探析生活中的数学知识

在我们的生活中,各类问题都可以通过数学知识进行解答,而数学知识也能够通过生活体现出来,例如购买商品、规划时间、计算方位及距离等,都与数学知识存在一定的相关性,因此我们在学习数学知识时,要善于寻找数学知识与实际生活的关联点,促进数学知识与生活的有效结合,从而通过生活检验数学学习效果,并运用数学知识解决生活中的难题,这样数学学习就不再像我们想象中那样抽象难懂,对于我们的数学学习及生活来说都是大有裨益的。

经济增长中的产业政策实施及其作用研究——以“东亚奇迹”中的台湾经济增长为例

1980年以前,产业政策(industrial policy)一词在经济理论中并无地位,但是在1980年以后随着发达国家为扭转市场经济生产力之低落,对供给面经济的政策性干预成功,以及发展中国家(地区)以发展策略为目的的产业政策奏效,各国(地区)经济主管当局、学者对产业政策的重视程度与日俱增,尤其在20世纪80年代的中国台湾、韩国、日本等国家和地区塑造的"东亚奇迹"最为显著。

Response functions of hot and dense matter in the Nambu-Jona-Lasino model

We investigate current-current correlation functions,or the so-called response functions of a two-flavor Nambu-Jona-Lasino model at finite temperature and density.The linear response is investigated introducing the conjugated gauge fields as external sources within the functional path integral approach.The response functions can be obtained by expanding the generational functional in powers of the external sources.We derive the response functions parallel to two well-established approximations for equilibrium thermodynamics,namely mean-field theory and a beyond-mean-field theory,taking into account mesonic contributions.Response functions based on the mean-field theory recover the so-called quasiparticle random phase approximation.We calculate the dynamical structure factors for the density responses in various channels within the random phase approximation,showing that the dynamical structure factors in the baryon axial vector and isospin axial vector channels can be used to reveal the quark mass gap and the Mott dissociation of mesons,respectively.Noting that the mesonic contributions are not taken into account in the random phase approximation,we also derive the response functions parallel to the beyond-mean-field theory.We show that the mesonic fluctuations naturally give rise to three kinds of famous diagrammatic contributions:the Aslamazov-Lakin contribution,the self-energy or density-of-state contribution,and the Maki-Thompson contribution.Unlike the equilibrium case,in evaluating the fluctuation contributions,we need to carefully treat the linear terms in external sources and the induced perturbations.In the chiral symmetry breaking phase,we find an additional chiral order parameter induced contribution,which ensures that the temporal component of the response functions in the static and long-wavelength limit recovers the correct charge susceptibility defined using the equilibrium thermodynamic quantities.These contributions from mesonic fluctuations are expected to have significant effects on the transport properties of hot and dense matter around the chiral phase transition or crossover,where the mesonic degrees of freedom are still important.

Equal-time kinetic equations in a rotational field

We investigate quantum kinetic theory for a massive fermion system under a rotational field.From theDirac equation in rotating frame we derive the complete set of kinetic equations for the spin components of the 8-and 7-dimensional Wigner functions.While the particles are no longer on a mass shell in the general case due to therotation-spin coupling,there are always only two independent components,which can be taken as the number andspin densities.With help from the off-shell constraint we obtain the closed transport equations for the two independent components in the classical limit and at the quantum level.The classical rotation-orbital coupling controls thedynamical evolution of the number density,but the quantum rotation-spin coupling explicitly changes the spin density.

Relativistic Borromean states

In this work,the existence of Borromean states is discussed for bosonic and fermionic cases in both therelativistic and non-relativistic limits from the 3-momentum shell renormalization.With the linear bosonic model,we check the existence of Efimov-like states in the bosonic system.In both limits a geometric series of singularities is found in the 3-boson interaction vertex,while the energy ratio is reduced by around 70%in the relativistic limit because of the anti-particle contribution.Motivated by the quark-diquark model in heavy baryon studies,we have carefully examined the p-wave quark-diquark interaction and found an isolated Borromean pole at finite energy scale.This may indicate a special baryonic state of light quarks in high energy quark matter.In other cases,trivialresults are obtained as expected.In the relativistic limit,for both bosonic and fermionic cases,potential Borromean states are independent of the mass,which means the results would also be valid even in the zero-mass limit.