We study the quantum-classical correspondence in terms of coherent wave functions of a charged particle in two-dimensional central-scalar-potentials as well as the gauge field of a magnetic flux in the sense that the probability clouds of wave functions are well localized on classical orbits. For both closed and open classical orbits, the non-integer angular-momentum quantization with the level-space of angular momentum being greater or less than is determined uniquely by the same rotational symmetry of classical orbits and probability clouds of coherent wave functions, which is not necessarily 2π-periodic. The gauge potential of a magnetic flux impenetrable to the particle cannot change the quantization rule but is able to shift the spectrum of canonical angular momentum by a flux-dependent value, which results in a common topological phase for all wave functions in the given model. The quantum mechanical model of anyon proposed by Wilczek (Phys. Rev. Lette. 48, 1144) becomes a special case of the arbitrary-quantization.
Hupelactones A (1) and B (2), two new eudesmanolide-type enantiomers of the corresponding compounds, along with four mono-(3-6) and nine dimeric-(7-15) known sesquiterpenoids were isolated from the whole plant of Chloranthus henryi var. hupehensis (syn. C. henryi). The new structures including the absolute configurations were determined by comparison with previously reported enantiomers, extensive spectroscopic methods in combination with electronic circular dichroism (ECD) calculations. All the isolates were evaluated for their inhibitory activities against the lipopolysaccharide (LPS)-induced nitric oxide (NO) production in murine BV-2 microglial cells. Among them, the dimeric lindenane sesquiterpenoids shizukaols F (8) and G (11) exhibited the most potent activities, with IC50 values of 2.65 and 4.60 μM, respectively.
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