数学专业师范生教学技能的调查研究--以四川文理学院为例

教学技能是教师最重要的专业素质，是师范生在大学期间需要掌握的基础职业技能。通过调查研究表明，数学专业大学生教学基本功发展不平衡，不同年级学生的教学技能水平存在显著差异。教学实践、课改认知、教学交流、自主练习是影响教学技能的四个主因子。男女生在表达技能、教学设计技能、几何作图技能等方面差异显著，而在教材分析、多媒体使用方面不存在显著性差异。要通过完善教学技能培养机制，夯实师范基础技能培养，改革教学技能培养方式等途径，合力提高师范生的教学技能，增强就业竞争力。     

课堂教学应注重严密完整的数学语言

数学是一门语言精辟、逻辑严密的学科，课堂教学中注重严密、完整的数学语言，才能保证知识传授的准确性，使学生获得准确无误的知识。本文分析了造成数学语言不够严密完整的各种原因及改进方法，要求教师在课堂教学中做到数学语言准确规范，严密完整、形象生动。     

加强数学语言教学增强数学语言应用意识

数学教学中应加强数学语言教学,增强数学语言的应用意识,以提高学生数学应用能力.     

电力系统状态估计算法研究

对已有状态估计算法进行了分析,并结合实际电网的一些特点,在最小二乘法的基础上,对PQ分解法的病态线路提出了一种新的解决方法,即将电压量测量和功率、电流量测量分解开来进行计算,建立了相应的数学模型。和其它方法进行了比较,认为该方法具有收敛性好、计算速度快的优点。     

Random matrix theory for transition strength densities in finite quantum systems: Results from embedded unitary ensembles

Embedded random matrix ensembles are generic models for describing statistical properties of finite isolated interacting quantum many-particle systems. For the simplest spinless fermion (or boson) systems, with say m<math altimg="si456.gif" overflow="scroll">mmath> fermions (or bosons) in N<math altimg="si457.gif" overflow="scroll">Nmath> single particle states and interacting via k<math altimg="si458.gif" overflow="scroll">kmath>-body interactions, we have EGUE(k<math altimg="si459.gif" overflow="scroll">kmath>) [embedded GUE of k<math altimg="si460.gif" overflow="scroll">kmath>-body interactions] with GUE embedding and the embedding algebra is U(N)<math altimg="si461.gif" overflow="scroll">U(N)math>. A finite quantum system, induced by a transition operator, makes transitions from its states to the states of the same system or to those of another system. Examples are electromagnetic transitions (then the initial and final systems are same), nuclear beta and double beta decay (then the initial and final systems are different), particle addition to or removal from a given system and so on. Towards developing a complete statistical theory for transition strength densities (transition strengths multiplied by the density of states at the initial and final energies), we have derived formulas for the lower order bivariate moments of the strength densities generated by a variety of transition operators. Firstly, for a spinless fermion system, using EGUE(k<math altimg="si462.gif" overflow="scroll">kmath>) representation for a Hamiltonian that is k<math altimg="si463.gif" overflow="scroll">kmath>-body and an independent EGUE(t<math altimg="si464.gif" overflow="scroll">tmath>) representation for a transition operator that is t<math altimg="si465.gif" overflow="scroll">tmath>-body and employing the embedding U(N)<math altimg="si466.gif" overflow="scroll">U(N)math> algebra, finite-N<math altimg="si467.gif" overflow="scroll">Nmath> formulas for moments up to order four are derived, for the first time, for the transition strength densities. Secondly, formulas for the moments up to order four are also derived for systems with two types of spinless fermions and a transition operator similar to beta decay and neutrinoless beta decay operators. In addition, moments formulas are also derived for a transition operator that removes k₀<math altimg="si468.gif" overflow="scroll">k0math> number of particles from a system of m<math altimg="si469.gif" overflow="scroll">mmath> spinless fermions. In the dilute limit, these formulas are shown to reduce to those for the EGOE version derived using the asymptotic limit theory of Mon and French (1975). Numerical results obtained using the exact formulas for two-body (k=2<math altimg="si470.gif" overflow="scroll">k=2math>) Hamiltonians (in some examples for k=3<math altimg="si471.gif" overflow="scroll">k=3math> and 4<math altimg="si472.gif" overflow="scroll">4math>) and the asymptotic formulas clearly establish that in general the smoothed (with respect to energy) form of the bivariate transition strength densities take bivariate Gaussian form for isolated finite quantum systems. Extensions of these results to bosonic systems and EGUE ensembles with further symmetries are discussed.