HPLC-DAD data coupled with second-order calibration method applied to food analysis: Simultaneous determination of six benzoylurea insecticides in various fruit samples by selecting time region of chromatogram

This work presents a novel application of second-order calibration based on self-weighted alternating trilinear decomposition(SWATLD)algorithm for analyzing the HPLC-DAD data.The proposed method makes it possible to simultaneously determine teflubenzuron,hexaflumuron,flufenoxuron,chlorfluazuron,diflubenzuron and benzoylurea in different fruit samples,i.e.pear,apple and banana,in the selected time region of chromatogram.The concentration,elution time and spectral information of these benzoylurea insecticides are selectively extracted from complex matrices even in the presence of unknown interferences.The root-mean-square error of prediction(RMSEP)and figures of merit,including sensitivity(SEN),selectivity(SEL)and limit of detection(LOD)are employed to access the performance of the method.The LODs obtained for these insecticides are within the range 0.017–0.26 ppm in pears,0.039–0.33 ppm in apples,0.041–0.44 ppm in bananas,respectively.Such a chemometrics-based protocol holds great potential to be extended as a promising alternative for more practical applications in food safety and quality monitoring.

Simultaneous determination of metronidazole and tinidazole in plasma by using HPLC-DAD coupled with second-order calibration

A method using HPLC-DAD coupled with second-order calibration was developed to simultaneously determine metronidazole and tinidazole in plasma samples in this paper. The second-order calibration method based on APTLD （alternating penalty trilinear decomposition） algorithm was proposed to analyze the three-way HPLC-DAD data from both standard and prediction samples, which makes it possible that calibration can be performed even in the presence of unknown interferences with a simple and green chromatographic condition and short analysis time. The results showed that good recoveries were obtained although the chromatographic and spectral profiles of the analytes of interest as well as background were partially overlapped with each other in plasma samples.

Second-order calibration applied to quantification of two active components of Schisandra chinensis in complex matrix

The effectiveness of traditional Chinese medicine (TCM) against various diseases urges more low cost, speed and sensitive analytical methods for investigating the phamacology of TCM and providing a theoretical basis for clinical use. The potential of second-order calibration method was validated for the quantification of two effective ingredients of Schisandra chinensis in human plasma using spectrofluorimetry. The results obtained in the present study demonstrate the advantages of this strategy for multi-target determination in complex matrices. Although the spectra of the analytes are similar and a large number of interferences also exist, second-order calibration method could predict the accurate concentrations together with reasonable resolution of spectral profiles for analytes of interest owing to its ‘second-order advantage’. Moreover, the method presented in this work allows one to simply experimental procedure as well as reduces the use of harmful chemical solvents.

Pharmacokinetic Analysis of Four Bioactive Iridoid and Secoiridoid Glycoside Components of Radix Gentianae Macrophyllae and Their Synergistic Excretion by HPLC-DAD Combined with Second-Order Calibration

An HPLC-DAD method combined with second-order calibration based on the alternating trilinear decomposition(ATLD)algorithm with the aid of region selection was developed to simultaneously and quantitatively characterize the synergistic relationships and cumulative excretion of the four bioactive ingredients of Radix Gentianae Macrophyllae in vivo.Although the analytes spectra substantially overlapped with that of the biological matrix,the overlapping profiles between analytes and co-eluting interferences can be successfully separated and accurately quantified by the ATLD method on the basis of the strength of region selection.The proposed approach not only determined the content change but also revealed the synergistic relationships and the cumulative excretion in vivo of the four ingredients in urine and feces samples collected at different excretion time intervals.In addition,several statistical parameters were employed to evaluate the accuracy and precision of the method.Quantitative results were confirmed by HPLC-mass spectrometry.Satisfactory results indicated that the proposed approach can be utilized to investigate the pharmacokinetics of Radix Gentianae Macrophyllae excretion in vivo.

Method for array gain and phase uncertainties calibration based on ISM and ESPRIT

A new method for array calibration of array gain and phase uncertainties, which severely degrade the performance of spatial spectrum estimation, is presented. The method is based on the idea of the instrumental sensors method （ISM）, two well-calibrated sensors are added into the original array. By applying the principle of estimation of signal parameters via rotational invariance techniques （ESPRIT）, the direction-of-arrivals （DOAs） and uncertainties can be estimated simultaneously through eigen-decomposition. Compared with the conventional ones, this new method has less computational complexity while has higher estimation precision, what＇s more, it can overcome the problem of ambiguity. Both theoretical analysis and computer simulations show the effectiveness of the proposed method.

