2—溴甲基萘荧光和室温磷光性质研究

研究了２－溴甲基萘（２－ＢｒＭＮ）的荧光及磷光性质。２－溴甲基萘是一种优良的荧光试剂,λｅｘ／λｅｍ＝２７４／３３４ｎｍ,其浓度在１．０×１０＾－６～１．２×１０＾－４ｍｏｌ·Ｌ＾－１范围内与荧光强度呈良好的线性关系,相关系数ｒ＝０．９９９,最低检测限为４．７×１０＾－８ｍｏｌ·Ｌ＾－１。以β－环糊精（β－ＣＤ）作保护剂和１,２－二溴丙烷（ＤＢＰ）为重原子微扰剂的２－ＢｒＭＮ／β－ＣＤ／ＤＢＰ体系     

A 3-D ellipsoidal flaw model for brittle fracture in compression

Engineering materials are rarely free of flaws. Mode I cracking from pre-existing flaws is the major cause of the brittle fracture in compression of materials such as concrete and rock. A 3-D ellipsoidal flaw model is used to show the significant influence of flaw geometry on crack initiation in uniform uniaxial, biaxial and triaxial compression. The model shows that the governing criterion for crack initiation may change from energy to stress with increasing crack size, and that for voids of similar size a spherical void is the most critical shape for crack initiation. The model thus provides a basis for a better understanding of both the phenomenon and the mechanism of brittle fracture in compression.     

Settling and spreading behaviour of particle clusters in quiescent liquids in confined vessels

Here we report experiments on particle cluster settling at high Reynolds number in quiescent liquid contained in a vessel. The particles were observed to spread at the vessel bottom surface in a near-circular annular shape after settling irrespective of the shape of the vessel cross-section and particle shape, size, and types. Effect of different parameters such as mass, type and aspect ratio of the particles, height, and viscosity of liquid was investigated on spreading behaviour. Formation of the hemispherical bottom cap of the cluster that bounces upon hitting the vessel bottom surface was found to be responsible for the final circular annular shape of the settled structure. Particle leakage from the cluster was seen in the form of a tail. In the liquid having viscosity beyond 100 cP, cluster breakage was observed that resulted in hindered settling and asymmetric shapes of finally settled particles. The observations are useful to understand the overall area over which settling and spreading of such clusters can be observed.     

一类具非标准增长条件和零阶项的抛物方程的存在性结果

在变指数背景下,我们考虑了一类具零阶项的抛物方程解的存在性结果. 存在性的证明在本质上依赖于选取合适的检验函数,这些检验函数要同时兼顾方程右端源项的可积性和零阶项. 利用先验估计和极限分析,借助于Young测度方法确立了非线性项的弱收敛元.     

非奇异M-矩阵Hadamard积的最小特征值的新下界

针对非奇异M-矩阵B与非奇异M-矩阵A的逆矩阵A~(-1)的Hadamard积的最小特征值τ(B·A~(-1))的估计问题,首先利用矩阵A的元素给出A~(-1)各元素的上下界序列,然后利用这些序列和Brauer定理给出τ(B·A~(-1))单调递增收敛的下界序列.最后,通过数值算例验证理论结果,显示所得下界序列比现有结果精确,且能收敛到真值.     

团簇连接对Cu10Ag90快速凝固中晶体结构的影响

快速凝固得到的晶体通常都会形成多种孪晶结构,但其成因一直是一个谜。本文采用分子动力学模拟Cu10Ag90合金在0、20和40 GPa压强下的快速凝固过程,分别形成了五重孪晶、层片状孪晶和复杂晶体,通过最大标准团簇方法(LaSCA)分析了短程有序结构的演变和晶体团簇之间的连接形式。结果发现,结晶转变温度Tc随着压强的增大而升高,平均原子势能也随之增加。非晶共有近邻子团簇(CNS)会在温度降至Tc时转变为晶体CNS,同时晶体团簇数量急剧增加,结构有序度提升。此外,通过分析晶体团簇之间的连接方式发现,五重孪晶中心团簇截边十面体(tDh)只能与具有相同S422的HCP相连形成五重孪晶轴;FCC与HCP有相同的S421,但只能以彼此的顶层或者底层原子作为彼此的中心原子连接形成层片状结构;BCC与FCC、HCP虽然没有共同的CNS,但是可以通过D-S6结构及其变形体连接,其连接方式的多样性是形成复杂晶体的主要原因。这些结果为研究晶体结构不同排列方式提供了新的理解。     

非局部Allen-Cahn模型全离散数值格式的误差估计

在这项工作中,我们研究了求解非局部体积守恒Allen-Cahn (AC)方程的全离散傅里叶伪谱数值格式的误差估计.该数值格式的时间行军方法基于著名的不变能量平方法(IEQ). 我们证明了所提出的全离散数值方法是唯一可解,无条件能量稳定的,并获得了该方案在空间和时间上的最优误差估计.此外,我们还进行了一些数值检验来验证理论结果.     

Teaching children to add and subtract

At a 1980 conference, leading mathematics educators synthesized previous knowledge on children's early understanding of addition and subtraction and proposed central parameters for future research in these areas form a cognitive science perspective. We have, since 1980, increased our knowledge about how children learn to add and subtract, but we need to know more about the best ways for teachers to guide children as they construct knowledge of addition and subtraction.In this article, we review several studies that focus on an enhanced role for teachers in enabling children to learn addition and subtraction. These studies describe efforts that have been made to teach children to use diagrams and mediational representations, number sentences, or algorithms and procedures. The studies report improvement in children's problem-solving performance, but the impact of the efforts described on children's conceptual understanding is less clear. Thus, we analyze this research, pose questions on the relationship of instruction to children's knowledge construction, and propose a research agenda that we believe will enable us to understand how teaching can best help children learn to add and subtract.     

完全Heusler合金Cr2ZrSb/Sc2FeSn(100)异质结的结构、电磁特性及电子性质

本文采用基于密度泛函理论的第一性原理计算,系统研究了完全Heusler合金Cr₂ZrSb/Sc₂FeSn(100)异质结中六种界面CrCr-ScFe-T、ZrSb-ScSn-T、CrCr-ScSn-B、ZrSb-ScFe-B、CrCr-ScFe-V和 ZrSb-ScSn-V的电磁特性及电子性质。结果表明,界面原子间的相互作用造成了界面间原子层的不均匀,导致界面层的力学失配率加大。与块体中的高自旋极化率相比,异质结的自旋极化率遭到不同程度的破坏。但是,ZrSb-ScFe-B界面保留了较高的自旋极化率值,通过Julliere模型预测该异质结在低温下隧道磁电阻值约为429.29%,在自旋电子学器件中具有潜在的应用前景。