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The critical limit of the eight-vertex model eigenvectors obtained by means of the generalized Bethe Ansatz is shown to give the six-vertex eigenvectors as constructed in a previous paper by two of the authors. Furthermore, an explicit mapping is established between these eigenvectors and the usual Bethe Ansatz eigenvectors of the six-vertex model. This allows one to show that the indexv labeling the eight-vertex eigenstates becomes exactly the third component of the total spin in the critical limit. 相似文献
3.
Berardi R Cainelli G Galletti P Giacomini D Gualandi A Muccioli L Zannoni C 《Journal of the American Chemical Society》2005,127(30):10699-10706
This work is concerned with the rationalization and prediction of solvent and temperature effects in nucleophilic addition to alpha-chiral carbonyl compounds leading to facial diastereoselectivity. We study, using molecular dynamics simulations, the facial solvation of (R)-2-phenyl-propionaldehyde in n-pentane and n-octane at a number of temperatures and compare it with experimental selectivity data for the nBuLi addition leading to syn- and anti-(2R)-2-phenyl-3-heptanol, which give nonlinear Eyring plots with the presence of inversion temperatures. We have found from simulations that the facial solvation changes with temperature and alkane. Moreover, by introducing a suitable molecular chirality index we have been able to predict break temperatures (T(CI)) for the two solvents within less than 20 degrees of the inversion temperatures experimentally observed in the diastereoselective nBuLi addition. We believe this could lead to a viable approach for predicting inversion temperatures and other subtle solvent effects in a number of stereoselective reactions. 相似文献
4.
Gianfranco Cainelli Paola Galletti Daria Giacomini Andrea Gualandi Arianna Quintavalla 《Helvetica chimica acta》2003,86(11):3548-3559
The enantiomeric ratio E of enzyme‐catalyzed (Candida antarctica lipase and lipase PS) and chemo‐catalyzed (L ‐proline‐based diamines) acylation reactions of 1‐(naphthalen‐2‐yl)ethanol, 2‐phenylpropanol, and 2‐benzylpropane‐1,3‐diol is dependent on solvent and temperature. Plots of ln E vs. 1/T showed the presence of inversion temperatures (Tinv). The Tinv values for the bio‐catalyzed and the chemo‐catalyzed reactions are fairly in agreement, and correspond as well to the TNMR values obtained by variable‐temperature 13C‐NMR experiments on the substrates in the same solvent of the resolution. This result demonstrates that clustering effects in the substrate solvation manage the chemical and the enzymatic enantioselectivity, and, moreover, that the solute? solvent cluster is always the real reacting species in solution for chemical as well as for enzymatic reactions. 相似文献
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Isaac A. García Héctor Giacomini Maite Grau 《Journal of Dynamics and Differential Equations》2011,23(2):251-281
In this paper we study the maximum number of limit cycles that can bifurcate from a focus singular point p
0 of an analytic, autonomous differential system in the real plane under an analytic perturbation. We consider p
0 being a focus singular point of the following three types: non-degenerate, degenerate without characteristic directions and
nilpotent. In a neighborhood of p
0 the differential system can always be brought, by means of a change to (generalized) polar coordinates (r, θ), to an equation over a cylinder in which the singular point p
0 corresponds to a limit cycle γ
0. This equation over the cylinder always has an inverse integrating factor which is smooth and non-flat in r in a neighborhood of γ
0. We define the notion of vanishing multiplicity of the inverse integrating factor over γ
0. This vanishing multiplicity determines the maximum number of limit cycles that bifurcate from the singular point p
0 in the non-degenerate case and a lower bound for the cyclicity otherwise. Moreover, we prove the existence of an inverse
integrating factor in a neighborhood of many types of singular points, namely for the three types of focus considered in the
previous paragraph and for any isolated singular point with at least one non-zero eigenvalue. 相似文献
9.
Cairó Laurent Giacomini Hector Llibre Jaume 《Rendiconti del Circolo Matematico di Palermo》2003,52(3):389-418
We complete the classication of all Lotka-Volterra systemsx=x(ax+by+c),y=y(Ax+By+C), having a Liouvillian first integral. In our classification we take into account the first integrals coming from the existence
of exponential factors. 相似文献
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In this work we study the centers of planar analytic vector fields which are limit of linear type centers. It is proved that all the nilpotent centers are limit of linear type centers and consequently the Poincaré-Liapunov method to find linear type centers can be also used to find the nilpotent centers. Moreover, we show that the degenerate centers which are limit of linear type centers are also detectable with the Poincaré-Liapunov method. 相似文献