Calibration of Soil Electromagnetic Conductivity in Inverted Salinity Profiles with an Integration Method

Various calibration methods have been propounded to determine profiles of apparent bulk soil electrical conductivity (ECa) and soil electrical conductivity of a saturated soil paste extract (ECe) or a 1:5 soil water extract (EC1:5) using an electromagnetic induction instrument (EM38). The modeled coefficients, one of the successful and classical methods hitherto, were chosen to calibrate the EM38 measurements of the inverted salinity profiles of characteristic coastal saline soils at selected sites of Xincao Farm, Jiangsu Province, China. However, this method required three parameters for each depth layer. An integration approach, based on an exponential decay profile model, was proposed and the model was fitted to all the calibration sites. The obtained model can then be used to predict EC1:5 at a certain depth from electromagnetic measurements made using the EM38 device positioned in horizontal and vertical positions at the soil surface. This exponential decay model predicted the EC1:5 well according to the results of a one-way analysis of variance, and the further comparison indicated that the modeled coefficients appeared to be slightly superior to, but not statistically different from, this exponential decay model. Nevertheless, this exponential decay model was more significant and practical because it depended on less empirical parameters and could be used to perform point predictions of EC1:5 continuously with depth.

A Second-Order Method for the Electromagnetic Scattering from a Large Cavity

In this paper,we study the electromagnetic scattering from a two dimen- sional large rectangular open cavity embedded in an infinite ground plane,which is modelled by Helmholtz equations.By introducing nonlocal transparent boundary con- ditions,the problem in the open cavity is reduced to a bounded domain problem.A hypersingular integral operator and a weakly singular integral operator are involved in the TM and TE cases,respectively.A new second-order Toeplitz type approximation and a second-order finite difference scheme are proposed for approximating the hyper- singular integral operator on the aperture and the Helmholtz in the cavity,respectively. The existence and uniqueness of the numerical solution in the TE case are established for arbitrary wavenumbers.A fast algorithm for the second-order approximation is pro- posed for solving the cavity model with layered media.Numerical results show the second-order accuracy and efficiency of the fast algorithm.More important is that the algorithm is easy to implement as a preconditioner for cavity models with more general media.

Static output feedback stabilization for second-order singular systems using model reduction methods

In this paper,the static output feedback stabilization for large-scale unstable second-order singular systems is investigated.First,the upper bound of all unstable eigenvalues of second-order singular systems is derived.Then,by using the argument principle,a computable stability criterion is proposed to check the stability of secondorder singular systems.Furthermore,by applying model reduction methods to original systems,a static output feedback design algorithm for stabilizing second-order singular systems is presented.A simulation example is provided to illustrate the effectiveness of the design algorithm.

Practical calibration method for instantaneous polarization radar systems utilizing a metal sphere

A practical calibration method is proposed for instantaneous polarization radar systems.The method only needs one measurement by using a metal sphere.The distortions of system and the actual polarization scattering matrix（PSM）of target can be obtained.First,an instantaneous polarization radar system is presented.The system can obtain PSM by a single pulse echo.The dual-polarization antenna can transmit and receive two orthogonal polarization waves.The multilayer micro-strip patch antenna is adopted for this kind of radar system.Second,based on the multi-port network theory,the operation and system errors of instantaneous polarization radar system are analyzed.By making assumption on the cross-talk factors of antenna,distortion matrices of R and Tare derived.Finally,the calibration method based on instantaneous polarization measurement is introduced.Simulation results show the performance of this calibration method.The values of calibrated PSM are in agreement with the actual ones after calibration.

Differential Quadrature Method for Steady Flow of an Incompressible Second-Order Viscoelastic Fluid and Heat Transfer Model

The two-dimensional steady flow of an incompressible second-order viscoelastic fluid between two parallel plates was studied in terms of vorticity, the stream function and temperature equations. The governing equations were expanded with respect to a snmll parameter to get the zeroth- and first-order approximate equations. By using the differenl2al quadrature method with only a few grid points, the high-accurate numerical results were obtained.

Study on the Drift Calibration Method and Device for the Tin Oxide pH Electrode

Drift phenomenon has been known as the drawback of sensors and causes inaccuracy on the long-term measurement. In general,there are two methods to reduce the drift problem.One is to tune the parameters of the fabrication process to improve the properties of the front-ended device.Another is to compensate the drift phenomenon by adding extra drift compensation circuit or software in the back-ended readout circuit.In this study,a drift calibration method for the potentiometric sensor was presented and the drift calibration method was performed by using the circuit.According to experimental results,the drift phenomenon of the SnO_2 pH electrode was reduced by the drift calibration device.

