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1.
ACS Omega ; 7(44): 39574-39585, 2022 Nov 08.
Artigo em Inglês | MEDLINE | ID: mdl-36385878

RESUMO

Recent publications are reviewed concerning the development of sensors for the determination of mercury in drinking water, based on spectroscopic methodologies. A critical analysis is made of the specific details and figures of merit of the developed protocols. Special emphasis is directed to the validation and applicability to real samples in the usual concentration range of mercury, considering the maximum allowed limits in drinking water established by international regulations. It was found that while most publications describe in detail the synthesis, structure, and physicochemical properties of the sensing phases, they do not follow the state of the art in the analytical developments. Recommendations are provided regarding the proper method development and validation, including the setting of the calibration concentration range, the correct estimation of the limits of detection and quantitation, the concentration levels to be set for producing spiked water samples, the number of real samples for adequate validation, the comparison of the developed method with a reference technique, and other analytical features which should be followed.

2.
Molecules ; 26(21)2021 Oct 21.
Artigo em Inglês | MEDLINE | ID: mdl-34770766

RESUMO

In this review, recent advances and applications using multi-way calibration protocols based on the processing of multi-dimensional chromatographic data are discussed. We first describe the various modes in which multi-way chromatographic data sets can be generated, including some important characteristics that should be taken into account for the selection of an adequate data processing model. We then discuss the different manners in which the collected instrumental data can be arranged, and the most usually applied models and algorithms for the decomposition of the data arrays. The latter activity leads to the estimation of surrogate variables (scores), useful for analyte quantitation in the presence of uncalibrated interferences, achieving the second-order advantage. Recent experimental reports based on multi-way liquid and gas chromatographic data are then reviewed. Finally, analytical figures of merit that should always accompany quantitative calibration reports are described.

3.
Talanta ; 219: 121288, 2020 Nov 01.
Artigo em Inglês | MEDLINE | ID: mdl-32887030

RESUMO

A new method to quantify the mycotoxin ochratoxin A (OTA) in coffee and tea samples is proposed based on second-order multivariate calibration and excitation-emission fluorescence matrix (EEFM) data. Experimental conditions were optimized by studying the effect of pH and various organized media on the fluorescence signal of OTA. For each analysed matrix (coffee grains and tea leaves), several sample pretreatments and calibration methods (external or standard addition) and data processing by chemometric models (e.g., parallel factor analysis/PARAFAC and multivariate curve resolution-alternating least squares/MCR-ALS) were evaluated and discussed. The MCR-ALS algorithm provided an adequate fit to the data for both samples, while PARAFAC was satisfactory only for the tea samples. Regarding the figures of merit, the limits of detection were in the range of 0.2-0.3 ng mL-1; furthermore, low relative prediction errors, between 2% and 4%, were achieved in both the fortified and real samples. Accordingly, the proposed methodology was applied to analyse fortified roasted and green coffee and real tea leaf samples. Satisfactory recoveries were achieved (ranging from 92 to 110%), and the obtained concentrations were in agreement with the values obtained by the reference method (based on high-performance liquid chromatography with fluorescence detection/HPLC-FLD). In addition, all samples contained OTA levels lower than the maximum permissible levels. Finally, the proposed strategy allows the use of green analytical chemistry principles; for instance, the use of organic solvents and the generation of waste products were significantly lower than for similar analytical methods reported in the literature.


Assuntos
Café , Chá , Calibragem , Cromatografia Líquida de Alta Pressão , Ocratoxinas , Espectrometria de Fluorescência
4.
Talanta ; 204: 700-712, 2019 Nov 01.
Artigo em Inglês | MEDLINE | ID: mdl-31357356

RESUMO

A review is presented of recent multi-way calibration protocols involving three-, four- and five-way data. A brief description of the various data structures and processing models is shown, with emphasis on model selection based on the matching between the data structure and the physicochemical model assumptions. Calibration research works are then discussed, classified according to the type of measured instrumental data and model/algorithm selection.

