Manifolds with S 1-category 2 have cyclic fundamental groups

A closed topological n-manifold M ⁿ is of S ¹-category 2 if it can be covered by two open subsets W ₁, W ₂ such that the inclusions W _i → M ⁿ factor homotopically through maps W _i → S ¹. We show that for n > 3 the fundamental group of such an n-manifold is either trivial or infinite cyclic.     

Coverings of 3-manifolds by open balls and two open solid tori

Hempel and McMillan showed that a closed 3-manifold that can be covered by three open balls is a connected sum of S³- and S²-bundles over S¹. In this paper we obtain a classification of all closed 3-manifolds that can be covered by two open balls and one open solid torus or by one open ball and two open solid tori.     

A technique for flow-enhanced magnetic resonance angiography of the lower extremities

A two-dimensional, flow-enhanced gradient echo pulse sequence for nuclear magnetic resonance angiography is described. It employs interleaved, presaturated slices to acquire data efficiently on imagers which favor interleaved acquisition over sequential acquisition for multislice imaging. It is useful on any imager when the effective TR is extended to enhance the sensitivity to slow flow. The technique was applied to the region from aortic bifurcation to the iliac bifurcations of three normal volunteers. The right and left common iliac arteries and veins, the separation of the external and internal iliac arteries, and secondary branches were clearly depicted.     

Ueber die Aenderungen physikalisch-chemischer Eigenschaften im Uebergangsgebiet zwischen kolloiden und molekulardispersen Systemen,III

Ohne Zusammenfassung     

Control of continuous sedimentation of ideal suspensions as an initial and boundary value problem

We present the control of continuous sedimentation in an ideal thickener as an initial and boundary value problem and construct the entropy solution.