数学建模与素质教育

面对二十一世纪知识经济的挑战 ,我国高等教育模式应由应试教育 ,专业教育向素质教育转变 ,培养学生自主意识 ,效率意识 ,竞争意识 ,创新意识和民主意识 ,即高校教育应重视大学生的创新能力、实践能力和创业精神 ,普遍提高大学生的人文素质和科学素质 .本文拟就提高大学生素质的有效层面 ,对开展数学建模教学与实践进行深入分析 ,以窥探数学建模与素质教育之关系 .在深入把握数学建模教学与实践内涵的同时 ,分析得出这种以不打扰现行正常秩序的教育是提高大学生素质的有效途径之一     

企业发展的多目标决策模糊优化模型

企业多目标决策优化是企业生产管理以及发展的一项非常重要的工作 .企业生产管理以及发展受多种因素影响 ,而且企业的多目标决策优化问题具有模糊性 ,本文将针对其模糊性 ,运用模糊数学理论进行研究 ,并给出具体应用实例 ,其结果令人满意 ,且具有较强的可靠性和实用性     

非交换陈特征的一个注记

此注记利用Moscovici的一个想法和热核渐近展开技术,给出了Clifford模 上Dirac算子的整循环陈特征的一个计算公式.     

全纯扩充的BHW定理的推广

本文得到关于全纯扩充的BHW定理的一个全新的证明,同时也对BHW定 理做出了更一般的推广,并且给出了推广后的BHW定理的两种不同的证明方法.     

复流形局部q-凸楔形上带权的同伦公式

本文得到复流形局部q-凸楔形上(r,s)型微分形式的带权的同伦公式和(r,s)型的方程的带权的连续解,并给出(r,s)型微分形式的不含边界积分的新的带权的同伦公式和(r,s)型的方程的新的带权的连续解.这些新的带权公式尤其适用于具有非光滑边界的局部q-凸楔形,这时不但可以避免边界积分的复杂估计,而且积分密度也不必在边界有定义,只要在区域上有定义就行.其次,引进权因子,带权的积分公式在应用上(比如在函数的插值方面)具有更大的灵活性.     

Generalized coulomb barrier transmission coefficient for solar neutrino and astrophysical problems

For astrophysical calculations, it is customary to extrapolate higher-energy (20keV) data using the Gamow transmission coefficient in estimating the nonresonance nuclear fusion reaction cross sections (E) for charged particles at low energies (<20 keV). We present a general extrapolation method based on a more realistic Coulomb barrier transmission coefficient, which can accommodate simultaneously both nonresonance and resonance contributions.     

Thermodynamics of solids: Corrections from electron-phonon interactions

Anomalous room-temperature specific heats have been seen experimentally by Knapp and coworkers in highT _c superconductors. The measurements depart from 3N k _B + ₀ T by an amount of order ₀ T. We present a theory for this, based on the fact that electronphonon interactions cause both electron band energies _{k n} and phonon frequencies _{Q µ} to be weakly temperature-dependent. First an observation is made which we call Brook's Theorem: the shiftE _{k n} (Q µ) of the electron energy _{k n} due to adding one phonon in modeQ µ, is identical to the shift _{Q µ} (k n) of the phonon energy _Qµ due to adding one electron in the statek n. Second, we assert that to sufficient accuracy whenT> _D , entropy of the system of interacting electrons and phonons equals the entropy which would be calculated for non-interacting particles, except that theT-dependent energiesE _kn (T) and _{Q µ} (T) should be used. A proof to orderu ² (whereu is phonon displacement amplitude) was given in the thesis of one of us. Third, we use Brook's Theorem to show that the corrections C _el and C _ph to the specific heat due toT-dependence of electron and phonon energies respectively, are identically equal and have order of magnitude ₀ T. All these results are valid in adiabatic approximation to orderu ², and fail at low temperatures where non-adiabatic corrections are large.