Resolvent criteria for similarity to a normal operator with spectrum on a curve

Dritschel, Michael A.; Estévez, Daniel; Yakubovich, Dmitry V.

doi:10.1016/j.jmaa.2018.03.026

Cited by 2 publications

(1 citation statement)

References 39 publications

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“…is helps to visually verify whether the PCE received at the construction site is acceptable using the quantitative method. Most researchers believe that similarity is an effective parameter to distinguish different spectra [25][26][27]. After literature retrieval, there are many methods to calculate the similarity, among which the angle cosine formula and correlation coefficient formula are more commonly used, which can be evaluated by…”

Section: Ftir Measurements Atr-ftir Spectra Were Obtained Using Ermomentioning

confidence: 99%

Rapid Identification and Quantitative Analysis of Polycarboxylate Superplasticizers Using ATR-FTIR Spectroscopy Combined with Chemometric Methods

Zhao³

et al. 2021

Mathematical Problems in Engineering

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Although the quality inspection method of polycarboxylate superplasticizers (PCE) based on macroperformance is still widely used, it has the drawbacks of time-consuming and low precision. This study aims to develop a practicable alternative method for quality inspection of PCE. For this, spectra collection, feature extraction, and cluster analysis were performed up on the PCE samples to demonstrate the feasibility of the method. Also, a new similarity calculation method was introduced in this work. Results show that the solid PCE sample for spectrum collection can be prepared using the simple heating method. High-quality spectra can be rapidly collected by infrared spectrometer combined with ATR accessory. Meanwhile, the accuracy of classification and clustering is high, suggesting that the feature extraction method based on principal component analysis (PCA) is effective. In addition, compared with conventional similarity calculation methods of cosine angle and correlation coefficient, the new similarity calculation method achieves better classification results and better generalization ability. This work provides a method of quantitative analysis and rapid identification of PCE for the construction site.

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Section: Ftir Measurements Atr-ftir Spectra Were Obtained Using Ermomentioning

confidence: 99%

Rapid Identification and Quantitative Analysis of Polycarboxylate Superplasticizers Using ATR-FTIR Spectroscopy Combined with Chemometric Methods

Zhao³

et al. 2021

Mathematical Problems in Engineering

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show abstract

On the Work by Serguei Naboko on the Similarity to Unitary and Selfadjoint Operators

Yakubovich

2023

Operator Theory: Advances and Applications

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Resolvent criteria for similarity to a normal operator with spectrum on a curve

Cited by 2 publications

References 39 publications

Rapid Identification and Quantitative Analysis of Polycarboxylate Superplasticizers Using ATR-FTIR Spectroscopy Combined with Chemometric Methods

Rapid Identification and Quantitative Analysis of Polycarboxylate Superplasticizers Using ATR-FTIR Spectroscopy Combined with Chemometric Methods

On the Work by Serguei Naboko on the Similarity to Unitary and Selfadjoint Operators

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