5.
Talanta ; 197: 348-355, 2019 May 15.
Artigo em Inglês | MEDLINE | ID: mdl-30771946

RESUMO

The endocrine disrupting chemicals bisphenol A (BPA) and 4-nonylphenol (NP) were simultaneously quantified through third-order/four-way calibration. Excitation-emission fluorescence matrix-kinetic (EEFM-K) third-order data were generated by measuring the EEFMs of these priority xenoestrogens as a function of reaction time during their Fenton degradation. Third-order/four-way calibration notably improves the sensitivity of the method and provides the required selectivity for quantifying analytes with critically overlapped fluorescence signals. In fact, collinearity between BPA and NP emission spectra prevented their quantification using EEFM second-order data and three-way PARAFAC (parallel factor analysis); however, the addition of a third instrumental mode allowed the correct chemometric modeling with four-way PARAFAC. In this way, the compliance of Kruskal's theorem extended to higher-order data was verified. The method was applied for the determination of the analytes in samples of different plastic materials, which are in contact with food and/or beverages. In these cases, where unmodelled constituents are present, good results for BPA were achieved with four-way PARAFAC, but the predictions for NP using this model were deficient. A better predictive capability for NP in real samples was achieved when either U-PLS/RTL (unfolded partial least-squares combined with residual trilinearization) or MCR-ALS (multivariate curve resolution with alternating least-squares) was applied for data processing, demonstrating the power of these latter models for the resolution of more complex systems.


Assuntos
Compostos Benzidrílicos/análise , Fluorescência , Contaminação de Alimentos/análise , Fenóis/análise , Plásticos/química , Cinética , Análise dos Mínimos Quadrados
6.
J Chromatogr A ; 1587: 2-13, 2019 Feb 22.
Artigo em Inglês | MEDLINE | ID: mdl-30651205

RESUMO

This review discusses recent advances in both theory and experiment regarding multi-way chromatographic calibration. The focus is directed towards the chemometric processing of multi-way data arrays in which one or more instrumental modes describe the elution time behavior across liquid or gas chromatographic columns, and the remaining ones are of spectroscopic nature, e.g. UV-vis absorption, fluorescence emission (either as vectors or matrices) or mass spectrometry. Successful multi-way data decomposition into profiles for the contributing components allows one to perform quantitative analysis of complex samples. Quantitative applications usually make appropriate use of the second-order advantage which is inherent to multi-way data processing, and reduce the complexity of the data to a virtual univariate calibration which is typical of classical analytical chemistry. A number of recent experimental works will be discussed to illustrate the above concepts.


Assuntos
Cromatografia Gasosa-Espectrometria de Massas/tendências , Calibragem , Técnicas de Química Analítica/tendências , Cromatografia Gasosa-Espectrometria de Massas/normas
7.
Talanta ; 189: 509-516, 2018 Nov 01.
Artigo em Inglês | MEDLINE | ID: mdl-30086953

RESUMO

For the first time, a third-order/four-way system having instrumental modes depending on each other was experimentally generated and it was successfully resolved. Non-quadrilinear type 4 data, constituted by liquid chromatographic elution times (LC) and excitation-emission fluorescence matrices (EEFMs), were on-line measured using conventional equipment. Thus, third-order/four-way data, valuable for giving rise to highly sensitive and selective methods, were obtained minimizing significantly the experimental work and time, in comparison with the reported strategies for the acquisition of LC-EEFM data. The usefulness of MCR-ALS (multivariate curve resolution-alternating least square) for attaining reliable results from data with two mutually dependent instrumental modes, namely elution time and excitation wavelength modes, was established through the simultaneous quantitation of benz[a]anthracene, chrysene, benzo[b]fluoranthene, and benzo[a]pyrene. Limits of detection in the range 1.0-1.4 ng mL-1 were achieved for the target polycyclic aromatic hydrocarbons, allowing their determination in about 9 min per sample in leaves of different types of tea.

8.
ACS Omega ; 3(11): 15771-15779, 2018 Nov 30.
Artigo em Inglês | MEDLINE | ID: mdl-31458227

RESUMO

Third-order liquid chromatographic data were generated online for the simultaneous quantitation of six organic environmental pollutants. The employed strategy consists in reducing the linear flow rate at the column outlet. A postcolumn UV reactor and a fluorimetric detector allowed to properly record both photoinduced and native excitation-emission fluorescence matrices (EEPIFMs and EEFMs, respectively). The obtained third-order liquid chromatography data were chemometrically processed with the multivariate curve resolution-alternating least-squares model. The sensitivity of the overall analytical method was enhanced by a very simple solid-phase extraction with C18 membranes, to be able to successfully apply it to natural water samples tested as real matrices. Favorable detection limits for the investigated pollutants, ranging from 0.02 to 0.27 ng mL-1, were attained, with relative prediction errors between 2 and 7%. Since the studied samples contain uncalibrated interferents, the applied strategy achieves the second-order advantage. Implications regarding the potential achievement of the third-order advantage are discussed.

