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2.
Regular local hyperrings and hyperdomains
Hashem Bordbar, Irina Elena Cristea, Sanja Rasovic, 2022, original scientific article

Abstract: This paper falls in the area of hypercompositional algebra. In particular, it focuses on the class of Krasner hyperrings and it studies the regular local hyperrings. These are Krasner hyperrings R with a unique maximal hyperideal M having the dimension equal to the dimension of the vectorial hyperspace M. The aim of the paper is to show that any regular local hyperring is a hyperdomain. M2 For proving this, we make use of the relationship existing between the dimension of the vectorial hyperspaces related to the hyperring R and to the quotient hyperring R = R , where a is an element in M \ M2, and of the regularity of R.
Keywords: hyperring, hypermodule, vectorialhyperspace, dimension, regularhyperring, regular parameter element, hyperdomain
Published in RUNG: 27.09.2022; Views: 1306; Downloads: 22
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Time series analysis of duty cycle induced randomness in thermal lens system
Mohanachandran Nair Sindhu Swapna, 2020, original scientific article

Abstract: The present work employs time series analysis, a proven powerful mathematical tool, for investigating the complex molecular dynamics of the thermal lens (TL) system induced by the duty cycle (C) variation. For intensity modulation, TL spectroscopy commonly uses optical choppers. The TL formation involves complex molecular dynamics that vary with the input photothermal energy, which is implemented by varying the duty cycle of the chopper. The molecular dynamics is studied from the fractal dimension (D), phase portrait, sample entropy (S), and Hurst exponent (H) for different duty cycles. The increasing value of C is found to increase D and S, indicating that the system is becoming complex and less deterministic, as evidenced by the phase portrait analysis. The value of H less than 0.5 conforms the evolution of the TL system to more anti-persistent nature with C. The increasing value of C increases the enthalpy of the system that appears as an increase in full width at half maximum of the refractive index profile. Thus the study establishes that the sample entropy and thermodynamic entropy are directly related.
Keywords: Time series analysis Fractal analysis Photothermal lens spectroscopy Fractal dimension Hurst exponent Sample entropy
Published in RUNG: 05.07.2022; Views: 1477; Downloads: 0
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Neural net pattern recognition based auscultation of croup cough and pertussis using phase portrait features
Mohanachandran Nair Sindhu Swapna, 2021, original scientific article

Abstract: Cough signal analysis for understanding the pathological condition has become important from the outset of the exigency posed by the epidemic COVID-19. The present work suggests a surrogate approach for the classification of cough signals - croup cough (CC) and pertussis (PT) – based on spectral, fractal, and nonlinear time-series techniques. The spectral analysis of CC reveals the presence of more frequency components in the short duration cough sound compared to PT. The musical nature of CC is unveiled not only through the spectral analysis but also through the phase portrait features – sample entropy (S), maximal Lyapunov exponent (L), and Hurst exponent (Hb). The modifications in the internal morphology of the respiratory tract, giving rise to more frequency components associated with the complex airflow dynamics, get staged through the higher fractal dimension of CC. Among the two supervised classification tools, cubic KNN (CKNN) and neural net pattern recognition (NNPR), used for classifying the CC and PT signals based on nonlinear time series parameters, NNPR is found better. Thus, the study opens the possibility of identification of pulmonary pathological conditions through cough sound signal analysis.
Keywords: Croup cough Pertussis Fractal dimension Phase portrait Sample entropy Machine learning techniques
Published in RUNG: 04.07.2022; Views: 1287; Downloads: 0
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7.
Evolution of fractal dimension in pulsed laser deposited MoO3 film with ablation time and annealing temperature
Mohanachandran Nair Sindhu Swapna, 2021, original scientific article

