互联网B/S架构交互式软件在核心概念教学中的应用*——以国际IB课程中“电解质”内容为例

基于核心概念教学的思路,国际IB课程互联网B/S架构交互式软件能够使学生围绕“电解质”核心概念,通过自行操作软件获得多个从微观到宏观、定性与定量相结合、可视化的实验证据,有利于学生深度理解概念与概念之间的逻辑和发展关系,促进学科知识系统框架的形成。     

气-固流化床反应器内双流体力学模型及其验证 Ⅱ.单组分两维射流床内流场特性分析

由以质量、动量和能量三大守恒定律为基础的湍流两相流理论出发,建立了描述气固流化床内两相流动的数学模型;在微型计算机上编写了相应的数值计算和图形处理程序;为了验证模型的可靠性,本文着手模拟与分析了单组分颗粒体系两维射流流化床内气、固相速度场、空隙度和压力场随时间、空间变化规律;得到了与前人实验结果相吻合的结论。     

Hamiltonian group actions on symplectic Deligne–Mumford stacks and toric orbifolds

We develop differential and symplectic geometry of differentiable Deligne–Mumford stacks (orbifolds) including Hamiltonian group actions and symplectic reduction. As an application we construct new examples of symplectic toric DM stacks.     

Lp-based combinatorial problem solving

A tutorial outline of the polyhedral theory that underlies linear programming (LP)-based combinatorial problem solving is given. Design aspects of a combinatorial problem solver are discussed in general terms. Three computational studies in combinatorial problem solving using the polyhedral theory developed in the past fifteen years are surveyed: one addresses the symmetric traveling salesman problem, another the optimal triangulation of input/output matrices, and the third the optimization of large-scale zero-one linear programming problems.     

维也纳分析方法及其应用

介绍了软件开发方法中的一种形式化分析方法：Vienna Development Method(VDM)。阐述了形式化分析方法的特点，具体说明了维也纳分析方法规格说明的两种规范：模块化说明与非模块化说明，及程序证明性依据：基于函数与操作的形式化规格说明。然后通过一个应用实例来说明如何利用VDM技术进行软件开发，及利用函数与操作的形式化规格说明来证明程序是正确的。     

超临界CO2磨料射流流场影响因素的模拟分析

为了揭示超临界CO₂磨料射流流场特性,利用计算流体动力学模拟软件,对超临界CO₂磨料射流结构及不同因素对射流流场的影响规律进行了研究。结果表明:超临界CO₂磨料射流轴向速度和冲击力随着喷距的增大,先增大后减小,即存在最优喷距,喷射压差为10~30 MPa时最优喷距为3~6倍喷嘴直径;喷射压差一定时,围压由10 MPa增至30 MPa对射流速度场及液相冲击力会造成较小的负面影响。通过超临界CO₂射流破岩实验对上述2因素进行了辅助对比验证;流体温度由333 K增至413 K,固液两相轴向速度增大,而流体密度降低,导致液相冲击力减弱;磨料浓度由3.0%连续增至11.0%,射流固液两相轴向速度逐渐降低,降幅逐渐减小。     

Explicit formulas for the reflection and transmission coefficients of one-component waves through a stack of an arbitrary number of layers

The transmission and reflection of one-component elastic, acoustic, optical waves on a stack of arbitrary number of different homogeneous layers have been intensively studied in the literature. However, all obtained formulas for the reflection and transmission coefficients are in implicit form. In this paper, we provide the explicit formulas for them. From these formulas we immediately arrive at the explicit formulas for the reflection and transmission coefficients of one-component waves through an FGM layer. Based on the obtained exact formulas, approximate formulas for the reflection and transmission coefficients are established for a stack of thin layers and for a thin FGM layer. It is numerically shown that they are good approximations. Since the obtained formulas are totally explicit, they are useful in evaluating, not only numerically but also analytically, the transmission and reflection coefficients of one-component waves.     

‘New mathematics’ and teaching

Inside the scientific world it is not always understood that the mood of mathematics, which is a product and a part of culture, can change with time. This is partly why many have been surprised by the coming of the so‐called new mathematics.

In the truly creative mathematical mind two opposite tendencies coexist: the logical and the imaginative. Apparently it seems that new mathematics can be reduced to a purely logical machinery. In fact it contains as much imaginative contributions as classical mathematics. But it is difficult to show simultaneously the logical sequence of propositions and the clumsy progression of research itself. Mathematical exposition does not always follow the ‘ most natural slopes’ of the mind. Unfamiliar presentations often give an impression of ‘ abstraction ‘, more familiar ones an impression of concreteness ‘.

So it appears that difficulties with new mathematics are mostly of psychological origin. Misuses of it can easily raise up intolerance reactions and emotional blocks. Perhaps insisting upon the fact that, here as elsewhere, it is important to be able to guess, to realize that intuition and imagination are essential, could help to make new mathematics better understood, more useful and more able to be considered as a unifing element among sciences.     

Note on Characterization of Projective Spaces

We prove a numerical characterization of ?ⁿ for varieties with at worst isolated local complete intersection quotient singularities. In dimension 3, we prove such a numerical characterization of ?³ for normal ?-Gorenstein projective varieties.     

Using interactive algebra software to support a discourse community

In this work we studied the impact of using NuCalc, an interactive computer algebra software, on the development of a discourse community in a college level mathematics class. Qualitative and quantitative data were collected over the course of 3 weeks of instruction. We examined the influence of the software on: group interactions; the mathematical investigations of learners; and the teacher’s interactions with students. Data points to four distinct ways in which the presence of NuCalc positively impacted the learning community we studied: (1) it served as a tool for extending students’ mathematical thinking, (2) it motivated students’ engagement in group discourse, (3) it became a tool for mediating discourse, (4) it became a catalyst for refining the culture of classroom, shifting the patterns of interactions between the teacher and learners.