In this paper, we lift Fermions to functors acting on some homotopy category by the Boson–Fermion correspondence and get the categorified relations of Fermions. In this way, both the categorified Bosons and the categ...In this paper, we lift Fermions to functors acting on some homotopy category by the Boson–Fermion correspondence and get the categorified relations of Fermions. In this way, both the categorified Bosons and the categorified Fermions can be viewed as functors on the same category. We also give actions of these functors on the charged Young diagrams(or equivalently, Maya diagrams), so that the classical theory of Boson–Fermion correspondence is very well recovered as a result of such a categorification.展开更多
The authors consider the homogenization of a class of nonlinear variational inequalities,which include rapid oscillations with respect to a parameter.The homogenization of the corresponding class of differential equat...The authors consider the homogenization of a class of nonlinear variational inequalities,which include rapid oscillations with respect to a parameter.The homogenization of the corresponding class of differential equations is also studied.The results are applied to some models for the pressure in a thin fluid film fluid between two surfaces which are in relative motion.This is an important problem in the lubrication theory.In particular,the analysis includes the effects of surface roughness on both faces and the phenomenon of cavitation.Moreover,the fluid can be modeled as Newtonian or non-Newtonian by using a Rabinowitsch fluid model.展开更多
基金Supported by National Nature Science Foundation of China under Grant Nos.11031005 and 11475116Beijing Municipal Commission of Education under Grant Nos.KZ201210028032 and KZ201410028033
文摘In this paper, we lift Fermions to functors acting on some homotopy category by the Boson–Fermion correspondence and get the categorified relations of Fermions. In this way, both the categorified Bosons and the categorified Fermions can be viewed as functors on the same category. We also give actions of these functors on the charged Young diagrams(or equivalently, Maya diagrams), so that the classical theory of Boson–Fermion correspondence is very well recovered as a result of such a categorification.
文摘The authors consider the homogenization of a class of nonlinear variational inequalities,which include rapid oscillations with respect to a parameter.The homogenization of the corresponding class of differential equations is also studied.The results are applied to some models for the pressure in a thin fluid film fluid between two surfaces which are in relative motion.This is an important problem in the lubrication theory.In particular,the analysis includes the effects of surface roughness on both faces and the phenomenon of cavitation.Moreover,the fluid can be modeled as Newtonian or non-Newtonian by using a Rabinowitsch fluid model.