9.
J Chromatogr A ; 1527: 61-69, 2017 Dec 08.
Artigo em Inglês | MEDLINE | ID: mdl-29102061

RESUMO

For the first time, third-order liquid chromatography with excitation-emission fluorescence matrix detection (LC-EEFM) data were generated on-line and chemometrically processed for the simultaneous quantitation of the heavy-polycyclic aromatic hydrocarbons fluoranthene, pyrene, benz[a]anthracene, chrysene, benzo[b]fluoranthene, benzo[k]fluoranthene, benzo[a]pyrene, and dibenz[a,h]anthracene. The applied experimental strategy is very simple, and is based on the reduction of the linear flow rate by fitting a larger diameter connecting-tube between the column outlet and the fluorimetric detector. In this way, EEFMs were successfully recorded on-line, without involving a large total analysis time. Because in the studied system quadrilinearity was fulfilled, four-way parallel factor (PARAFAC) analysis was applied for data processing. The second-order advantage, which is an intrinsic property of data of at least second-order, allowed the quantification of the analytes in interfering media. Moreover, resolution of the system with a high degree of collinearity was achieved thanks to the third-order advantage. In addition to a selectivity improvement, third-order/four-way calibration increased the sensitivity, with limits of detection in the range of 0.4-2.9ngmL-1. After a solid-phase extraction procedure with C18 membranes, considerably lower concentrations (between 0.033-2.70ngmL-1) were determined in real waters, with most recoveries in the range 90-106%.


Assuntos
Técnicas de Química Analítica/métodos , Cromatografia Líquida , Monitoramento Ambiental/métodos , Hidrocarbonetos Policíclicos Aromáticos/análise , Poluentes Químicos da Água/análise , Técnicas de Química Analítica/instrumentação , Fluorescência , Fluorometria , Limite de Detecção , Extração em Fase Sólida , Água/química
10.
Analyst ; 142(16): 2862-2873, 2017 Aug 07.
Artigo em Inglês | MEDLINE | ID: mdl-28713888

RESUMO

A large number of experimental applications of multi-way calibration are known, and a variety of chemometric models are available for the processing of multi-way data. While the main focus has been directed towards three-way data, due to the availability of various instrumental matrix measurements, a growing number of reports are being produced on order signals of increasing complexity. The purpose of this review is to present a general scheme for selecting the appropriate data processing model, according to the properties exhibited by the multi-way data. In spite of the complexity of the multi-way instrumental measurements, simple criteria can be proposed for model selection, based on the presence and number of the so-called multi-linearity breaking modes (instrumental modes that break the low-rank multi-linearity of the multi-way arrays), and also on the existence of mutually dependent instrumental modes. Recent literature reports on multi-way calibration are reviewed, with emphasis on the models that were selected for data processing.

11.
Anal Chem ; 89(5): 3029-3035, 2017 03 07.
Artigo em Inglês | MEDLINE | ID: mdl-28192965

RESUMO

For the first time, liquid chromatography-diode array detection (LC-DAD) and liquid-chromatography fluorescence detection (LC-FLD) second-order data, collected in a single chromatographic run, were fused and chemometrically processed for the quantitation of coeluting analytes. Two different experimental mixtures composed of fluorescent and nonfluorescent endocrine disruptors were analyzed. Adequate pretreatment of the matrices before their fusion was crucial to attain reliable results. Multivariate curve resolution-alternating least-squares (MCR-ALS) was applied to LC-DAD, LC-FLD, and fused LC-DAD-FLD data. Although different degrees of improvement are observed when comparing the fused matrix results in relation to those obtained using a single detector, clear benefits of data fusion are demonstrated through: (1) the obtained limits of detection in the ranges 2.1-24 ng mL-1 and 0.9-6.3 ng mL-1 for the two evaluated systems and (2) the low relative prediction errors, below 7% in all cases, indicating good recoveries and precision. The feasibility of fusing data and its advantages in the analysis of real samples was successfully assessed through the study of spiked tap, underground, and river water samples.

