Simultaneous spectrophotometric determination of ethinylestradiol and levonorgestrel by partial least squares and principal component regression multivariate calibration

Two spectrophotometric methods for the determination of Ethinylestradiol (ETE) and Levonorgestrel (LEV) by using the multivariate calibration technique of partial least square (PLS) and principal component regression (PCR) are presented. In this study the PLS and PCR are successfully applied to quantify both hormones using the information contained in the absorption spectra of appropriate solutions. In order to do this, a calibration set of standard samples composed of different mixtures of both compounds has been designed. The results found by application of the PLS and PCR methods to the simultaneous determination of mixtures, containing 4–11 μg ml⁻¹ of ETE and 2–23 μg ml⁻¹ of LEV, are reported. Five different oral contraceptives were analyzed and the results were very similar to that obtained by a reference liquid Chromatographic method.     

Simultaneous Kinetic‐Spectrophotometric Determination of Hydrazine and its Derivatives by Partial Least Squares and Principle Component Regression Methods

Simultaneous kinetic‐spectrophotometric determination of a ternary mixture of hydrazine (HZ) and its derivatives by principal component regression (PCR) and partial least squares (PLS) calibration is described. The methods were based on the difference observed in the reduction rate of iron(III) with HZ, thiosemicarbazide (TSCZ) and phenylhydrazine (PHZ) in the presence of 2,2′‐bipyridine (Bpy). The colored complex of [Fe(Bpy)₃]²⁺ was formed in sodium dodecyl sulfate (SDS) as micellar media, and then monitored at 520 nm. The results showed that simultaneous determination of HZ, TSCZ and PHZ could be performed in their concentration ranges of 1.0–70.0, 0.2–6.0 and 0.1–10.0 μg mL^?1, respectively. The root mean squares errors of prediction (RMSEP) of HZ, TSCZ and PHZ were 0.719, 0.164 and 0.105 (for PLS) 0.788, 0.166 and 0.993 (for PCR), respectively. Both methods (PCR and PLS) were validated using a set of synthetic sample mixtures and then applied for simultaneous determination of HZ, TSCZ and PHZ in water samples.     

Conjugate-gradient method for computing the Moore-Penrose inverse and rank of a matrix

A conjugate-gradient method is developed for computing the Moore-Penrose generalized inverseA of a matrix and the associated projectors, by using the least-square characteristics of both the method and the inverseA . Two dual algorithms are introduced for computing the least-square and the minimum-norm generalized inverses, as well asA . It is shown that (i) these algorithms converge for any starting approximation; (ii) if they are started from the zero matrix, they converge toA ; and (iii) the trace of a sequence of approximations multiplied byA is a monotone increasing function converging to the rank ofA. A practical way of compensating the self-correcting feature in the computation ofA is devised by using the duality of the algorithms. Comparison with Ben-Israel's method is made through numerical examples. The conjugate-gradient method has an advantage over Ben-Israel's method.After having completed the present paper, the author received from Professor M. R. Hestenes his paper entitledPseudo Inverses and Conjugate Gradients. This paper treated the same subject and appeared in Communications of the ACM, Vol. 18, pp. 40–43, 1975.     

Differential Pulse Voltammetric Simultaneous Determination of Four Anti‐Inflammatory Drugs by Using Soft Modelling

An application of a partial least squares calibration method for the simultaneous voltammetric determination of indomethacin, acemethacin, piroxicam and tenoxicam is suggested. It was shown that it is possible to resolve complex mixtures of analytes even when they have strongly overlapped signals. In order to check the proposed method, statistical analysis of the results was performed by mean of hypothesis tests. The method developed was applied to the electrochemical reduction region of four anti‐inflammatory drugs and allowed the drugs to be quantified at concentrations between 0.52 and 4.09 μg mL^?1 for acemethacin, 0.44 and 3.50 μg mL^?1 for indomethacin, 0.43 and 3.40 μg mL^?1 for piroxicam, and 0.42 and 3.30 μg mL^?1 for tenoxicam with good results. The average absolute value of relative errors was 2.25%, 4.31%, 1.68% and 2.49%, respectively.     

