Invariants sémantiques et constructions syntaxiques

This article looks at the conditions under which a construction has an own interpretation. Interpreting the first proposal of the type constructions modalisante I think that P is considered. It is shown that these interpretations can be fully explained by parsing of the sequence I think than a subordinated, resulting in a set of undesirable consequences. The ability to handle this sequence as a construction in the theoretical that gives this constructionnelle grammar concept is envisaged to assess the relationships between form, meaning sense, compositionnalité and invariant. Cet article s'intéresse aux conditions suivant lesquelles une construction possède une interprétation qui lui est propre. L'interprétation modalisante de la première proposition des constructions du type Je crois que P est considérée. Il est montré que ces interprétations ne peuvent être pleinement expliquées par l'analyse syntaxique faisant de la séquence Je crois que une subordonnée, qui entraîne un ensemble de conséquences indésirables. La possibilité de traiter cette séquence comme une construction dans le sens théorique que donne à cette notion la Grammaire constructionnelle est envisagée, permettant d'apprécier les rapports entre forme, sens, compositionnalité et invariant.

Simple one-electron invariants of molecular chirality

Pseudoscalar measures of electronic chirality for molecular systems are derived using the spectral moment theory applied to the frequency-dependent rotational susceptibility. In this scheme a one-electron chirality operator κ^ naturally emerges as a quantum counterpart of the triple scalar product, involving velocity, acceleration and second acceleration. Averaging κ^ over an electronic state vector gives rise to an additive chirality invariant (κ-index), considered as a quantitative measure of chirality. A simple computational technique for quick calculation of the κ-index is developed and various structural classes (cyclic hydrocarbons, cage-shaped systems, etc.) are studied. Reasonable behaviour of the chirality index is demonstrated. The chirality changes during the β-turn formation in Leu-Enkephalin is presented as a useful example of the chirality analysis for conformational transitions.

Vacuum spacetimes with constant Weyl eigenvalues

Einstein spacetimes (that is vacuum spacetimes possibly with a non-zero cosmological constant A) with constant non-zero Weyl eigenvalues are considered. For type Petrov II & D this assumption allows one to prove that the non-repeated eigenvalue necessarily has the value 2A/3 and it turns out that the only possible spacetimes are some Kundt-waves considered by Lewandowski which are type II and a Robinson-Bertotti solution of type D. For Petrov type I the only solution turns out to be a homogeneous pure vacuum solution found long ago by Petrov using group theoretic methods. These results can be summarised by the statement that the only vacuum spacetimes with constant Weyl eigenvalues are either homogeneous or are Kundt spacetimes. This result is similar to that of Coley et al. who proved their result for general spacetimes under the assumption that all scalar invariants constructed from the curvature tensor and all its derivatives were constant.