药品近红外光谱通用性定量模型评价参数的选择

为寻找药品近红外通用性定量模型在建立过程中用于确立最优模型的关键评价参数组合,收集整理了目前各种商品化化学计量学软件及文献中的13个常用于评价近红外定量模型的统计学参数,结合人用药品注册技术要求国际协调会对于药品定量分析方法验证基本要求,对92个药品近红外通用性定量分析模型的这些参数进行了计算和分析。通过对各个参数之间相互关系的研究,确定了适合于药品近红外通用性定量分析模型评价的参数组合,并统计出了这些参数的数值范围：用于模型准确性评价的关键参数为交叉验证均方根误差/预测均方根误差、平均相对偏差和相对分析误差;大部分交叉验证均方根误差/预测均方根误差结果在3%以内,其中交叉验证均方根误差在数值上与平均绝对偏差相当,大部分相对分析误差值大于2,而平均相对偏差的数值与所建模型的类型(剂型、样品的包装形式)和待测成分含量的分布有关。模型线性评价关键参数为决定系数;大部分模型的决定系数在80%～100%之间。模型耐用性关键评价参数为预测均方根误差与交叉验证均方根误差的比值,大部分模型该参数在1.5以内。精密度评价关键参数为重复测定结果的标准差;该参数对于规范近红外的操作,以及考核模型能否在不同仪器间传递具有重要的意义,但目前药品近红外通用性定量模型对于分析精密度的关注较少,无法估计出具体数值范围。该研究不仅为药品近红外通用性模型的建立者和使用者提供了评价模型优劣的依据,也为完善药品近红外光谱通用性定量分析模型的参数评价体系提供了基础数据。     

Universal fluctuations of the AEX index

We compute the analytic expression of the probability distributions F_AEX,+ and F_AEX,− of the normalized positive and negative AEX (Netherlands) index daily returns r(t). Furthermore, we define the α re-scaled AEX daily index positive returns r(t)^α and negative returns (−r(t))^α, which we call, after normalization, the α positive fluctuations and α negative fluctuations. We use the Kolmogorov-Smirnov statistical test as a method to find the values of α that optimize the data collapse of the histogram of the α fluctuations with the Bramwell-Holdsworth-Pinton (BHP) probability density function. The optimal parameters that we found are α⁺=0.46 and α⁻=0.43. Since the BHP probability density function appears in several other dissimilar phenomena, our result reveals a universal feature of stock exchange markets.     

取代基效应(SCS)与乙烯-α-烯烃共聚物的序列结构Ⅲ.定量分析

本文在分析乙烯-α-烯烃共聚物序列结构时,把代表共单体反接单元的亚甲基(CH₂)βγ和γδ分别归属给了二元组VV和三元组EEV。与此同时,CH₂-δδ和δδ⁺归属给了二元组EE。表征乙烯长序列的CH₂-δ⁺δ⁺分属二元组EE和三元组EEE,对应峰强度在EE和EEE之间的分配是处理序列分布的关键。在本文中运用序列结构的Bovey关系和Randall统计进行演算,求得了修正值△的数学表达式,严格解和近似解。在规则链条件下得到的近似解与G.J.Ray的结果完全相同。当共单体含量较少时,谱峰强度Iδ⁺δ⁺的分配接近相等。在二元组和三元组的水平上,乙烯-α-稀烃共聚物的¹³C NMR谱中共有十三个峰,属于CH₂的有十个,属于CH的有三个。利用这些谱峰的强度数据可以建立一套计算公式,由此提供共聚物序列结构的全部信息。因此这是一个研究乙烯-α-烯烃共聚物序列结构的普适方法。     

On Gouvêa's conjecture in the unobstructed case

In this article, for a residual modular representation defined over an arbitrary finite field, Gouvêa's conjecture which says that the universal deformation ring is isomorphic to a certain Hecke algebra is proven in the unobstructed case.     

固体的热膨胀系数

 本文由Grüneisen第二定则出发，采用普适能量函数作为原子间相互作用势能函数，计算立方晶体金属元素和几种NaCl型结构的碱卤晶体的线膨胀系数。计算值与实验值符合得很好。     

Combinatorial and approximative analyses in a spatially random division process

For a spatial characteristic, there exist commonly fat-tail frequency distributions of fragment-size and -mass of glass, areas enclosed by city roads, and pore size/volume in random packings. In order to give a new analytical approach for the distributions, we consider a simple model which constructs a fractal-like hierarchical network based on random divisions of rectangles. The stochastic process makes a Markov chain and corresponds to directional random walks with splitting into four particles. We derive a combinatorial analytical form and its continuous approximation for the distribution of rectangle areas, and numerically show a good fitting with the actual distribution in the averaging behavior of the divisions.     

Stylized facts in internal rates of return on stock index and its derivative transactions

Universal features in stock markets and their derivative markets are studied by means of probability distributions in internal rates of return on buy and sell transaction pairs. Unlike the stylized facts in normalized log returns, the probability distributions for such single asset encounters incorporate the time factor by means of the internal rate of return, defined as the continuous compound interest. Resulting stylized facts are shown in the probability distributions derived from the daily series of TOPIX, S & P 500 and FTSE 100 index close values. The application of the above analysis to minute-tick data of NIKKEI 225 and its futures market, respectively, reveals an interesting difference in the behavior of the two probability distributions, in case a threshold on the minimal duration of the long position is imposed. It is therefore suggested that the probability distributions of the internal rates of return could be used for causality mining between the underlying and derivative stock markets. The highly specific discrete spectrum, which results from noise trader strategies as opposed to the smooth distributions observed for fundamentalist strategies in single encounter transactions may be useful in deducing the type of investment strategy from trading revenues of small portfolio investors.