12.
Talanta ; 165: 52-63, 2017 Apr 01.
Artigo em Inglês | MEDLINE | ID: mdl-28153292

RESUMO

For the first time, a simple and environmentally friendly third-order/four-way calibration was applied for the simultaneous determination of five heavy-polycyclic aromatic hydrocarbons (PAHs) in interfering environments. The kinetic evolution of the Fenton degradation of benzo[a]pyrene, dibenz[a,h]anthracene, benzo[b]fluoranthene, benzo[k]fluoranthene and benz[a]anthracene was followed by recording full excitation-emission fluorescence matrices (EEFMs) of the samples at different reaction times, obtaining third-order EEFM-kinetic (EEFM-K) data. The sensitivity of the method was increased by carrying out the reaction in the presence of methyl-ß-cyclodextrin. The four-way parallel factor (PARAFAC) algorithm, which was used for data processing, exploits the second-order advantage, allowing analyte concentrations to be estimated even in the presence of an uncalibrated fluorescent background. The clear superiority of the applied approach in comparison with second-order/three-way calibration performed with unreacting EEFMs is demonstrated, using two sets of samples with foreign compounds with particular spectral profiles. In one of the latter sets, the existence of a third-order advantage was explored and discussed. The feasibility to directly determine parts-per-trillion concentration levels of PAHs after a very simple solid-phase extraction with C18 membranes is established with natural water samples containing uncalibrated constituents.

13.
J Agric Food Chem ; 64(43): 8254-8262, 2016 Nov 02.
Artigo em Inglês | MEDLINE | ID: mdl-27717286

RESUMO

This work presents a strategy for quantitating polycyclic aromatic hydrocarbons (PAHs) in smoked paprika samples. For this, a liquid chromatographic method with fluorimetric detection (HPLC-FLD) was optimized. To resolve some interference co-eluting with the target analytes, the second-order multivariate curve resolution-alternating least-squares (MCR-ALS) algorithm has been employed combined with this liquid chromatographic method. Among the eight PAHs quantified (fluorene, phenanthrene, anthracene, pyrene, chrysene, benzo[a]anthracene, benzo[b]fluoranthene, and benzo[a]pyrene) by HPLC-FLD, only in the case of fluorene, pyrene, and benzo[b]fluoranthene was it necessary to apply the second-order algorithm for their resolution. Limits of detection and quantitation were between 0.015 and 0.45 mg/kg and between 0.15 and 1.5 mg/kg, respectively. Good recovery results (>80%) for paprika were obtained via the complete extraction procedure, consisting of an extraction from the matrix and the cleanup of the extract by means of silica cartridges. Higher concentrations of chrysene, benzo[a]anthracene, benzo[b]fluoranthene, and benzo[a]pyrene were found in the paprika samples, with respect to the maximal amounts allowed for other spices that are under European Regulation (EU) N° 2015/1933.


Assuntos
Capsicum/química , Cromatografia Líquida/métodos , Análise de Alimentos/métodos , Hidrocarbonetos Policíclicos Aromáticos/análise , Algoritmos , Calibragem , Contaminação de Alimentos/análise , Análise dos Mínimos Quadrados , Análise Multivariada , Reprodutibilidade dos Testes
14.
Talanta ; 159: 336-343, 2016 Oct 01.
Artigo em Inglês | MEDLINE | ID: mdl-27474316

RESUMO

The aim of this study was to develop a novel analytical method for the determination of bisphenol A, nonylphenol, octylphenol, diethyl phthalate, dibutyl phthalate and diethylhexyl phthalate, compounds known for their endocrine-disruptor properties, based on liquid chromatography with simultaneous diode array and fluorescent detection. Following the principles of green analytical chemistry, solvent consumption and chromatographic run time were minimized. To deal with the resulting incomplete resolution in the chromatograms, a second-order calibration was proposed. Second-order data (elution time-absorbance wavelength and elution time-fluorescence emission wavelength matrices) were obtained and processed by multivariate curve resolution-alternating least-squares (MCR-ALS). Applying MCR-ALS allowed quantification of the analytes even in the presence of partially overlapped chromatographic and spectral bands among these compounds and the potential interferents. The obtained results from the analysis of beer, wine, soda, juice, water and distilled beverage samples were compared with gas chromatography-mass spectrometry (GC-MS). Limits of detection (LODs) in the range 0.04-0.38ngmL(-1) were estimated in real samples after a very simple solid-phase extraction. All the samples were found to contain at least three EDs, in concentrations as high as 334ngmL(-1).


