In geodesy, hypothesis testing is applied to a wide area of applications e.g. outlier detection, deformation analysis or, more generally, model optimisation. Due to the possible far-reaching consequences of a decision, high statistical test power of such a hypothesis test is needed. The Neyman-Pearson lemma states that under strict assumptions the often-applied likelihood ratio test has highest statistical test power and may thus fulfill the requirement. The application, however, is made more difficult as most of the decision problems are non-linear and, thus, the probability density function of the parameters does not belong to the well-known set of statistical test distributions. Moreover, the statistical test power may change, if linear approximations of the likelihood ratio test are applied. The influence of the non-linearity on hypothesis testing is investigated and exemplified by the planar coordinate transformations. Whereas several mathematical equivalent expressions are conceivable to evaluate the rotation parameter of the transformation, the decisions and, thus, the probabilities of type 1 and 2 decision errors of the related hypothesis testing are unequal to each other. Based on Monte Carlo integration, the effective decision errors are estimated and used as a basis of valuation for linear and non-linear equivalents.
EPR of Fe3+ in distorted tetrahedral sites in single crystals of β-Ga2O3 has been measured for the first time, and the second-order zero-field splitting (ZFS) parameters and principal axes directions were determined. The data for the sixfold coordinated Fe3+ are in good agreement with results from the literature. Comparison of the ZFS patterns with those calculated from the crystal structure data using the superposition model (SPM) shows reasonable agreement in the orientations of the principal axes, but only for the tetrahedral site is a reasonable value of the intrinsic ZFS parameter obtained. Besides large uncertainties in the sizes of the distortions the crystal structure data also appear to be systematically wrong. For Cr3+ in sixfold coordinated sites the discrepancies are even larger, but for this ion a reduced validity of the SPM may also be involved.
A series of new planar bis(α,β-dionedioximato) metal(II) complexes of the ions Ni(II), Pd(II), Pt(II)using unsymmetrically substituted glyoximes as ligands are reported. Typical ligands being unsymmetrically substituted benzildioximes, phenylglyoxime or butan-1,2-dionedioxime.The solid state properties and in some cases the X-ray data suggest, that most of the isolated complexes crystallize in columnar stacks. Compared with the known symmetrical derivatives the solubility of the isolated neutral compounds in organic solvents like ethanol, chloroform or 1,2-dichlorobenzene is highly increased. Most of the compounds can therefore be obtained in good crystalline form. The good solubility is an advantage in the efforts to extend the polarizable ligand system of the complexes.