X iv : m at h . M G / 0 50 80 37 v 2 2 A ug 2 00 5 POWER DIAGRAMS AND THEIR APPLICATIONS
نویسندگان
چکیده
We remark that the power diagrams from computer science are the spines of amoebas in algebraic geometry, or the hypersurfaces in tropical geometry. Our concept of a Morse poset generalizes to power diagrams. We show that there exists a discrete Morse function on the coherent triangulation, dual to the power diagram, such that its critical set equals the Morse poset of the power diagram. In the final section we use Maslov dequantization to compute the medial axis.
منابع مشابه
ar X iv : 0 80 8 . 30 76 v 1 [ co nd - m at . s of t ] 2 2 A ug 2 00 8 Phase behavior of C 18 monoglyceride in hydrophobic solutions
We apply a set of different techniques to analyze the physical properties and phase transitions of monoglycerides (MG) in oil. In contrast to many studies of MG in water or aqueous systems, we find a significant difference in the phase structure at different concentrations and temperatures. By adding small quantities of water to our base MG/oil systems we test the effect of hydration of surfact...
متن کاملar X iv : m at h - ph / 0 30 80 30 v 1 2 5 A ug 2 00 3 Colored Hofstadter butterflies
I explain the thermodynamic significance, the duality and open problems associated with the two colored butterflies shown in figures 1 and 4. 1 Overview My aim is to explain what is known about the thermodynamic significance of the two colored butterflies shown in figures 1 and 4 and what remains open. Both diagrams were made by my student, D. Osadchy [14], as part of his M.Sc. thesis. I shall ...
متن کاملar X iv : m at h / 05 04 42 3 v 1 [ m at h . O A ] 2 1 A pr 2 00 5 NON - SEPARABLE AF - ALGEBRAS
We give two pathological phenomena for non-separable AF-algebras which do not occur for separable AF-algebras. One is that non-separable AFalgebras are not determined by their Bratteli diagrams, and the other is that there exists a non-separable AF-algebra which is prime but not primitive.
متن کاملA ug 2 00 5 POWER DIAGRAMS AND THEIR APPLICATIONS
We remark that the power diagrams from computer science are the spines of amoebas in algebraic geometry, or the hypersurfaces in tropical geometry. Our concept of a Morse poset generalizes to power diagrams. We show that there exists a discrete Morse function on the coherent triangulation, dual to the power diagram, such that its critical set equals the Morse poset of the power diagram. In the ...
متن کاملar X iv : 0 80 2 . 06 76 v 1 [ as tr o - ph ] 5 F eb 2 00 8 MS , S and C Stars in the Infrared . Luminosities and Mass Loss Rates
In this note I present an outline of infrared (IR) photometric AGB properties, based on two samples of Galactic Long Period Variables (Cand S-type respectively). I show the various selection criteria used during the choice of the sources and describe the motivations of observing them at nearand mid-IR wavelengths. I discuss the problems encountered in estimating their luminosity and distance an...
متن کامل