Assuntos
Bebidas/análise , Cromatografia Líquida , Disruptores Endócrinos/análise , Análise de Alimentos/métodos , Plásticos/química , Fluorescência , Análise de Alimentos/instrumentação
15.
Environ Pollut ; 209: 114-22, 2016 Feb.
Artigo em Inglês | MEDLINE | ID: mdl-26650083

RESUMO

A green method is reported based on non-sophisticated instrumental for the quantification of seven natural and synthetic estrogens, three progestagens and one androgen in the presence of real interferences. The method takes advantage of: (1) chromatography, allowing total or partial resolution of a large number of compounds, (2) dual detection, permitting selection of the most appropriate signal for each analyte and, (3) second-order calibration, enabling mathematical resolution of incompletely resolved chromatographic bands and analyte determination in the presence of interferents. Consumption of organic solvents for cleaning, extraction and separation are markedly decreased because of the coupling with MCR-ALS (multivariate curve resolution/alternating least-squares) which allows the successful resolution in the presence of other co-eluting matrix constituents. Rigorous IUPAC detection limits were obtained: 6-24 ng L(-1) in water, and 0.1-0.9 ng g(-1) in sediments. Relative prediction errors were 2-10% (water) and 1-8% (sediments).


Assuntos
Cromatografia Líquida de Alta Pressão/métodos , Fluorometria/métodos , Sedimentos Geológicos/análise , Hormônios Esteroides Gonadais/análise , Poluentes Químicos da Água/análise , Cromatografia Líquida de Alta Pressão/instrumentação , Hormônios Esteroides Gonadais/síntese química
16.
Talanta ; 143: 162-168, 2015 Oct 01.
Artigo em Inglês | MEDLINE | ID: mdl-26078144

RESUMO

The aim of this work was to quantify two relevant priority chemicals, bisphenol A (BPA) and 4-nonylphenol (NP), coupling the sensitivity of fluorescence in organized media and the selectivity of multivariate calibration, measuring excitation-emission fluorescence matrices in an aqueous methyl-ß-cyclodextrin solution. The studied priority pollutants are two of the most frequently found xenoestrogens in the environment, and are therefore of public health concern.The data were successfully processed by applying unfolded partial least-squares coupled to residual bilinearization (U-PLS/RBL), which provided the required selectivity for overcoming the severe spectral overlapping among the analyte spectra and also those for the interferents present in real samples. A rigorous International Union of Pure and Applied Chemistry (IUPAC)-consistent approach was applied for the calculation of the limits of detection. Values in the ranges of 1-2 and 4-14 ng mL(-1) were obtained in validation samples for BPA and NP, respectively. On the other hand, low relative prediction errors between 3% and 8% were achieved. The proposed method was successfully applied to the determination of BPA and NP in different plastics. In positive samples, after an easy treatment with a small volume of ethanol at 35°C, concentrations were found to range from 26 to 199 ng g(-1) for BPA, and from 95 to 30,000 ng g(-1) for NP.


Assuntos
Compostos Benzidrílicos/análise , Compostos Benzidrílicos/química , Ciclodextrinas/química , Informática , Fenóis/análise , Fenóis/química , Plásticos/química , Estudos de Viabilidade , Embalagem de Alimentos , Química Verde , Espectrometria de Fluorescência , Fatores de Tempo
17.
Talanta ; 134: 215-223, 2015 Mar.
Artigo em Inglês | MEDLINE | ID: mdl-25618660

RESUMO

An eco-friendly strategy for the simultaneous quantification of three emerging pharmaceutical contaminants is presented. The proposed analytical method, which involves photochemically induced fluorescence matrix data combined with second-order chemometric analysis, was used for the determination of carbamazepine, ofloxacin and piroxicam in water samples of different complexity without the need of chromatographic separation. Excitation-emission photoinduced fluorescence matrices were obtained after UV irradiation, and processed with second-order algorithms. Only one of the tested algorithms was able to overcome the strong spectral overlapping among the studied pollutants and allowed their successful quantitation in very interferent media. The method sensitivity in superficial and underground water samples was enhanced by a simple solid-phase extraction with C18 membranes, which was successful for the extraction/preconcentration of the pollutants at trace levels. Detection limits in preconcentrated (1:125) real water samples ranged from 0.04 to 0.3 ng mL(-1). Relative prediction errors around 10% were achieved. The proposed strategy is significantly simpler and greener than liquid chromatography-mass spectrometry methods, without compromising the analytical quality of the results.