Abstract: The multifractal analysis is a potential method for assessing thin flm surface morphology and its changes due to diferent deposition conditions and post-deposition treatments. In this work, the multifractal analysis is carried out to understand the surface morphology—root mean square (RMS) surface roughness—of nanostructured MoO3 flms prepared by pulsed laser deposition technique by varying the ablation time and post-deposition annealing. The XRD analysis shows the evolution of crystalline nature with annealing temperature. The XRD pattern of all the annealed flms shows the characteristic peak of the orthorhombic MoO3 phase. The FESEM and AFM analysis reveals the morphological modifcation with ablation time and annealing temperature. The multifractal analysis of the AFM images shows that the box—counting, information and correlation dimension varies with the annealing temperature. The study also reveals the inverse relation between the fractal dimension and the RMS surface roughness due to the annealing induced particle size variation and reorientation. The fractal dimension’s evolution in the pulsed laser deposited MoO3 flm with ablation time and annealing temperature is also investigated. Thus, the study reveals the potential of multifractal analysis in the thin flm surface characterizatio
Keywords: Multifractal analysis · Pulsed laser deposition · Molybdenum oxide · Atomic force microscopy · Fractal dimension
Published in RUNG: 04.07.2022; Views: 1476; Downloads: 0
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8.
The efflorescent carbon allotropes: Fractality preserved blooming through alkali treatment and exfoliation
Mohanachandran Nair Sindhu Swapna, Sankararaman S, 2020, original scientific article

Abstract: The work reported in the paper elucidates morphological modification induced nanoart and surface area enhancement of graphite, graphene, and soot containing carbon allotropes through ultrasonication and alkali-treatment. The field emission scanning electron microscopic (FESEM) analysis of the samples before and after exfoliation reveals the formation of brilliant flower-like structures from spindle-like basic units due to Ostwald ripening. The x-ray diffraction analysis of the samples gives information about structural composition. The fractal analysis of the FESEM images indicates a multifractal structure with the dimensions—box-counting dimension D0 (1.72), information dimension D1 (1.66), and correlation dimension D2 (1.63)—preserved upon exfoliation. The process of ultra-sonication assisted liquid phase exfoliation resembles blooming as if the carbon allotropes are efflorescent.
Keywords: carbon allotropes, fractal dimension, soot, fractality, alkali treatment, exfoliation
Published in RUNG: 04.07.2022; Views: 1468; Downloads: 0
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9.
Fractal and inertia moment analyses for thin film quality monitoring
Mohanachandran Nair Sindhu Swapna, 2022, original scientific article

Abstract: The widespread applications of thin films in optronics demand innovative techniques for its characterizations. The work reported here proposes electronic speckle pattern interferometry and fractal-based methods for assessing the quality of thin films taking the industrially relevant molybdenum oxide (MoO3) incorporated niobium oxide (Nb2O5) films. The films with different levels of MoO3 incorporation (1, 2, 3, 5, and 10 wt. %) are prepared by radio frequency sputtering. The study reveals the structure modifications of Nb2O5 from the orthorhombic to monoclinic phases with an associated morphological variation revealed through atomic force microscopy and field-emission scanning electron microscopy analyses. The films’ specklegrams are recorded under thermal stress; the inertia moment (IM) and fractal analyses are computed and compared with the root-mean-square surface roughness of the films. The lacunarity analysis of the AFM films agrees well with the specklegrams. Thus, the lower IM and lacunarity values of the specklegrams can be regarded as indicators of the good quality of thin films.
Keywords: cross-correlation, fractal dimension, inertia moment, lacunarity, speckle, surface roughness.
Published in RUNG: 30.06.2022; Views: 1481; Downloads: 0
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10.
Is SARS CoV-2 a multifractal? : unveiling the fractality and fractal structure
Mohanachandran Nair Sindhu Swapna, S. Sreejyothi, Vimal Raj, Sankaranarayana Iyer Sankararaman, 2021, original scientific article

Abstract: A first report of unveiling the fractality and fractal nature of severe acute respiratory syndrome coronavirus (SARS CoV-2) responsible for the pandemic disease widely known as coronavirus disease 2019 (COVID 19) is presented. The fractal analysis of the electron microscopic and atomic force microscopic images of 40 coronaviruses (CoV), by the normal and differential box-counting method, reveals its fractal structure. The generalised dimension indicates the multifractal nature of the CoV. The higher value of fractal dimension and lower value of Hurst exponent (H) suggest higher complexity and greater roughness. The statistical analysis of generalised dimension and H is understood through the notched box plot. The study on CoV clusters also confirms its fractal nature. The scale-invariant value of the box-counting fractal dimension of CoV yields a value of 1.820. The study opens the possibility of exploring the potential of fractal analysis in the medical diagnosis of SARS CoV-2.
Keywords: Fractality, SARS CoV, Coronavirus, Fractal dimension, Multifractal
Published in RUNG: 30.06.2022; Views: 1380; Downloads: 0
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