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We use Bernstein's Theorem  to obtain combinatorial bounds for the number of embeddings of Laman graph frameworks modulo rigid motions. For this, we study the mixed volume of suitable systems of polynomial equations obtained from the edge length constraints. The bounds can easily be computed and for some classes of graphs, the bounds are tight.
An optimal concentration range of aqueous ethanol produces 5-10-fold increases in nitroglycerin flux across skin and ethanol skin permeation that are far greater than reported previously. For aqueous ethanol solutions saturated with nitroglycerin with an ethanol volume fraction less than or equal to 0.7, the flux of nitroglycerin across skin is linear with… (More)
Let g 1 ,. .. , g k be tropical polynomials in n variables with Newton polytopes P 1 ,. .. , P k. We study combinatorial questions on the intersection of the tropical hyper-surfaces defined by g 1 ,. .. , g k , such as the f-vector, the number of unbounded faces and (in case of a curve) the genus. Our point of departure is Vigeland's work  who… (More)
The aim of this thesis is the discussion of mixed volumes, their interplay with algebraic geometry, discrete geometry and tropical geometry and their use in applications such as linkage configuration problems. Namely we present new technical tools for mixed volume computation, a novel approach to Ehrhart theory that links mixed volumes with counting integer… (More)
The solution properties of aqueous ethanol donor solutions were characterized for the particular case of an increased flux nitroglycerin transdermal system. Permeation through porous and nonporous polymer membranes was investigated and modelled. While the permeation of ethanol through the porous membranes is adequately described by theory, clogging of pores… (More)
We give some new technical tools which simplify mixed volume computation for larger polynomial systems and allow the computation of mixed volume bounds for polynomial systems of arbitrary dimension arising in various applications as seen in .
For a series of bases, which penetrate through human skin in vitro at similar rates (0.056-0.49 microM/cm2/hr), penetrant pKa is shown to correlate with erythema, edema, and color meter readings. As estimates of irritation, erythema, edema, and redness measurements are highly linearly correlated. For the selected series, irritation becomes significant for… (More)