Assuntos
Carbamazepina/análise , Água Potável/química , Água Doce/química , Ofloxacino/análise , Piroxicam/análise , Poluentes Químicos da Água/análise , Algoritmos , Fluorescência , Química Verde , Humanos , Limite de Detecção , Espectrometria de Fluorescência , Raios Ultravioleta
18.
Anal Chim Acta ; 852: 105-11, 2014 Dec 10.
Artigo em Inglês | MEDLINE | ID: mdl-25441886

RESUMO

This work presents a green and very simple approach which enables the accurate and simultaneous determination of benzo[a]pyrene, dibenz[a,h]anthracene, benz[a]anthracene, and chrysene, concerned and potentially carcinogenic heavy-polycyclic aromatic hydrocarbons (PAHs) in interfering samples. The compounds are extracted from water samples onto a device composed of a small rotating Teflon disk, with a nylon membrane attached to one of its surfaces. After extraction, the nylon membrane containing the concentrated analytes is separated from the Teflon disk, and fluorescence excitation-emission matrices are directly measured on the nylon surface, and processed by applying parallel factor analysis (PARAFAC), without the necessity of a desorption step. Under optimum conditions and for a sample volume of 25 mL, the PAHs extraction was carried out in 20 min. Detection limits based on the IUPAC recommended criterion and relative errors of prediction were in the ranges 20-100 ng L(-1) and 5-7%, respectively. Thanks to the combination of the ability of nylon to strongly retain PAHs, the easy rotating disk extraction approach, and the selectivity of second-order calibration, which greatly simplifies sample treatment avoiding the use of toxic solvents, the developed method follows most green analytical chemistry principles.


Assuntos
Membranas Artificiais , Nylons/química , Hidrocarbonetos Policíclicos Aromáticos/análise , Extração em Fase Sólida/métodos , Espectrometria de Fluorescência/métodos , Poluentes Químicos da Água/análise , Desenho de Equipamento , Limite de Detecção , Hidrocarbonetos Policíclicos Aromáticos/isolamento & purificação , Extração em Fase Sólida/instrumentação , Espectrometria de Fluorescência/instrumentação , Poluentes Químicos da Água/isolamento & purificação
19.
Anal Chim Acta ; 835: 19-28, 2014 Jul 04.
Artigo em Inglês | MEDLINE | ID: mdl-24952625

RESUMO

Following the green analytical chemistry principles, an efficient strategy involving second-order data provided by liquid chromatography (LC) with diode array detection (DAD) was applied for the simultaneous determination of estriol, 17ß-estradiol, 17α-ethinylestradiol and estrone in natural water samples. After a simple pre-concentration step, LC-DAD matrix data were rapidly obtained (in less than 5 min) with a chromatographic system operating isocratically. Applying a second-order calibration algorithm based on multivariate curve resolution with alternating least-squares (MCR-ALS), successful resolution was achieved in the presence of sample constituents that strongly coelute with the analytes. The flexibility of this multivariate model allowed the quantification of the four estrogens in tap, mineral, underground and river water samples. Limits of detection in the range between 3 and 13 ng L(-1), and relative prediction errors from 2 to 11% were achieved.


Assuntos
Água Potável/química , Estrogênios/análise , Água Subterrânea/química , Águas Minerais/análise , Rios/química , Cromatografia Líquida/métodos , Cromatografia Líquida/normas , Poluentes Químicos da Água/análise
20.
Anal Chim Acta ; 806: 8-26, 2014 Jan 02.
Artigo em Inglês | MEDLINE | ID: mdl-24331038

RESUMO

An introduction to multi-way calibration based on second- and higher-order data generation and processing is provided, with emphasis on practical experimental aspects. After a discussion concerning a proper nomenclature scheme, a suitable classification of the obtainable data, and the general features of the available algorithms and their underlying models, a series of examples is discussed in detail, with the purpose of illustrating the great potentiality of the field for the analytical community. Emphasis is directed toward the most popular multi-way data, i.e., second-order or matrix data, which can be conveniently measured in a variety of instruments. Third-order data are being increasingly studied and are also discussed, along with the less explored field of fourth-order data. The estimation of figures of merit, which analysts need to report during method development, is now sufficiently mature to be provided for the general audience.

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