The Classical Theory of Light Colors: a Paradigm for Description of Particle Interactions

Mazilu, Nicolae; Agop, M.; Gatu, Irina; Iacob, Dan Dezideriu; Butuc, Irina; Ghizdovăţ, Vlad

doi:10.1007/s10773-015-2910-x

Cited by 2 publications

(3 citation statements)

References 14 publications

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“…We note that such a theoretical model can be applied to analyze various dynamics of complex systems (for details, see [29][30][31]); and (vii) The novelty of our method, when compared to other models, such as the ones from [32,33] resides in the fact that fractalization through stochasticization is imposed through group invariance, situation in which the group's transitivity manifolds of SL(2R)-type can be correlated with the scale resolution.…”

Section: Discussionmentioning

confidence: 99%

“…Further details on parameters families of manifolds invariant to groups action can be found in "Integral Geometry" by Stoka [17]. For the current necessities, we will extract only the part that is of importance to us, and that is the fact that group (31) has been produced by induction as a a, b, and c parameters group induced by group (30), under the condition of H(x, y) functions invariance, given by (29). Reciprocally, taking into account groups (30) and (31) for variables a, b, and c and parameters x, y, respectively, the resulting three parameters invariant manifolds families are, indeed, only the functions H(x, y).…”

Section: Sl(2r) Joint Invariant Functions-on the Parametrization Of A...mentioning

confidence: 99%

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Implications and Consequences of SL(2R) as Invariance Group in the Description of Complex Systems Dynamics from a Multifractal Perspective of Motion

Dobreci

Rusu

Vasincu

et al. 2022

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Possible implications and consequences of using SL(2R) as invariance groups in the description at any scale resolution of the dynamics of any complex system are analyzed. From this perspective and based on Jaynes’ remark (any circumstance left unspecified in the description of any complex system dynamics has the concrete expression in the existence of an invariance group), in the present paper one specifies such unspecified circumstances that result directly from the consideration of the canonical formalism induced by the SL(2R) as invariance group. It follows that both the Hamiltonian function and the Guassian distribution acquire the status of invariant group functions, the parameters that define the Hamiltonian acquire statistical significances based on a principle of maximizing informational energy, the class of statistical hypotheses specific to Gaussians of the same average acts as transitivity manifolds of the group (transitivity manifolds which can be correlated with the multifractal-non-multifractal scale transitions), joint invariant functions induced through SL(2R) groups isomorphism (the SL(2R) variables group, and the SL(2R) parameters group, etc.). For an ensemble of oscillators of the same frequency, the unspecified circumstances return to the ignorance of the amplitude and phase of each of the oscillators, which forces the recourse to a statistical ensemble traversed by the transformations of the Barbilian-type group. Finally, the model is validated based on numerical simulations and experimental results that refer to transient phenomena in ablation plasmas. The novelty of our model resides in the fact that fractalization through stochasticization is imposed through group invariance, situation in which the group’s transitivity manifolds can be correlated with the scale resolution.

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Section: Discussionmentioning

confidence: 99%

Section: Sl(2r) Joint Invariant Functions-on the Parametrization Of A...mentioning

confidence: 99%

Implications and Consequences of SL(2R) as Invariance Group in the Description of Complex Systems Dynamics from a Multifractal Perspective of Motion

Dobreci

Rusu

Vasincu

et al. 2022

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“…11 Journal of Immunology Research a relation that can describe the standard dynamics of release at various differentiable scale resolutions, through a convenient choice of variables and parameters (Figure 10). It results that standard release dynamics are explained by temporary kink-type multifractal behaviors (for details on nonlinear kink solutions, see [67][68][69]). We notice also that such a particular solution of our model fits well the experimental data.…”

Section: 2mentioning

confidence: 99%

Poly(vinyl alcohol boric acid)-Diclofenac Sodium Salt Drug Delivery Systems: Experimental and Theoretical Studies

Ailincai¹,

Dorobanțu

Dima

et al. 2020

Journal of Immunology Research

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The main aim of the paper was to simulate the drug release by a multifractal theoretical model, as a valuable method to assess the drug release mechanism. To do this, drug delivery films were prepared by mixing poly(vinyl alcohol boric acid) (PVAB) and diclofenac (DCF) sodium salt drug in different mass ratios from 90/10 to 70/30, in order to obtain drug delivery systems with different releasing rates. The different drug content of the three systems was confirmed by energy-dispersive spectroscopy (EDAX) analysis, and the encapsulation particularities were investigated by scanning electron microscopy (SEM), atomic force microscopy (AFM), and polarized optical microscopy (POM) techniques. The ability of the PVAB matrix to anchor the DCF was assessed by Fourier transform infrared (FTIR) spectroscopy. The in vitro release of the diclofenac sodium salt from the formulations was investigated in biomimetic conditions (pH=7.4 and 37°C) by UV-Vis spectroscopy, measuring the absorbance of the drug at 275 nm and fitting the results on a previously drawn calibration curve. An estimation of the drug release kinetics was performed by fitting three traditional mathematical models on experimental release data. Further, the drug delivery was simulated by the fractal theory of motion, in which the release dynamics of the polymer-drug complex system is described through various Riccati-type “regimes.” To explain such dynamics involved multifractal self-modulation in the form of period doubling, quasiperiodicity, intermittency, etc., as well as multifractal self-modulation of network type. Standard release dynamics were explained by multifractal behaviors of temporary kink type. The good correlation between the traditional mathematical models and the new proposed theoretical model demonstrated the validity of the multifractal model for the investigation of the drug release.

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The Classical Theory of Light Colors: a Paradigm for Description of Particle Interactions

Cited by 2 publications

References 14 publications

Implications and Consequences of SL(2R) as Invariance Group in the Description of Complex Systems Dynamics from a Multifractal Perspective of Motion

Implications and Consequences of SL(2R) as Invariance Group in the Description of Complex Systems Dynamics from a Multifractal Perspective of Motion

Poly(vinyl alcohol boric acid)-Diclofenac Sodium Salt Drug Delivery Systems: Experimental and Theoretical Studies

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