Principal Component Analysis In Radar Polarimetry

Second order moments of multivariate (often Gaussian) joint probability density functions can be described by the covariance or normalised correlation matrices or by the Kennaugh matrix (Kronecker matrix). In Radar Polarimetry the application of the covariance matrix is known as target decomposition theory, which is a special application of the extremely versatile Principle Component Analysis (PCA). The basic idea of PCA is to convert a data set, consisting of correlated random variables into a new set of uncorrelated variables and order the new variables according to the value of their variances. It is important to stress that uncorrelatedness does not necessarily mean independent which is used in the much stronger concept of Independent Component Analysis (ICA). Both concepts agree for multivariate Gaussian distribution functions, representing the most random and least structured distribution. </p><p style=&quot;line-height: 20px;&quot;> In this contribution, we propose a new approach in applying the concept of PCA to Radar Polarimetry. Therefore, new uncorrelated random variables will be introduced by means of linear transformations with well determined loading coefficients. This in turn, will allow the decomposition of the original random backscattering target variables into three point targets with new random uncorrelated variables whose variances agree with the eigenvalues of the covariance matrix. This allows a new interpretation of existing decomposition theorems

A Census Of Highly Symmetric Combinatorial Designs

As a consequence of the classification of the finite simple groups, it has been possible in recent years to characterize Steiner t-designs, that is t-(v,k,1) designs, mainly for t = 2, admitting groups of automorphisms with sufficiently strong symmetry properties. However, despite the finite simple group classification, for Steiner t-designs with t > 2 most of these characterizations have remained longstanding challenging problems. Especially, the determination of all flag-transitive Steiner t-designs with 2 < t < 7 is of particular interest and has been open for about 40 years (cf. [11, p. 147] and [12, p. 273], but presumably dating back to 1965). The present paper continues the author's work [20, 21, 22] of classifying all flag-transitive Steiner 3-designs and 4-designs. We give a complete classification of all flag-transitive Steiner 5-designs and prove furthermore that there are no non-trivial flag-transitive Steiner 6-designs. Both results rely on the classification of the finite 3-homogeneous permutation groups. Moreover, we survey some of the most general results on highly symmetric Steiner t-designs.Comment: 26 pages; to appear in: "Journal of Algebraic Combinatorics

Langzeitige Änderungen des Salzgehaltes in der Unterweser

Anhand hundertjähriger Meßreihen wurden langfristige Salzgehaltsänderungen in der Unterweser und ihre möglichen Ursachen untersucht. Dabei wurde angestrebt, die natürlichen und die anthropogenen Einflüsse auf den Salzgehalt zu trennen. Trotz des unvollständigen Datensatzes konnten der Einfluß des Einzugsgebietes und Salzgehaltsschwankungen des angrenzenden Meeresgebietes nahezu eliminiert werden. Wegen der langzeitigen Änderungen der Gezeiten in der Nordsee waren genaue Aussagen über die Auswirkung der in den letzten hundert Jahren in der Unterweser durchgeführten Baumaßnahmen auf den Salzgehalt nicht möglich. Unsere Ergebnisse geben Hinweise für moderne Meßnetze zur Bestimmung der Wasserqualität

Canonical Bases and Huyness Decomposition.

Es wird gezeigt, dass Huynen's Zerlegung kohaerenter Targets in symmetrische und unsymmetrische Targets in engem Zusammenhang steht mit der Diagonalisierung normaler Streumatrizen durch reelle orthogonale Transformationen

Plane Waveguides and the Riemann-Hilbert Method: An Alternative to the Wiener-Hopf-Technique.

Es wird gezeigt, da sich zwei neue kanonische Beugungsprobleme fuer Plattenwellenleiter mit zwei eingeschobenen Halbebenen, die von Rawlins nach der Daniele-Khrapkov-Methode loesbar sind, sich auch mit der Methode von Riemann-Hilbert behandeln lassen

Diffraction of an obliquely incident plane wave by a two-face impedance half plane: Wiener-Hopf approach

The problem of diffraction of plane electromagnetic waves at an imperfectly conducting half plane with different impedances on upper and lower faces for oblique (skew) incidence either leads to a Wiener-Hopf equation with a 4×4 Fourier symbol matrix for the tangential field components or to two formally decoupled Wiener-Hopf equations with 2×2 symbol matrices of the Daniele-Khrapkov form for the electric and magnetic field components perpendicular to the diffracting edge. The higher-order edge singularity of the normal field components leads to undetermined constants in the classical Wiener-Hopf solution that are used to eliminate `unphysical' leaky wave poles that appear in the final solution by the residue calculus technique. The interrelation between both formulations involves an analytic family of polynomial transformation matrices. Consideration of the range restriction of this mapping is shown to be equivalent to the pole elimination procedure

On Rawlin's Trifurcated Waveguide Problem.

Es wird gezeigt, dass ein 3-Teil-Parallel-Wellenleiterproblem mit zwei eingeschobenen Halbebenen mit Schallweichen und Schallkarten Randbedingungen, dessen Loesung vor kurzem von Rawlins angegeben wurde, sich auch nach der Riemann-Hilbert-Methode (Lueneburg/Westpfahl) loesen laesst