LA-ICP-MS Calibrations for Intact Rock Samples with Internal Standard and Modified Constant-Sum Methods

Laser ablation coupled with inductively coupled plasma-mass spectrometry (LA-ICP-MS) calibration was conducted with multiple spot analyses on eleven intact rock samples using both an internal standard (IS) method and a modified constant-sum (MCS) method. Methods were then compared for reported bulk elemental composition of the rocks. The MCS method was based on the sum of eight major elements, which is spatially more stable than one single major ele-ment as used in the IS method, and is quite constant among different rock samples. Calibrations were performed with standard reference materials NIST SRM 610, 612, 614, and 616. Little difference was found between using a single standard and a set of standards, because of the good linearity shown by the reference materials. Comparison of the two calibration methods shows that the MCS method produced better and more stable results than the IS method for heterogeneous samples. With the MCS method, approximately 94% to 95% of the total measurements are within the range of ±100% relative deviation, compared with 82% to 86% with the IS method. The IS method resulted insubstantial overestimations for some rock samples (e.g., 648% for Basalt BCR-2 using NIST SRM 610 as the calibration standard), while the largest deviation with the MCS method was 216% for U in Eagle Ford shale #80 sample. For Quartz latite QLO-1, a relative homogeneous sample, the IS method generated slightly better results than the MCS method. Regardless of method, spatially heterogeneous distribution of elements in the intact rock at the scale of the laser spot is considered to be the main reason for the large relative deviations seen in our work compared to published results.

Second-order two-scale computational method for ageing linear viscoelastic problem in composite materials with periodic structure

The correspondence principle is an important mathematical technique to compute the non-ageing linear viscoelastic problem as it allows to take advantage of the computational methods originally developed for the elastic case. However, the correspon- dence principle becomes invalid when the materials exhibit ageing. To deal with this problem, a second-order two-scale （SOTS） computational method in the time domain is presented to predict the ageing linear viscoelastic performance of composite materials with a periodic structure. First, in the time domain, the SOTS formulation for calcu- lating the effective relaxation modulus and displacement approximate solutions of the ageing viscoelastic problem is formally derived. Error estimates of the displacement ap- proximate solutions for SOTS method are then given. Numerical results obtained by the SOTS method are shown and compared with those by the finite element method in a very fine mesh. Both the analytical and numerical results show that the SOTS computational method is feasible and efficient to predict the ageing linear viscoelastic performance of composite materials with a periodic structure.

Optimised Calibration Method for Six-Port Junction

A dual-tone technique is used to produce multi-samples in optimising calibration of six-port junction. More accurate results are achieved by using the least-square method and excluding those samples which may cause bigger errors. A 0.80 -1.10 GHz microwave integrated circuit （MIC） six-port reflectometer is constructed. Nine test samples are used in the measurement. With Engen＇s calibration procedure, the difference between the HP8510 and the six-port reflectrometer is in the order of 0.20 dB/1.5° for most cases, above 0.50 dB/5.0° at boundary frequency. With the optimised method, the difference is less than 0. 10 dB/1.0° for most cases, and the biggest error is 0.42 dB/2.1° for boundary frequencies.

Calibration Method of Magnetometer Based on BP Neural Network

Due to the influence of processing technology and environmental factors, there are errors in attitude measurement with the three-axis magnetometer, and the change of parameters during the operation of the magnetometer in orbit will have a great impact on the measurement accuracy. This paper studies the calibration method of magnetometer based on BP neural network, which reduces the influence of model error on calibration accuracy. Firstly, the error model of the magnetometer and the structural characteristics of the BP neural network are analyzed. Secondly, the number of hidden layers and hidden nodes is optimized. To avoid the problem of slow convergence and low accuracy of basic BP algorithm, this paper uses the Levenberg Marquardt backpropagation training method to improve the training speed and prediction accuracy and realizes the on-orbit calibration of magnetometer through online training of the neural network. Finally, the effectiveness of the method is verified by numerical simulation. The results show that the neural network designed in this paper can effectively reduce the measurement error of magnetometer, while the online training can effectively reduce the error caused by the change of magnetometer parameters, and reduce the measurement error of magnetometer to less than 10 nT.

Stochastic Second-Order Two-Scale Method for Predicting the Mechanical Properties of Composite Materials with Random Interpenetrating Phase

In this paper,a stochastic second-order two-scale(SSOTS)method is proposed for predicting the non-deterministic mechanical properties of composites with random interpenetrating phase.Firstly,based on random morphology description functions(RMDF),the randomness of the material properties of the constituents as well as the correlation among these random properties are fully characterized through the topologies of the constituents.Then,by virtue of multiscale asymptotic analysis,the random effective quantities such as stiffness parameters and strength parameters along with their numerical computation formulae are derived by a SSOTS strategy combined with the Monte-Carlo method.Finally,the SSOTS method developed in this paper shows an excellent computational accuracy,and therefore present an important advance towards computationally efficient multiscale modeling frameworks considering microstructure uncertainties.