LapRLSR for NIR spectral modeling and its application to online monitoring of the column separation of Salvianolate

A novel near infrared (NIR) modeling method—Laplacian regularized least squares regression (LapRLSR) was presented, which can take the advantage of many unlabeled spectra to promote the prediction performance of the model even if there are only few calibration samples. Using LapRLSR modeling, NIR spectral analysis was applied to the online monitoring of the concentration of salvia acid B in the column separation of Salvianolate. The results demonstrated that LapRLSR outperformed partial least squares (PLS) significantly, and NIR online analysis was applicable.     

On a class of least-element complementarity problems

The present paper studies the linear complementarity problem of finding vectorsx andy inR ₊ ⁿ such thatc + Dx + y 0,b – x 0 andx ^T (c + Dx + y) = y ^T (b – x) = 0 whereD is aZ-matrix andb > 0. Complementarity problems of this nature arise, for example, from the minimization of certain quadratic functions subject to upper and lower bounds on the variables. Two least-element characterizations of solutions to the above linear complementarity problem are established first. Next, a new and direct method to solve this class of problems, which depends on the idea of least-element solution is presented. Finally, applications and computational experience with its implementation are discussed.Research partially supported by the National Science Foundation Grant MCS 71-03341 A04 and the Air Force Office of Scientific Research Contract F 44620 14 C 0079.     

Variational approximations for renormalization group transformations

Approximate recursion relations which give upper and lower bounds on the free energy are described. Optimal calculations of the free energy can then be obtained by treating parameters within the renormalization equations variationally. As an example, a particularly simple lower bound approximation which preserves the symmetry of the Hamiltonian (the one-hypercube approximation) is described. The approximation is applied to both the Ising model and the Wilson-Fisher model. At the fixed point a parameter is set variationally and critical indices are calculated. For the Ising model the agreement with the exact results atd = 2 is surprisingly good, 0.1%, and is good atd=3 and evend=4. For the Wilson-Fisher model the recursion relation is reduced to a one-dimensional integral equation which can be solved numerically givingv=0.652 atd=3, or by expansion in agreement with the results of Wilson and Fisher to leading order in . The method is also used to calculate thermodynamic functions for thed = 2 Ising model; excellent agreement with the Onsager solution is found.Supported in part by the National Science Foundation under Grants Nos. MPS73-04886A01 and GH-41512 and by the Brown University Materials Research Laboratory supported by the National Science Foundation. M.C.Y. was supported by a grant from the Scientific and Technical Research Council of Turkey.     

Optimization of Ultrasonic-Assisted Extraction of Active Components and Antioxidant Activity from Polygala tenuifolia: A Comparative Study of the Response Surface Methodology and Least Squares Support Vector Machine

Dried roots of Polygala tenuifolia (YuanZhi in Chinese) are widely used in Chinese herbal medicine. These components in YuanZhi have significant anti-oxidation properties owing to high levels of 3,6’-disinapoylsucrose (DISS) and Polygalaxanthone III (PolyIII). In order to efficiently extract natural medicines, response surface methodology (RSM) and least squares support vector machine (LSSVM) were used for the modeling and optimization of ultrasound-assisted extraction of DISS and PolyIII together to determine the antioxidant activity of the extracts obtained from YuanZhi. For the optimal combination of the comprehensive yield of DISS and PolyIII (Y), the Box-Behnken design (BBD) was used to improve extraction time (X₁), extraction temperature (X₂), liquid–solid ratio (X₃), and ethanol concentration (X₄). The optimal process parameters were determined to be as follows: extraction time, 93 min; liquid–solid ratio, 40 mL/g; extraction temperature, 48 °C; and ethanol concentration, 67%. With these conditions, the predictive optimal combination comprehensive evaluation value is 13.0217. It was clear that the LS-SVM model had higher accuracy in predictive and optimization capabilities, with higher antioxidant activity and lower relative deviations values, than did RSM. Hence, the LS-SVM model proved to be more effective for the analysis and improvement of the extraction process.     

精确确定光路中四分之一波片光轴方位的新方法

为了准确安装四分之一波片,介绍了一种精确确定光路中四分之一波片光轴方位的新方法,并利用米勒矩阵理论分析了影响测量结果的误差因素.测试方法所用的主要理论有米勒矩阵理论、傅里叶分析方法和最小二乘法.该方法利用最小二乘法得到了最优傅里叶系数,利用消光比测试原理实现了检偏棱镜的精确安装,利用反馈环控制系统对步进电机的步进角进行了控制.误差分析表明该方法的测量误差与四分之一波片光轴方位角本身的大小有关.实验结果表明该方法的标准不确定度为0.03.