三个不同领域实际问题相结合的教学方法探讨

通过建立肿瘤增长动力学模型,研究肿瘤增长动态规律时发现:肿瘤增长的全过程与龚珀兹增长曲线描述的经济增长过程完全相符;进一步给出了龚珀兹增长曲线与描述种群的增长与调节的逻辑斯蒂增长曲线完全相似.将上述三个属性完全不同的实际应用问题打包传授给学生的授课方法是有别于孤立地介绍三个具体问题的,学生的学习效果也会不同.     

Mutual solubilities of hydrocarbons and water with the CPA EoS

The knowledge of hydrocarbon/water phase equilibria is important in the design and operation of equipment for petroleum transport and refining and petrochemical plants. The presence of water in a hydrocarbon mixture can affect the product quality and damage the operation equipment due to corrosion and formation of gas hydrates. Tracing the concentration of hydrocarbons in aqueous media is also important for technical purposes like preventing oil spills and for ecological concerns such as predicting the fate of these organic pollutants in the environment.     

二氧化钛含量对铈稳定立方氧化锆陶瓷的性能影响

本文用无压烧结法成功制备了高硬度的立方氧化锆陶瓷,研究了氧化锆陶瓷的物相,Vickers硬度,显微结构,相对密度等性能,主要分析了TiO2添加量对Zr0.8Ce0.2O2陶瓷硬度和相对密度的影响。结果表明:烧结助剂TiO2可以有效抑制陶瓷晶粒异常生长,加快气孔排除,促进氧化锆陶瓷烧结致密化,提高陶瓷硬度。最高维氏硬度为20.2 GPa,最高相对密度达到了99.8%。     

Proton Conduction at High Temperature in High-Symmetry Hydrogen-Bonded Molecular Crystals of RuIII Complexes with Six Imidazole-Imidazolate Ligands

A new H-bonded crystal [Ru^III(Him)₃(Im)₃] with three imidazole (Him) and three imidazolate (Im⁻) groups was prepared to obtain a higher-temperature proton conductor than a Nafion membrane with water driving. The crystal is constructed by complementary N−H⋅⋅⋅N H-bonds between the Ru^III complexes and has a rare Icy-c* cubic network topology with a twofold interpenetration without crystal anisotropy. The crystals show a proton conductivity of 3.08×10⁻⁵ S cm⁻¹ at 450 K and a faster conductivity than those formed by only HIms. The high proton conductivity is attributed to not only molecular rotations and hopping motions of HIm frameworks that are activated at ∼113 K, but also isotropic whole-molecule rotation of [Ru^III(Him)₃(Im)₃] at temperatures greater than 420 K. The latter rotation was confirmed by solid-state ²H NMR spectroscopy; probable proton conduction routes were predicted and theoretically considered.     

粗糙表面分维计算的立方体覆盖法

针对三角形棱柱表面积法和投影覆盖法在计算粗糙表面分形维数中存在的问题,提出了计算粗糙表面分维的立方体覆盖法,对计算结果进行了对比分析,并进一步对表面分维计算中的有关理论问题进行了分析,发现立方体覆盖法作为一种几何意义上的覆盖法,并计算结果比三角形棱柱表面积法和投影覆盖法更接近实际。     

聚晶立方氮化硼刀具切削高锰钢的磨损机制

在半精加工试验条件(切削深度ap=0．5mm，进给量f=0．3mm／r，干切)下研究了聚晶立方氮化硼刀具切削奥氏体高锰钢时的磨损机制，用WDH-Ⅱ型光电温度计测量了切削温度，用工具显微镜测量后刀面磨损量，进而考察了切削时间和切削速度对后刀面磨损量的影响，采用S-250MK型扫描电子显微镜观察刀具前、后刀面的磨损形貌和组成变化．结果表明：当切削温度为400～750℃时，聚晶立方氮化硼刀具同高锰钢中的γ相及其析出相(Fe，Mn)3C之间产生严重的机械磨损；当切削温度超过800℃时，聚晶立方氮化硼刀具同高锰钢单一γ相之间产生扩散磨损；聚晶立方氮化硼刀具适合于高速切削.     

一类排序问题的求解及效果评估

对一类排序问题给出了一种有效的排序方法.我们将该类排序问题中的属性分为正向属性和负向属性,建立了属性规范化处理的数学模型,得到属性之间无差异的偏好比重,并对偏好比重进行汇总,得到对象之间的排序.最后,利用带自然边界条件的三次样条插值的三弯矩算法对该排序方法进行误差估计.     

倾斜入射的波前编码系统的点扩散函数扩大效应分析

通过对坐标系统进行旋转，计算得到了三次型波前编码系统的倾斜入射的光瞳函数，并给出了近似表达式. 分析表明倾斜入射会产生三次相位扩大效应和离焦扩大效应，它们和入射角的正负无关，且随着入射角绝对值的增大而增大. 这表现在点扩散函数(point spread function, PSF)上会扩展PSF包络的两条直角边，表现在调制传递函数(modulation transfer function, MTF)上会降低MTF值. 子午面倾斜入射时，子午方向的三次相位扩大效应和离焦放大效应大于弧矢方向，从而导致子午方向     

On the Stability of the O(N)-Invariant and the Cubic-Invariant Three-Dimensional N-Component Renormalization-Group Fixed Points in the Hierarchical Approximation

We compute renormalization-group fixed points and their spectrum in an ultralocal approximation. We study a case of two competing nontrivial fixed points for a three-dimensional real N-component field: the O(N)-invariant fixed point vs. the cubic-invariant fixed point. We compute the critical value N _c of the cubic ⁴-perturbation at the O(N)-fixed point. The O(N)-fixed point is stable under a cubic ⁴-perturbation below N _c; above N _c it is unstable. The Critical value comes out as 2.219435<N _c<2.219436 in the ultralocal approximation. We also compute the critical value of N at the cubic invariant fixed point. Within the accuracy of our computations, the two values coincide.