I will describe a few basic properties of the Euler characteristic and then I use them to prove special case of a cute formula due to Bernstein-Khovanskii-Koushnirenko. 1. Basic properties of the Euler characteristic The Euler characteristic is a function χ which associates to each reasonable topological space X an integer χ(X). For us a reasonable space would be a space which admits a finite s...

Let k be an algebraically closed field of characteristic exponent p ≥ 1. Let G be a connected reductive algebraic group over k and let g be the Lie algebra of G. Note that G acts on G and on g by the adjoint action. Let UG be the variety of unipotent elements of G. Let Ng be the variety of nilpotent elements of g. In [L2], we have proposed a definition of a partition of UG into smooth locally c...

OBJECTIVE Preoperative anxiety influences the result of the treatment in patients. To assess preoperative anxiety the Amsterdam Preoperative Anxiety and Information Scale (APAIS) [1] was developed. The APAIS measures anxiety and the need-for-information with 6 items, with good reliability and validity. This article presents the first test of the German version of this screening instrument. ME...

In this study, the authors report on the development of English and German versions of the Adolescent Time Attitude Scale (ATAS). The ATAS consists of six subscales assessing Past Positive, Past Negative, Present Positive, Present Negative, Future Positive, and Future Negative time attitudes. The authors describe the development of the scales and present data on the reliability and structural v...

BACKGROUND The quality of patients' recovery following surgery and anesthesia has been a matter of focus and concern over the past decade. The Quality of Recovery-40 (QoR-40) questionnaire was developed and validated for post-anesthesia patient evaluation. The QoR-40, however, is English-based and was tested and validated in Caucasian patients, a population that is culturally and behaviorally d...

While discrete choice experiments (DCEs) are increasingly used in the field of environmental valuation, they remain controversial because of their hypothetical nature and the contested reliability and validity of their results. We systematically reviewed evidence on the validity and reliability of environmental DCEs from the past thirteen years (Jan 2003-February 2016). 107 articles met our inc...