Linearly Induced Mappings between Cones of Quadratic Forms
This paper deals with mappings between cones of positive quadratic forms which are induced by linear mappings between the underling vector spaces, i.e., the spaces which are the domains of the forms. Three fundamental results are proved, two of which were previously announced by the second author. The first result states that there is an inclusion-reversing one-to-one correspondence between the lattice of subspaces of a given space and the lattice of faces of the cone of quadratic forms on that space. The second result states that all cone-isomorphisms between cones of quadratic forms are induced by linear isomorphisms between the underlying spaces. The third result states that a given cone-linear mapping F between cones of quadratic forms is induced by some linear mapping between the underlying spaces if and only if both F and its transpose preserve faces.
Order-isomorphisms between cones of continuous functions
SummaryThis paper studies the structure of order-isomorphisms between the cones of strictly-positive-valued elements of subspaces of two spaces of continuous functions; a complete description is obtained in some cases. Conditions are also found that ensure that such an order-isomorphism is linear provided it is homogeneous along at least one ray.
Comparative study of in vitro flow characteristics between a human aortic valve and a designed aortic valve and six corresponding types of prosthetic heart valves.
A model of a pulsatile cardiovascular system is described including an electronic control, a hydraulic driving unit, a volume storage, a peripheral resistance and measuring equipment. Six different artificial heart valves, a designed aortic valve (Aachen pockett valve II) and a human aortic valve have been tested in the outflow position of the pump. Three of them are presently being used in clinical applications. Measurements of pressure and volume flow have been obtained for different frequencies n, pump volumes Vp and time ratios between pressure and suction phase. From the experimental results a comparative evaluation was deducted for different working conditions. In comparison to natural human aortic valve (NK) large volume flow is verified by the Aachen pocket valve II (AT), the Gott-Dagget value (GD), the Starr-Edwards valve (SE) and the Lillehei-Kaster valve (LK). The Gott-Daggett valve has the smallest back flow volume. The Smeloff-Cutter and in particular the Wada-Cutter valve have the largest regurgitation. This is to be expected since the Cutter valves are purposely so designed that they do not close tightly in order to avoid blood sedimentation. The human aortic valve, the Gott-Daggett valve and the Aachen pocket valve demonstrate the most favourable opening-closing characteristics. The human aortic valve achieves a negligible pressure loss, followed by the Björk-Shiley and the Lillehei-Kaster valve.