A Theoretical Model for Release Dynamics of an Antifungal Agent Covalently Bonded to the Chitosan.

The aim of the study was to create a mathematical model useful for monitoring the release of bioactive aldehydes covalently bonded to the chitosan by reversible imine linkage, considered as a polymer-drug system. For this purpose, two hydrogels were prepared by the acid condensation reaction of chitosan with the antifungal 2-formyl-phenyl-boronic acid and their particularities; influencing the release of the antifungal aldehyde by shifting the imination equilibrium to the reagents was considered, i.e., the supramolecular nature of the hydrogels was highlighted by polarized light microscopy, while scanning electron microscopy showed their microporous morphology. Furthermore, the in vitro fungicidal activity was investigated on two fungal strains and the in vitro release curves of the antifungal aldehyde triggered by the pH stimulus were drawn. The theoretical model was developed starting from the hypothesis that the imine-chitosan system, both structurally and functionally, can be assimilated, from a mathematical point of view, with a multifractal object, and its dynamics were analyzed in the framework of the Scale Relativity Theory. Thus, through Riccati-type gauges, two synchronous dynamics, one in the scale space, associated with the fungicidal activity, and the other in the usual space, associated with the antifungal aldehyde release, become operational. Their synchronicity, reducible to the isomorphism of two SL(2R)-type groups, implies, by means of its joint invariant functions, bioactive aldehyde compound release dynamics in the form of "kink-antikink pairs" dynamics of a multifractal type. Finally, the theoretical model was validated through the experimental data.

The Role of Information in Managing Interactions from a Multifractal Perspective.

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".

Toward Interactions through Information in a Multifractal Paradigm.

In a multifractal paradigm of motion, Shannon's information functionality of a minimization principle induces multifractal-type Newtonian behaviors. The analysis of these behaviors through motion geodesics shows the fact that the center of the Newtonian-type multifractal force is different from the center of the multifractal trajectory. The measure of this difference is given by the eccentricity, which depends on the initial conditions. In such a context, the eccentricities' geometry becomes, through the Cayley-Klein metric principle, the Lobachevsky plane geometry. Then, harmonic mappings between the usual space and the Lobachevsky plane in a Poincaré metric can become operational, a situation in which the Ernst potential of general relativity acquires a classical nature. Moreover, the Newtonian-type multifractal dynamics, perceived and described in a multifractal paradigm of motion, becomes a local manifestation of the gravitational field of general relativity.

Theoretical and Experimental Designs on Several Mechanical Properties of Cu-Al-Zn Shape Memory Alloys Used in the Processing Industry.

By assimilating shape memory alloys with mathematical multifractal-type objects, a theoretical model based on Scale Relativity Theory in the form of The Multifractal Theory of Motion, in order to explain the mechanical behavior of such material, is proposed. The model is validated by analyzing the mechanical behavior of Cu-Al-Zn shape memory alloy with various chemical compositions. More precisely, the multifractal tunnel effect can "mime" the mechanical hysteresis of such a material, a situation in which a direct correspondence for several mechanical properties of Cu-Al-Zn is highlighted (the chemical composition can be correlated with the shapes of the curves controlled through the multifractality degree, while the areas delimited by the same curves can be correlated with the multifractal specific potential, as a measure of the mechanical memory degree).

Theoretical model for the diclofenac release from PEGylated chitosan hydrogels.

Controlled drug delivery systems are of utmost importance for the improvement of drug bioavailability while limiting the side effects. For the improvement of their performances, drug release modeling is a significant tool for the further optimization of the drug delivery systems to cross the barrier to practical application. We report here on the modeling of the diclofenac sodium salt (DCF) release from a hydrogel matrix based on PEGylated chitosan in the context of Multifractal Theory of Motion, by means of a fundamental spinor set given by 2 × 2 matrices with real elements, which can describe the drug-release dynamics at global and local scales. The drug delivery systems were prepared by in situ hydrogenation of PEGylated chitosan with citral in the presence of the DCF, by varying the hydrophilic/hydrophobic ratio of the components. They demonstrated a good dispersion of the drug into the matrix by forming matrix-drug entities which enabled a prolonged drug delivery behavior correlated with the hydrophilicity degree of the matrix. The application of the Multifractal Theory of Motion fitted very well on these findings, the fractality degree accurately describing the changes in hydrophilicity of the polymer. The validation of the model on this series of formulations encourages its further use for other systems, as an easy tool for estimating the drug release toward the design improvement. The present paper is a continuation of the work 'A theoretical mathematical model for assessing diclofenac release from chitosan-based formulations,' published in Drug Delivery Journal, 27(1), 2020, that focused on the consequences induced by the invariance groups of Multifractal Diffusion Equations in correlation with the drug release dynamics.

Complex Behavior in the Dynamics of a Polymeric Biocomposite Material-"Liquid Wood". Experimental and Theoretical Aspects.

The purpose of the present paper is to analyze, both experimentally and theoretically, the behavior of the polymeric biocomposite generically known as "liquid wood", trademarked as Arbofill. The experimental part refers to the mechanical performance in tension and compression, having as finality the possibility of using "liquid wood" as a material suitable for the rehabilitation of degraded wooden elements in civil structures (ex. use in historical buildings, monuments etc.). The theoretical part refers to computer simulations regarding the mechanical behavior of "liquid wood" as well as to a theoretical model in the paradigm of motion, which describes the same behavior. This model is based on the hypothesis that "liquid wood" can be assimilated, both structurally and functionally, to a multifractal object, situation in which its entities are described through continuous, non-differentiable curves. Then, descriptions of the behavior of "liquid wood", both in the Schrödinger-type and in hydrodynamic-type representations at various scale resolutions, become operational. Since in the hydrodynamic-type representation, the constitutive law of "liquid wood" can be highlighted, several operational procedures (Ricatti-type gauge, differential geometry in absolute space etc.) will allow correlations between the present proposed model and the experimental data. The obtained results, both practical (81% bearing capacity in compression and 36% bearing capacity in tension, compared to control samples) and theoretical (validation of material performance in virtual environment simulations, stresses and strains correlations in a theoretical model) indicate that "liquid wood" could be used in the construction industry, as a potential rehabilitation material, but with more development clearly needed.