The population-sample decomposition approach to multivariate estimation methods

In this paper it is argued that all multivariate estimation methods, such as OLS regression, simultaneous linear equations systems and, more widely, what are known as LISREL methods, have merit as geometric approximation methods, even if the observations are not drawn from a multivariate normal parent distribution and consequently cannot be viewed as ML estimators. It is shown that for large samples the asymptotical distribution of any estimator, being a totally differentiable covariance function, may be assessed by the δ method. Finally, we stress that the design of the sample and a priori knowledge about the parent distribution may be incorporated to obtain more specific results. It turns out that some fairly traditional assumptions, such as assuming some variables to be non-random, fixed over repeated samples, or the existence of a parent normal distribution, may have dramatic effects on the assessment of standard deviations and confidence bounds, if such assumptions are not realistic. The method elaborated by us does not make use of such assumptions.     

Development of algorithms for automated spectrophotometric titrations

A versatile method for evaluation of equilibrium constants from automated spectrophotometric titrations is described. General algorithms were derived for normalized titration curves of reactions having various stoichiometric ratios. Normalization of data involve converting it from absorption versus time to product formed (0 to 1) versus equivalents of titrant added. Relevance of derived algorithms was assessed by the quality of their fit to real data. The demonstration system chosen for this investigation was the 1:3 complexation reaction of Fe(II) and 1,10-phenantroline (o-Phen). Titrations were performed at three distinct infusion rates under controlled pH of 5.0 and at 25.0 °C, with sets produced using both Fe(II) and o-Phen as the titrant. Direct fitting of titration curves yielded values for overall equilibrium constants. Furthermore, resulting curves revealed reproducible initial deviation, consistent with step-wise reaction, when titrating Fe(II) with o-Phen. No unusual deviations were evident anywhere in the titration curves when Fe(II) was the titrant. Overall, our approach facilitates adoption of automated titrimetry and data analysis methodologies for the determination of stoichiometries and equilibrium constants of many UV/Vis active reactions.     

基于模糊聚类分析和曲线拟合的FTIR不同产地鸡骨草、毛鸡骨草鉴别分析

利用傅里叶变换红外光谱技术结合模糊聚类分析法和曲线拟合对鸡骨草、毛鸡骨草进行产地鉴别。选用曼哈顿距离单位计算的相异度聚类分析结果最优,5个产地鸡骨草都可完全区分开来,毛鸡骨草则只能鉴别出3个产地,南宁和钦州2个产地发生重叠;为了进一步鉴别不同产地鸡骨草和毛鸡骨草,对鸡骨草和毛鸡骨草平均红外谱图中1 034 cm-1吸收峰进行曲线拟合,野生鸡骨草拟合出11个子峰,其他各产地鸡骨草均只能拟合出9个子峰,上林产毛鸡骨草拟合出9个子峰,其他各产地毛鸡骨草均只能拟合出8个子峰,而且不同产地鸡骨草和毛鸡骨草拟合出的子峰位置和归一化强度都不完全相同;模糊聚类分析法和曲线拟合法有机结合能够使产地鉴别结果更加准确。     

CE Determination of Monosaccharides in Pulp Using Indirect Detection and Curve-Fitting

In the present work a capillary electrophoretic method for the analysis of monosaccharides utilizing indirect UV-detection has been developed. Different probes for indirect detection have been assessed using model carbohydrate samples. Background electrolytes with or without addition of cetyltrimethylammonium bromide have also been evaluated regarding the separation power. Furthermore, a curve-fitting algorithm has been introduced to increase the separation resolution. The optimized method has been used for analysis of monosaccharides from an acidically hydrolyzed pulp sample.     

Describing the soil physical characteristics of soil samples with cubical splines

The Mualem-Van Genuchten equations have become very popular in recent decades. Problems were encountered fitting the equations’ parameters through sets of data measured in the laboratory: parameters were found which yielded results that were not monotonic increasing or decreasing. Due to the interaction between the soil moisture retention and the hydraulic conductivity relationship, some data sets yield a fit that seems not to be optimal. So the search for alternatives started. We ended with the cubical spline approximation of the soil physical characteristics. Software was developed to fit the spline-based curves to sets of measured data. Five different objective functions are tested and their results are compared for four different data sets. It is shown that the well-known least-square approximation does not always perform best. The distance between the measured points and the fitted curve, as can be evaluated numerically in a simple way, appears to yield good fits when applied as a criterion in the optimization procedure. Despite an increase in computational effort, this method is recommended over the least square method.     

