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This work is concerned with different aspects of spectrahedra and their projections, sets that are important in semidefinite optimization. We prove results on the limitations of so called Lasserre and theta body relaxation methods for semialgebraic sets and varieties. As a special case we obtain the main result of [19] on non-exposed faces. We also solve(More)
A finitely generated quadratic module or preordering in the real polynomial ring is called stable, if it admits a certain degree bound on the sums of squares in the representation of polynomials. Stability, first defined explicitly in [PS], is a very useful property. It often implies that the quadratic module is closed; furthermore it helps settling the(More)
OBJECTIVES To determine dose-related clinical and neurohumoral effects of angiotensin-converting enzyme (ACE) inhibitors in patients with chronic heart failure (CHF), we conducted a double-blind, placebo-controlled, randomized study of three doses (2.5 mg, 5 mg and 10 mg) of the long-acting ACE inhibitor imidapril. BACKGROUND The ACE inhibitors have(More)
If pathologists will benefit so much from using telepathology, why is it taking so long to be introduced? This question has been discussed between experts, but the potential users are rarely asked for their opinions. A questionnaire was sent to the 256 members of the Austrian Society of Pathology; this addressed general aspects of telemedicine,(More)
A questionnaire was distributed to 300 medical students attending a conference in 1996. The return rate was 32%. The majority of students believed that telemedicine will become very important in future. About a quarter of students had had practical experience of telemedicine in a hospital. More than 75% of the respondents said that they would attend(More)
Gewidmet meinen Eltern Marina und Michael Plaumann und meinem Onkel Peter Plaumann in tiefer Dankbarkeit Acknowledgements I would like to express my gratitude to my advisor Claus Scheiderer for the many ideas and insights into the topic that he shared with me, as well as for his constant encouragement. I am grateful for many interesting and helpful(More)
A linear matrix inequality (LMI) is a condition stating that a symmetric matrix whose entries are affine-linear combinations of variable,; is positive semidefinite. :dotiv11ted by the fact that diagonal LMIs define polyhedra, the solution set of an LMI is called a spectrahedron. Linear images of spectrahedra are called semidefinitely representable sets.(More)
A linear matrix inequality (LMI) is a condition stating that a symmetric matrix whose entries are affine linear combinations of variables is positive semidefinite. Motivated by the fact that diagonal LMIs define poly-hedra, the solution set of an LMI is called a spectrahedron. Linear images of spectrahedra are called semidefinite representable sets. Part of(More)
We consider the problem of writing real polynomials as determinants of symmetric linear matrix polynomials. This problem of algebraic geometry, whose roots go back to the nineteenth century, has recently received new attention from the viewpoint of convex optimization. We relate the question to sums of squares decompositions of a certain Her-mite matrix. If(More)