship between zooplankton community dynamics in the western English Channel and environmental indices. Thus, the zooplankton time-series often associated and represented as the Russell Cycle cannot be concluded as being truly cyclical.

Détection, reconstruction 3D et identification des êtres vivants du règne animal

L’automatisation de la détection et de l’identification des animaux est une tâche qui a de l’intérêt dans plusieurs domaines de recherche en biologie ainsi que dans le développement de systèmes de surveillance électronique. L’auteur présente un système de détection et d’identification basé sur la vision stéréo par ordinateur. Plusieurs critères sont utilisés pour identifier les animaux, mais l’accent a été mis sur l’analyse harmonique de la reconstruction en temps réel de la forme en 3D des animaux. Le résultat de l’analyse est comparé avec d’autres qui sont contenus dans une base évolutive de connaissances.

Influence of Cobalt on the Properties of Load-Sensitive Magnesium Alloys

In this study, magnesium is alloyed with varying amounts of the ferromagnetic alloying element cobalt in order to obtain lightweight load-sensitive materials with sensory properties which allow an online-monitoring of mechanical forces applied to components made from Mg-Co alloys. An optimized casting process with the use of extruded Mg-Co powder rods is utilized which enables the production of magnetic magnesium alloys with a reproducible Co concentration. The efficiency of the casting process is confirmed by SEM analyses. Microstructures and Co-rich precipitations of various Mg-Co alloys are investigated by means of EDS and XRD analyses. The Mg-Co alloys' mechanical strengths are determined by tensile tests. Magnetic properties of the Mg-Co sensor alloys depending on the cobalt content and the acting mechanical load are measured utilizing the harmonic analysis of eddy-current signals. Within the scope of this work, the influence of the element cobalt on magnesium is investigated in detail and an optimal cobalt concentration is defined based on the performed examinations.

Mean and variance of estimates of the bispectrum of a harmonic random process-an analysis including leakage effects

Analytical expressions are derived for the mean and variance, of estimates of the bispectrum of a real-time series assuming a cosinusoidal model. The effects of spectral leakage, inherent in discrete Fourier transform operation when the modes present in the signal have a nonintegral number of wavelengths in the record, are included in the analysis. A single phase-coupled triad of modes can cause the bispectrum to have a nonzero mean value over the entire region of computation owing to leakage. The variance of bispectral estimates in the presence of leakage has contributions from individual modes and from triads of phase-coupled modes. Time-domain windowing reduces the leakage. The theoretical expressions for the mean and variance of bispectral estimates are derived in terms of a function dependent on an arbitrary symmetric time-domain window applied to the record. the number of data, and the statistics of the phase coupling among triads of modes. The theoretical results are verified by numerical simulations for simple test cases and applied to laboratory data to examine phase coupling in a hypothesis testing framework