FTIR研究南方锈病侵染对玉米叶片中蛋白质和碳水化合物的影响

为深入研究南方锈病侵染玉米叶片时叶片的生化指标变化,使用傅里叶变换红外光谱仪分别获取感染和未感染玉米叶片的光谱,选用光谱中的特征区和指纹区吸收带分析玉米叶片中蛋白质和碳水化合物的变化情况.玉米叶片被感染后,其光谱的酰胺带发生变化,碳水化合物的主要吸收带变化不明显.通过对波数范围在1 800~1 480内的吸收带进行曲线拟合分析,发现感染后的叶片中折叠和螺旋结构在蛋白质二级结构中的含量比例降低;感染前期蛋白质二级结构中转角结构含量比例增大;感染后期玉米叶片中蛋白质二级结构的自由卷曲结构含量比例急剧增大,该结构在感染前期和健康叶片中均未出现.研究表明傅里叶变换红外光谱结合曲线拟合分析技术可用于探索玉米叶片被南方锈病侵染时所含化学物质的变化,为玉米抗病性研究提供重要依据.     

五种杂交玉米籽粒品质的FTIR光谱研究

为了研究傅里叶变换红外光谱在杂交玉米品质评定上的可行性,使用傅里叶变换红外光谱仪获得五种杂交玉米籽粒的光谱。1 776～952 cm-1范围内的光谱主要由蛋白质、淀粉和油脂的红外吸收带组成,淀粉的吸收带较为强烈,蛋白质和油脂的吸收带稍弱。该范围光谱中特征吸收带相互重叠,导致一些重要信息被掩盖。通过对1 776～952 cm-1范围内的红外光谱进行曲线拟合分析,发现1 051和1 548 cm-1吸收子峰的面积在1 776～952 cm-1范围内吸收带总面积中占的百分比与玉米籽粒中淀粉和蛋白质的含量存在着线性关系。研究结果显示傅里叶变换红外光谱结合曲线拟合分析技术可用以分析杂交玉米籽粒中淀粉和蛋白质的含量,为玉米品质的快速评定提供一种方法。     

煤系针状焦微晶结构的XRD与Raman分峰拟合定量研究

采用XRD和Raman光谱分析技术,结合分峰拟合的数学方法,对不同生产厂家的三种煤系针状焦Coke-N,Coke-H,Coke-P进行了研究。由XRD分析结果计算出了三种针状焦的石墨化度、晶体结构类型以及晶粒尺寸(La和Lc),通过对XRD的分峰拟合处理,得出了三种针状焦中趋于规整结构的碳微晶含量(Ig)。通过对样品的XRD分析可知,Coke-N和Coke-P的石墨化程度及Lc相接近,并且明显大于Coke-H;La之间的关系为:Coke-NCoke-PCoke-H。通过Raman光谱结合分峰拟合的数学方法对样品进行了定量分析。研究结果表明,三种针状焦在拉曼位移1 000~2 000cm-1处有5个一阶谱拟合峰(G,D1,D2,D3,D4)。对样品的拉曼一阶谱拟合后所得出的每个拟合峰面积进行计算,可以用来定量分析三种针状焦中碳微晶结构的分布情况。由I_G/I_(All),I_(D1)/I_G,I_(D2)/I_G,I_(D3)/I_G,I_(D4)/I_G的计算可知,Coke-N和Coke-P的微晶结构比Coke-H的微晶结构更规整。在Coke-N中理想石墨碳微晶所占比例为0.33,而Coke-H和Coke-P分别为0.086和0.311。另外,Coke-H在三个样品中的无定形碳比例明显大于另外两个样品。Raman光谱分析结果与XRD的分析结果相吻合。由此可以看出,采用XRD和拉曼光谱分析技术可以从微观层面判定宏观质量不同的煤系针状焦差异的实质。     

FTIR光谱法研究天花粉蛋白的热去折叠过程

本文利用ＦＴＩＲ光谱技术和计算机辅助解析技术（二阶导数、去卷积和曲线拟合）研究了天花粉蛋白的热诱导去折叠过程。结果表明：在２５～８５℃温度范围内,天花粉蛋白的热去折叠是一个不可逆的分子间聚集的过程;二级结构随温度的变化暗示了折叠中间体的存在。