Toward Interactions through Information in a Multifractal Paradigm

Agop, Maricel; Gavriluţ, Alina; Grigoraș-Ichim, Claudia Elena; Toma, Ştefan Lucian; Petrescu, Tudor-Cristian; Irimiciuc, Ștefan Andrei

doi:10.3390/e22090987

Cited by 3 publications

(2 citation statements)

References 20 publications

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“…The complex parameters

and

from Equation (54) now have a direct connection with the classic theory of Newtonian-type potentials (for details, see [ 12 , 13 , 28 , 29 , 30 ]) based on harmonic mappings [ 31 ]. In order to prove this, we need to rewrite

and

in the terms

.…”

Section: Investigations Of Interactions Through Harmonic Mappings mentioning

confidence: 99%

“…The utilized variational principle which gives the above-mentioned result (i.e., Equation (59)) is obtained from the metric in (53), which is invariant when related to a certain transformation group: the group

, to be precise (for details, see [ 11 , 12 , 13 , 28 , 29 , 30 , 31 ]). Now, if the functionality of the equivalence principle is admitted for an arbitrary manifold point, the coordinate

represents the intensity of the fields, while the previously mentioned group represents the transition between the various fields which act in that point.…”

Section: Investigations Of Interactions Through Harmonic Mappings mentioning

confidence: 99%

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The Role of Information in Managing Interactions from a Multifractal Perspective

Agop

Irimiciuc

Ghenadi

et al. 2021

Entropy

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In the framework of the multifractal hydrodynamic model, the correlations informational entropy–cross-entropy manages attractive and repulsive interactions through a multifractal specific potential. The classical dynamics associated with them imply Hubble-type effects, Galilei-type effects, and dependences of interaction constants with multifractal degrees at various scale resolutions, while the insertion of the relativistic amendments in the same dynamics imply multifractal transformations of a generalized Lorentz-type, multifractal metrics invariant to these transformations, and an estimation of the dimension of the multifractal Universe. In such a context, some correspondences with standard cosmologies are analyzed. Since the same types of interactions can also be obtained as harmonics mapping between the usual space and the hyperbolic plane, two measures with uniform and non-uniform temporal flows become functional, temporal measures analogous with Milne’s temporal measures in a more general manner. This work furthers the analysis published recently by our group in “Towards Interactions through Information in a Multifractal Paradigm”.

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“…The complex parameters

and

in the terms

.…”

Section: Investigations Of Interactions Through Harmonic Mappings mentioning

confidence: 99%

, to be precise (for details, see [ 11 , 12 , 13 , 28 , 29 , 30 , 31 ]). Now, if the functionality of the equivalence principle is admitted for an arbitrary manifold point, the coordinate

represents the intensity of the fields, while the previously mentioned group represents the transition between the various fields which act in that point.…”

Section: Investigations Of Interactions Through Harmonic Mappings mentioning

confidence: 99%

The Role of Information in Managing Interactions from a Multifractal Perspective

Agop

Irimiciuc

Ghenadi

et al. 2021

Entropy

Self Cite

View full text Add to dashboard Cite

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Experimental and Theoretical Design on the Development of Matrix Tablets with Multiple Drug Loadings Aimed at Optimizing Antidiabetic Medication

Sha’at,

Ochiuz,

Rusu

et al. 2024

Pharmaceutics

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Background: Diabetes is a growing global health crisis that requires effective therapeutic strategies to optimize treatment outcomes. This study aims to address this challenge by developing and characterizing extended-release polymeric matrix tablets containing metformin hydrochloride (M-HCl), a first-line treatment for type 2 diabetes, and honokiol (HNK), a bioactive compound with potential therapeutic benefits. The objective is to enhance glycemic control and overall therapeutic outcomes through an innovative dual-drug delivery system. Methods: The tablets were formulated using hydrophilic polymers, such as Carbopol® 71G NF and Noveon® AA-1. The release kinetics of M-HCl and HNK were investigated through advanced mathematical models, including fractal and multifractal dynamics, to capture the non-linear and time-dependent release processes. Traditional kinetic models (zero-order, first-order, Higuchi equations) were also evaluated for comparison. In vitro dissolution studies were conducted to determine the release profiles of the active ingredients under varying polymer concentrations. Results: The study revealed distinct release profiles for the two active ingredients. M-HCl exhibited a rapid release phase, with 80% of the drug released within 4–7 h depending on polymer concentration. In contrast, HNK demonstrated a slower release profile, achieving 80% release after 9–10 h, indicating a greater sensitivity to polymer concentration. At shorter intervals, drug release followed classical kinetic models, while multifractal dynamics dominated at longer intervals. Higher polymer concentrations resulted in slower drug release rates due to the formation of a gel-like structure upon hydration, which hindered drug diffusion. The mechanical properties and stability of the matrix tablets confirmed their suitability for extended-release applications. Mathematical modeling validated the experimental findings and provided insights into the structural and time-dependent factors influencing drug release. Conclusions: This study successfully developed dual-drug extended-release matrix tablets containing metformin hydrochloride and honokiol, highlighting the potential of hydrophilic polymers to regulate drug release. The findings emphasize the utility of advanced mathematical models for predicting release kinetics and underscore the potential of these formulations to improve patient compliance and therapeutic outcomes in diabetes management.

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Toward Complex Systems Dynamics through Flow Regimes of Multifractal Fluids

et al. 2021

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In the framework of the Multifractal Theory of Motion, which is expressed by means of the multifractal hydrodynamic model, complex system dynamics are explained through uniform and non-uniform flow regimes of multifractal fluids. Thus, in the case of the uniform flow regime of the multifractal fluid, the dynamics’ description is “supported” only by the differentiable component of the velocity field, the non-differentiable component being null. In the case of the non-uniform flow regime of the multifractal fluid, the dynamics’ description is “supported” by both components of the velocity field, their ratio specifying correlations through homographic transformations. Since these transformations imply metric geometries explained, for example, by means of Killing–Cartan metrics of the SL(2R)-type algebra, of the set of 2 × 2 matrices with real elements, and because these metrics can be “produced” as Cayleyan metrics of absolute geometries, the dynamics’ description is reducible, based on a minimal principle, to harmonic mappings from the usual space to the hyperbolic space. Such a conjecture highlights not only various scenarios of dynamics’ evolution but also the types of interactions “responsible” for these scenarios. Since these types of interactions become fundamental in the self-structuring processes of polymeric-type materials, finally, the theoretical model is calibrated based on the author’s empirical data, which refer to controlled drug release applications.

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Toward Interactions through Information in a Multifractal Paradigm

Cited by 3 publications

References 20 publications

The Role of Information in Managing Interactions from a Multifractal Perspective

The Role of Information in Managing Interactions from a Multifractal Perspective

Experimental and Theoretical Design on the Development of Matrix Tablets with Multiple Drug Loadings Aimed at Optimizing Antidiabetic Medication

Toward Complex Systems Dynamics through Flow Regimes of Multifractal Fluids

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