Foundations of estimation theory

The application of estimation theory renders the processing of experimental results both rational and effective, and thus helps not only to make our knowledge more precise but to determine the measure of its reliability. As a consequence, estimation theory is indispensable in the analysis of the measuring processes and of experiments in general.The knowledge necessary for studying this book encompasses the disciplines of probability and mathematical statistics as studied in the third or fourth year at university. For readers interested in applications, comparatively detailed chapter

Linear conform transformation: Errors in both coordinate systems

summary:Linear conform transformation in the case of non-negligible errors in both coordinate systems is investigated. Estimation of transformation parameters and their statistical properties are described. Confidence ellipses of transformed nonidentical points and cross covariance matrices among them and identical points are determined. Some simulation for a verification of theoretical results are presented

Regression models with a weak nonlinearity

SIGLEAvailable from TIB Hannover: RO 7297(1998,1) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekAlexander von Humboldt-Stiftung (AvH), Bonn (Germany)DEGerman

Azole assisted C-H bond activation promoted by an osmium-polyhydride: Discerning between N and NH

This is an open access article published under a Creative Commons Attribution (CC-BY) License.The capacity of the hexahydride complex OsH6(PiPr3)2 (1) to discern between the nitrogen atom and the NH unit in the azole assisted aryl C−H bond activation has been investigated. Complex 1 reacts with 2-phenylimidazole to give OsH3{κ2-C,N-(C6H4-imidazole)}(PiPr3)2 (2), which has been characterized by X-ray diffraction analysis. The structure proves the higher affinity of the metal center for the N atom in the presence of the NH unit, which remains unchanged, and reveals that in the solid state the molecules of this complex form infinite chains by means of intermolecular asymmetric 3-center bifurcated dihydrogen bonds. In solution, 1HDOSY NMR experiments suggest that the association degree decreases as the temperature increases. The fused six-membered ring of benzimidazole weakens the NH bond, enhancing its reactivity. As a consequence, complex 1 cannot discern between the N atom and the NH unit of 2-phenylbenzimidazole. Thus, the treatment of 1 with this substrate leads to a mixture of OsH3{κ2-C,N-(C6H4-benzimidazole)}(PiPr3)2 (3) and the dinuclear species (PiPr3)2H3Os(C6H4-benzimidazolate)OsH(η2-H2)(PiPr3)2 (4). The latter is the result of a N-assisted ortho-C−H bond activation of the phenyl group promoted by 0.5 equiv of 1 and the N−H bond activation promoted by the remaining 0.5 equiv of hexahydride 1 along with the agostic coordination of the remaining ortho-C−H bond to the metal center of the unsaturated fragment OsH(η 2-H2)(PiPr3)2. The comparison of the redox properties of 3 and 4 suggests that the interaction between the metal centers in the dinuclear compound is negligible. The replacement of the NH group of the azoles by a sulfur atom does not modify the behavior of the substrates. Thus, the reactions of 1 with 2-phenylthiazole and 2-phenylbenzothiazole afford OsH3{κ 2-C,N-(C6H4-thiazole)}(PiPr3)2 (5) and OsH3{κ2-C,N-(C6H4-benzothiazole)}(PiPr3)2 (6). In turn, complexes 2, 3, 5, and 6 are phosphorescent.Financial support from the Spanish MINECO and FEDER (Projects CTQ2013-46459-C2-01-P to M.A.S., CTQ2014-52799-P to M.A.E., CTQ2013-44303-P to I.F., CTQ2014-54071-P to A.L., and CTQ2014-51912-REDC, the DGA (E35), and the European Social Fund (FSE) is acknowledged.Peer Reviewe