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NOËL BONNEUIL 《The Journal of mathematical sociology》2014,38(2):95-114
The transformation over time of level sets—the sets of states for which a given function takes a given value—has no reason to be regular, especially in social science, where the structure of these level sets of a given variable may be altered by a fluctuating demography or disrupted by unexpected events, and where the actors contribute to shaping their space through investment policies. The pioneering construction of graphic derivatives of set-valued maps renews the understanding of dynamic level sets in social science. The exemplary case of schooling in 19th-century France shows the set derivatives of level sets and illustrates how the Franco-Prussian War of 1870–1871 disturbed the directions taken in 1867. A comparison of the observed changes of level sets with those observed under rational theoretical policies leads to the conclusion that the actors behaved with the ambition of optimizing the overall schooling incidence while reducing the gap between boys and girls. 相似文献
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Süleymanoğlu N Ustabaş R Alpaslan YB Eyduran F Ozyürek C Iskeleli NO 《Spectrochimica acta. Part A, Molecular and biomolecular spectroscopy》2011,83(1):472-477
In this work, 3,4-bis(isoproylamino)cyclobut-3-ene-1,2-dione C(10)H(16)N(2)O(2) (I), was synthesized and characterized by (13)C NMR, (1)H NMR, FT-IR, UV-vis spectroscopy and single-crystal X-ray diffraction. DFT method with 6-31G(d,p) basis set has been used to calculate the optimized geometrical parameters, atomic charges, vibrational frequencies and chemical shift values. The calculated vibrational frequencies and chemical shift values are compared with experimental FT-IR and NMR spectra. The results of the calculation shows good agreement between experimental and calculated values of the compound I. The existence of N-H?O type intermolecular ve C-H?O type intramolecular hydrogen bonds can be deduced from differences between experimental and calculated results of FT-IR and NMR. In addition, the molecular electrostatic potential map and frontier molecular orbitals and electronic absorption spectra were performed at B3LYP/6-31G(d,p) level of theory. HOMO-LUMO electronic transition of 4.90 eV are derived from the contribution of the bands π→π* and n→π* The spectral results obtained from FT-IR, NMR and X-ray of I revealed that the compound I is in predominantly enamine tautomeric form, which was supported by DFT calculations. 相似文献
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