R. Rimányi defined the incidence class of two singularities η and ζ as [η]|ζ, the restriction of the Thom polynomial of η
to ζ. He conjectured that (under mild conditions) [η]|ζ ≠ 0 ⇔ ζ ⊂ . Generalizing this notion we define the incidence class of two orbits η and ζ of a representation. We give a sufficient condition
(positivity) for ζ to have the property that [η]|ζ ≠ 0 ⇔ ζ ⊂ for any other orbit η. We show that for many interesting cases, e.g. the quiver representations of Dynkin type positivity
holds for all orbits. In other words in these cases the incidence classes completely determine the hierarchy of the orbits.
We also study the case of singularities where positivity doesn’t hold for all orbits.
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Two to four-basepair-short tandem repeats (i.e. microsatellites) are broadly utilized as genetic markers for mapping disease loci in whole genome search analyses. Based on their close vicinity on chromosome 11, the D11S1984 microsatellite was anticipated as a tentative marker for the dopamine D4 receptor gene. A capillary gel electrophoresis based genotype analysis method and an in-house made computational tool was developed for the analysis of the D11S1984 microsatellite marker to examine a healthy Hungarian population of n=106. The data obtained did not suggest significant linkage between the D11S1984 marker and the DRD4 gene. 相似文献
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Our purpose is to show that the various concepts of singularity of representable positive functionals on ?-algebras coincide, moreover to present a new characterization of singularity by means of Choquet theory of the state space. In the context of singularity, the paper includes an equivalent condition for a representable positive functional to be pure. 相似文献
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Various patterns of foldameric oligomers formed by trans-ABHC ((1S,2S,3S,5S)-2-amino-6,6-dimethylbicyclo[3.3.1]heptane-3-carboxylic acid) and β(3)-hSer residues were studied. NMR, ECD and molecular modelling demonstrated that octameric and nonameric sequences with multiple i-i+3 ABHC pair repulsions attain the β-H18 helix in CD(3)OH. As a close relative of the α-helix, this helix type is stabilized by i-i+4 backbone H-bond interactions. The formation of the β-H18 helix was found to be solvent- and concentration-dependent. Upon dilution, the β-H18 → β-H12 helix transition was revealed by concentration-dependent ECD, DOSY-NMR and TEM measurements. 相似文献
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