Proper Choice of XC Functionals and Calculations of Fluorescence-Emitting Energies for Coumarin Derivatives

A scheme of time-dependent density functional theory (TDDFT) combined with single-excitation configuration interaction (CIS) approach was employed to make a detailed investigation of the emitting energy for fifteen well-known coumarin derivatives. The results showed that the predicted emitting energies as well as the absorption ones were dominated mainly by the exchange-correlation (XC) functional to be used. So long as a functional is properly chosen, the experimental emitting energy of most derivatives can be accurately reproduced within 0.16 eV by a calculation at the TDDFT/6-31G(d)//CIS/3-21G(d) theoretical level. It was found that, nevertheless, the hybrid functional, B3LYP, well predicted the absorption energies for all the fifteen coumarin derivatives but none of the functionals could work equally well for the emitting energy calculations. Two pure functionals, OLYP and BLYP, yield good emitting energies for the 7-aminocoumarins or derivatives with a N atom connected to 7-position, which exhibit inconspicuous charge transfer (CT) in their excited states, whereas the B3LYP hybrid functional, with 20% Hartree-Fock (HF) exchange energy, performs significantly better than OLYP and BLYP for those 3-substituted coumarins with larger CT in excited states. Thus, in comparison with the absorption energies, the selection of proper functionals for the emitting energy calculations becomes more complex. In all probability, it is effective and doable to choose an XC-functional with alterable fraction of HF exchange energy according to the composition and structure characteristics of molecule.     

Reversibility of thought: An instance in multiplicative tasks

In line with current efforts to understand the piece-by-piece structure and articulation of children’s mathematical concepts, this case study compares the reversibility schemes of two eighth-grade students. The aim of the study was to identify the mechanism through which students reverse their thought processes in a multiplicative situation. Data collected through clinical interviews depict the precise strategies that the participants used to work back to find the missing values in an inverse proportional task. This study also illustrates how a conceptual template generated by one of the participants afforded him considerable flexibility in the multiplicative task. Another outcome of the study is that it shows how the numerical characteristics of the parameters in the problem affected the students’ ability to reverse their thought processes. We infer that there is a need for further research on how students might represent their reversibility schemes in the form of algebraic equations.     

傅里叶变换红外光谱固体制样技术

通过对溴化钾与纳米固体超强酸样品的比例进行了探讨 ,得出制样时溴化钾与样品比例范围为1∶ 0 .0 0 1— 1∶ 0 .0 2 9,其最佳比例范围为 1∶ 0 .0 0 98— 1∶ 0 .0 1 5 ,并且应用于其他固体样品的测定 ,结果基本一致。同时得出 ,固体样品的最少检测量为 2 .0× 1 0 -5g     

Composition of aromatic products in the catalytic degradation of the mixture of waste polystyrene and high-density polyethylene using spent FCC catalyst

In this chemical recycling process, spent FCC catalyst used had an advantage with an economical and environment aspect, such as a low catalyst price in liquid-phase reaction and a reuse of waste catalyst. The characteristics of oil product and its aromatic product distribution, as a function of reaction time in the reactor and also proportion of HDPE and PS in the mixture, were compared. Main products obtained were light hydrocarbons within the gasoline range that were mainly produced during initial reaction time. The formation of aromatic products such as styrene and ethylbenzene as major components depended appreciably on the reaction time, as well as the composition of HDPE and PS in the mixture used for degradation. For the distribution of C₉-C₁₂ alkylaromatic components as by-products, methylstyrene (C₁-styrene) and isopropylbenzene (C₃-benzene) components were the main products formed by β-scission and hydrogen transfer of PS, while the rest of alkylaromatic products showed very low fraction being 1% or less.     

Equal Insistence of Proportion of Colour on a 2D Surface

Katz conducted experiments on Insistence and Equal Insistence, using an episcotister, chromatic, and achromatic papers which he viewed under different intensities of a light sources and chromatic illumination. His principle of Equal Insistence, combined with Goethe's reputed proportions of surface colours according to their luminosity, and Strzeminski's concept of Unism in painting inspire the author's current painting practice. However, a whole new route of research has been opened by the introduction of Time as a phenomenon of Equal Insitence and Image Perception Fading, under contolled conditions of observer movement at different distances, viewing angles, and illumination. Visual knowledge of Equal Insistence indicates, so far, several apparent changes to the properties of surface colours, and its actual effect upon the shape and size of paintings and symbolism. Typical of the investigation are the achromatic images of an elephant and a mouse.     

Measurement as relational,intensive and analogical: Towards a minor mathematics

Minor mathematics refers to the mathematical practices that are often erased by state-sanctioned curricular images of mathematics. We use the idea of a minor mathematics to explore alternative measurement practices. We argue that minor measurement practices have been buried by a ‘major’ settler mathematics, a process of erasure that distributes ‘sensibility’ and formulates conditions of mathematics dis/ability. We emphasize how measuring involves the making and mixing of analogies, and that this involves attending to intensive relationships rather than extensive properties. Our philosophical and historical approach moves from the archeological origins of human measurement activity, to pivotal developments in modern mathematics, to configurations of curriculum. We argue that the project of proliferating multiple mathematics is required in order to disturb narrow (and perhaps white, western, male) images of mathematics—and to open up opportunities for a more pluralist and inclusive school mathematics.     

