36,112 research outputs found
Tropical images of intersection points
A key issue in tropical geometry is the lifting of intersection points to a
non-Archimedean field. Here, we ask: Where can classical intersection points of
planar curves tropicalize to? An answer should have two parts: first,
identifying constraints on the images of classical intersections, and, second,
showing that all tropical configurations satisfying these constraints can be
achieved. This paper provides the first part: images of intersection points
must be linearly equivalent to the stable tropical intersection by a suitable
rational function. Several examples provide evidence for the conjecture that
our constraints may suffice for part two.Comment: 13 pages, 9 figure
Spiral vane bioreactor
A spiral vane bioreactor of a perfusion type is described in which a vertical chamber, intended for use in a microgravity condition, has a central rotating filter assembly and has flexible membranes disposed to rotate annularly about the filter assembly. The flexible members have end portions disposed angularly with respect to one another. A fluid replenishment medium is input from a closed loop liquid system to a completely liquid filled chamber containing microcarrier beads, cells and a fluid medium. Output of spent medium is to the closed loop. In the closed loop, the output and input parameters are sensed by sensors. A manifold permits recharging of the nutrients and pH adjustment. Oxygen is supplied and carbon dioxide and bubbles are removed and the system is monitored and controlled by a microprocessor
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