Increasing scepticism toward potential liars: effects of existential threat on veracity judgments and the moderating role of honesty norm activation

With the present research, we investigated effects of existential threat on veracity judgments. According to several meta-analyses, people judge potentially deceptive messages of other people as true rather than as false (so-called truth bias). This judgmental bias has been shown to depend on how people weigh the error of judging a true message as a lie (error 1) and the error of judging a lie as a true message (error 2). The weight of these errors has been further shown to be affected by situational variables. Given that research on terror management theory has found evidence that mortality salience (MS) increases the sensitivity toward the compliance of cultural norms, especially when they are of focal attention, we assumed that when the honesty norm is activated, MS affects judgmental error weighing and, consequently, judgmental biases. Specifically, activating the norm of honesty should decrease the weight of error 1 (the error of judging a true message as a lie) and increase the weight of error 2 (the error of judging a lie as a true message) when mortality is salient. In a first study, we found initial evidence for this assumption. Furthermore, the change in error weighing should reduce the truth bias, automatically resulting in better detection accuracy of actual lies and worse accuracy of actual true statements. In two further studies, we manipulated MS and honesty norm activation before participants judged several videos containing actual truths or lies. Results revealed evidence for our prediction. Moreover, in Study 3, the truth bias was increased after MS when group solidarity was previously emphasized.

On Vessiot's Theory of Partial Differential Equations

The object of research presented here is Vessiot's theory of partial differential equations: for a given differential equation one constructs a distribution both tangential to the differential equation and contained within the contact distribution of the jet bundle. Then within it, one seeks n-dimensional subdistributions which are transversal to the base manifold, the integral distributions. These consist of integral elements, and these again shall be adapted so that they make a subdistribution which closes under the Lie-bracket. This then is called a flat Vessiot connection. Solutions to the differential equation may be regarded as integral manifolds of these distributions. In the first part of the thesis, I give a survey of the present state of the formal theory of partial differential equations: one regards differential equations as fibred submanifolds in a suitable jet bundle and considers formal integrability and the stronger notion of involutivity of differential equations for analyzing their solvability. An arbitrary system may (locally) be represented in reduced Cartan normal form. This leads to a natural description of its geometric symbol. The Vessiot distribution now can be split into the direct sum of the symbol and a horizontal complement (which is not unique). The n-dimensional subdistributions which close under the Lie bracket and are transversal to the base manifold are the sought tangential approximations for the solutions of the differential equation. It is now possible to show their existence by analyzing the structure equations. Vessiot's theory is now based on a rigorous foundation. Furthermore, the relation between Vessiot's approach and the crucial notions of the formal theory (like formal integrability and involutivity of differential equations) is clarified. The possible obstructions to involution of a differential equation are deduced explicitly. In the second part of the thesis it is shown that Vessiot's approach for the construction of the wanted distributions step by step succeeds if, and only if, the given system is involutive. Firstly, an existence theorem for integral distributions is proven. Then an existence theorem for flat Vessiot connections is shown. The differential-geometric structure of the basic systems is analyzed and simplified, as compared to those of other approaches, in particular the structure equations which are considered for the proofs of the existence theorems: here, they are a set of linear equations and an involutive system of differential equations. The definition of integral elements given here links Vessiot theory and the dual Cartan-Kähler theory of exterior systems. The analysis of the structure equations not only yields theoretical insight but also produces an algorithm which can be used to derive the coefficients of the vector fields, which span the integral distributions, explicitly. Therefore implementing the algorithm in the computer algebra system MuPAD now is possible.

Theory for the Photoacoustic Response to X-Ray Absorption

A microscopic theory is presented for the photoacoustic effect induced in solids by x-ray absorption. The photoacoustic effect results from the thermalization of the excited Auger electrons and photoelectrons. We explain the dependence of the photoacoustic signal S on photon energy and the proportionality to the x-ray absorption coefficient in agreement with recent experiments on Cu. Results are presented for the dependence of S on photon energy, sample thickness, and the electronic structure of the absorbing solid.

Theory for Optical Absorption in Small Clusters: Dependence on Atomic Structure and Cluster Size

We present a theory which permits for the first time a detailed analysis of the dependence of the absorption spectrum on atomic structure and cluster size. Thus, we determine the development of the collective excitations in small clusters and show that their broadening depends sensitively on the tomic structure, in particular at the surface. Results for Hg_n^+ clusters show that the plasmon energy is close to its jellium value in the case of spherical-like structures, but is in general between w_p/ \wurzel{3} and w_p/ \wurzel{2} for compact clusters. A particular success of our theory is the identification of the excitations contributing to the absorption peaks.

Theory for the optical properties of small Hg_n clusters

The static and dynamical polarizabilities of the Hg-dimer are calculated by using a Hubbard Hamiltonian to describe the electronic structure. The Hamiltonian is diagonalized exactly within a subspace of second-quantized electronic states from which only multiply ionized atomic configurations have been excluded. With this approximation we can describe the most important electronic transitions including the effect of charge fluctuations. We analyze the polarizability as a function of the intraatomic Coulomb interaction which represents the repulsion between electrons. We obtain that this interaction results in strong electronic correlations in the excited states and increases the first excitation energy of the dimer by 0.8 eV in comparison to a calculation which neglects correlations, resulting in a better agreement with the experiment.