A statistical method for estimating the proportion of differentially expressed genes

Microarrays have been widely used to identify differentially expressed genes. One related problem is to estimate the proportion of differentially expressed genes. For some complex diseases, the amount of differentially expressed genes may be relatively small and these genes may only have subtly differential expressions. For these microarray data, it is generally difficult to efficiently estimate the proportion of differentially expressed genes. In this study, I propose a likelihood-based method coupled with an expectation-maximization (E-M) algorithm for estimating the proportion of differentially expressed genes. The proposed method has favorable performances if either (i) the P values of differentially expressed genes are homogeneously distributed or (ii) the proportion of differentially expressed genes is relatively small. In both of these situations, I showed through simulations that the proposed method gave satisfactory performances when it was compared to other existing methods. As applications, these methods were applied to two microarray gene expression data sets generated from different platforms.     

两种荧光粉混合涂覆的白光LED的光谱方程的建立

为了有效地模拟两种荧光粉混合涂覆的白光LED的发光光谱,选用了硅酸盐系列的绿色荧光粉与高显粉系列的红色荧光粉,应用英国Edinburgh FLS920P型荧光光谱仪,对绿色荧光粉与红色荧光粉进行荧光光谱的实验测量,得到绿色荧光粉发射峰在527 nm,红色荧光粉发射峰在641 nm。配置浓度为7%~17%,比例为3∶1~3∶2的样本,共144个,应用杭州远方色谱有限公司的HAAS-2000高精度光谱辐射计测量LED发光光谱,最后处理数据,得到拟合函数,在这些函数的基础上构建出了光谱方程,该光谱方程是模拟两种荧光粉的浓度和比例的系统方法。为了较为准确的预测出两种荧光粉混合后涂覆于蓝光芯片的发光光谱,对于实验中的数据进行了三维曲面拟合,得出荧光粉的浓度与比例和绿修正系数与红修正系数之间的函数关系式。将得出的绿修正系数和红修正系数的函数关系式应用到光谱方程中,得出最终模拟白光LED发光光谱的一种新方法。并且用了两组的模拟光谱图与实验的光谱图进行对比,发现两种光谱图的吻合效果都较为良好。说明这种模拟白光LED的新方法确实可行,且预测的两种荧光粉混合后涂覆于蓝光芯片的发光光谱较为准确。该方法将具体的荧光粉的质量比和浓度与LED的发光光谱图联系了起来,而之前的大多数研究都是将光谱功率分布与LED发光光谱图联系起来,并未涉及到荧光粉的质量比与浓度。在建立了具体的光谱方程之后,可以在没有实验仪器和不做实验的情况下,根据两种荧光粉的质量比,以及与AB胶混合后的浓度直接得出最终的模拟白光光谱,可以摆脱实验仪器以及其他因素的限制。并且为制备具有特定光谱特性的白光LED提供了新思路,具有一定的实用价值。     

ESIPT和TICT荧光发射的电子结构特征及发射能计算

采用含时密度泛函理论(TDDFT)与单激发组态相互作用(CIS)相结合的计算方案对八种结构相似的水杨酰苯胺衍生物及其类似物第一激发单重态(S1)进行考察, 证实它们的荧光发射分属分子内质子转移(ESIPT)和分子扭转-电荷转移(TICT)两种不同机制且结论与已知实验事实相符. ESIPT发光的化合物在电子跃迁前后无明显的电荷转移发生, 发射能计算的适用泛函是OLYP和BLYP等无Hartree-Fock(HF)交换成分的纯泛函; TICT发光的化合物在电子跃迁前后发生明显的电荷转移, 其适用泛函为含约37% HF交换成分的混合型泛函(例如mPW1B95和MPW1K). 按上述原则来选择适用泛函, 即可在TDDFT/6-31G(d)//CIS/3-21G(d)理论水平上正确预测水杨酰苯胺衍生物和类似物的发射能, 平均精度可达0.2 eV. 兼具质子转移与电荷转移双反应通道的化合物, 两者的竞争遵从能量最小原理, 结果使荧光发射仅选择其中一个通道进行. 泛函的选择只与实际发生的反应有关, 与并未实际发生的反应通道无关. 附加的八个算例进一步表明, 此成功的计算方案可望推广应用于其它类型的ESIPT和TICT荧光有机物.     

Cluster validity for fuzzy clustering algorithms

The proportion exponent is introduced as a measure of the validity of the clustering obtained for a data set using a fuzzy clustering algorithm. It is assumed that the output of an algorithm includes a fuzzy nembership function for each data point. We show how to compute the proportion of possible memberships whose maximum entry exceeds the maximum entry of a given membership function, and use these proportions to define the proportion exponent. Its use as a validity functional is illustrated with four numerical examples and its effectiveness compared to other validity functionals, namely, classification entropy and partition coefficient.