iosr-Jm   Volume-21 ~ Issue-2 ~ Mar. – Apr. 2025

Abstract : This paper proposes a multi-substance identification and analysis algorithm based on Fourier Transform Infrared (FTIR) spectroscopy. The algorithm begins with baseline correction and data length normalization of the FTIR spectra. From the perspective of overall optimization, the mixture data is analyzed using the non-negative least squares algorithm to identify potential substances in the database. Subsequently, key features such as the maximum values of spectral peaks, peak widths, and the left and right minimum values are extracted to construct a feature.......

Keywords: Fourier Transform Infrared Spectroscopy; Multi-Substance Mixture; Qualitative Analysis; Overall Optimization; Local Optimization

[1]. Pan Dongning, Zhao Leihong, Xie Wenjun. Detection method of precursor mixed gases based on neural network and Fourier spectral analysis[J]. Infrared, 2024, 45(4): 46-52.
[2]. Shen Yunxia, Zhao Yanli, Zhang Ji, et al. Identification of different processed Gentiana rigescens by Fourier transform infrared spectroscopy[J]. Spectroscopy and Spectral Analysis, 2016, 36(5): 1369-1373.
[3]. Curk M C, Peledan F, Hubert J C. Fourier transform infrared (FTIR) spectroscopy for identifying Lactobacillus species[J]. FEMS microbiology letters, 1994,123, (3):241-248.
[4]. Jiang An. Research on qualitative analysis methods of complex mixtures based on infrared spectroscopy[D]. Graduate University of Chinese Academy of Sciences, 2012.
[5]. Liu Caizheng, Zhu Qibing, Huang Min, et al. Component identification method of mixtures based on Raman spectroscopy[J]. Laser & Optoelectronics Progress, 2019, 56(8): 253-259.

Abstract : Fermatean fuzzy sets (FFSs), an extension of intuitionistic fuzzy sets and Pythagorean fuzzy sets, provide a more generalized framework for handling uncertainty. In this paper, we introduce the concept of (𝛼,𝛽)-cut in the context of FFSs over near ring and investigate some algebraic structure of (𝛼,𝛽)-cut sets in FFSs over near rings. The notions cut sets of Fermatean fuzzy ideals (FFIs) are discussed. Also, we establish some conditions for which cut set of FFI over near ring form FFI over near rings.

Keywords: Intuitionistic fuzzy set, pythagorean fuzzy set, fermatean fuzzy set, fermatean fuzzy ideals, cut set of fermatean fuzzy set, fermatean fuzzy homomorphism near-rings.

[1] A. Abou-Zaid, On Fuzzy Subnear-Ring, Fuzzy Sets And Systems, 81 (1989) 383-393.
[2] A. K. Adak And M. Bhowmik, Interval Cut-Set Of Interval-Valued Intuitionistic Fuzzy Sets, African Journal Of Mathematics And Computer Sciences, 4(4) (2011) 192-200.
[3] A. K. Adak, M. Bhowmik And M. Pal, Semiring Of Interval-Valued Intuitionistic Fuzzy Matrices, Global Journal Of Computer Application And Technology, 1(3) (2011) 340-347.
[4] A. K. Adak, M. Bhowmik And M. Pal, Interval Cut-Set Of Generalized Interval-Valued Intuitionistic Fuzzy Sets, International Journal Of Fuzzy System Applications, 2 (3) (2012) 35-50.
[5] A. K. Adak, M. Bhowmik And M. Pal, Intuitionistic Fuzzy Block Matrix And Its Some Properties, Annals Of Pure And Applied Mathematics, 1(1) (2012) 13-31.

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Abstract : A new exponentially fitted three term method is developed for the numerical treatment of linear second order singularly perturbed delay differential equations which involves the small delay in first- differentiated term. The solution of such equations with the interval and boundary conditions exhibits left layer or right layer behaviour. The method uses the Taylor's series expansion for constructing an equivalent valid version of the original problem first and then, to derive a new three term finite difference recurrence relationship/scheme. The non-uniformity in the solution is resolved by the introduction of a suitable fitting parameter in the derived new scheme using the theory of singular......

Keywords: Differential-difference equation, singular perturbation problem, boundary layer, Stability and convergence

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