P-and S-wavefield simulations using both the firstand second-order separated wave equations through a high-order staggered grid finite-difference method

In seismic exploration, it is common practice to separate the P-wavefield from the S-wavefield by the elastic wavefield decomposition technique, for imaging purposes. However, it is sometimes difficult to achieve this, especially when the velocity field is complex. A useful approach in multi-component analysis and modeling is to directly solve the elastic wave equations for the pure P- or S-wavefields, referred as the separate elastic wave equa- tions. In this study, we compare two kinds of such wave equations： the first-order （velocity-stress） and the second- order （displacement-stress） separate elastic wave equa- tions, with the first-order （velocity-stress） and the second- order （displacement-stress） full （or mixed） elastic wave equations using a high-order staggered grid finite-differ- ence method. Comparisons are given of wavefield snap- shots, common-source gather seismic sections, and individual synthetic seismogram. The simulation tests show that equivalent results can be obtained, regardless of whether the first-order or second-order separate elastic wave equations are used for obtaining the pure P- or S-wavefield. The stacked pure P- and S-wavefields are equal to the mixed wave fields calculated using the corre- sponding first-order or second-order full elastic wave equations. These mixed equations are computationallyslightly less expensive than solving the separate equations. The attraction of the separate equations is that they achieve separated P- and S-wavefields which can be used to test the efficacy of wave decomposition procedures in multi-com- ponent processing. The second-order separate elastic wave equations are a good choice because they offer information on the pure P-wave or S-wave displacements.

Resolving double-sided inverse heat conduction problem using calibration integral equation method

In this paper, a novel calibration integral equation is derived for resolving double-sided, two-probe inverse heat conduction problem of surface heat flux estimation. In contrast to the conventional inverse heat conduction techniques, this calibration approach does not require explicit input of the probe locations, thermophysical properties of the host material and temperature sensor parameters related to thermal contact resistance, sensor capacitance and conductive lead losses. All those parameters and properties are inherently contained in the calibration framework in terms of Volterra integral equation of the first kind. The Laplace transform technique is applied and the frequency domain manipulations of the heat equation are performed for deriving the calibration integral equation. Due to the ill-posed nature, regularization is required for the inverse heat conduction problem, a future-time method or singular value decomposition (SVD) can be used for stabilizing the ill-posed Volterra integral equation of the first kind.

Mathematical Programming Method as a Means of Calibration of NIR Analyzers

In addition to the conventional methods of the calibration model construction, such as PCR （principal components regression） and PLS （partial least-squares）, a MPM （mathematical programming method） is developed and proposed for practical use in NIR analyses of agricultural and food products. The proposed method involves the mathematical programming techniques to seek the regression coefficients for the calibration model calculation. It is based on the optimization theory used for finding the extremum of the objective function in the given domain of a vector space and employs the method of the complementarity problems solving. The MPM algorithm is described in detail. The MPM was tested on an InfraLUM FT-10 NIR analyzer of Lumex company with samples of dry milk （for fat）, corn （for protein） and rye flour （for moisture）. The obtained results show that the MPM can be used for constructing multivariate calibrations with the qualitative characteristics superior over those of the classical PCR and PLS methods of analysis.

Improved calibration method for displacement transformation coefficient in optical and visual measurements

Optical and visual measurement technology is used widely in fields that involve geometric measurements,and among such technology are laser and vision-based displacement measuring modules(LVDMMs).The displacement transformation coefficient(DTC)of an LVDMM changes with the coordinates in the camera image coordinate system during the displacement measuring process,and these changes affect the displacement measurement accuracy of LVDMMs in the full field of view(FFOV).To give LVDMMs higher accuracy in the FFOV and make them adaptable to widely varying measurement demands,a new calibration method is proposed to improve the displacement measurement accuracy of LVDMMs in the FFOV.First,an image coordinate system,a pixel measurement coordinate system,and a displacement measurement coordinate system are established on the laser receiving screen of the LVDMM.In addition,marker spots in the FFOV are selected,and the DTCs at the marker spots are obtained from calibration experiments.Also,a fitting method based on locally weighted scatterplot smoothing(LOWESS)is selected,and with this fitting method the distribution functions of the DTCs in the FFOV are obtained based on the DTCs at the marker spots.Finally,the calibrated distribution functions of the DTCs are applied to the LVDMM,and experiments conducted to verify the displacement measurement accuracies are reported.The results show that the FFOV measurement accuracies for horizontal and vertical displacements are better than±15μm and±19μm,respectively,and that for oblique displacement is better than±24μm.Compared with the traditional calibration method,the displacement measurement error in the FFOV is now 90%smaller.This research on an improved calibration method has certain significance for improving the measurement accuracy of LVDMMs in the FFOV,and it provides a new method and idea for other vision-based fields in which camera parameters must be calibrated.