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Related publications (28)

Additive and geometric transversality of fractal sets in the integers

Florian Karl Richter

By juxtaposing ideas from fractal geometry and dynamical systems, Furstenberg proposed a series of conjectures in the late 1960's that explore the relationship between digit expansions with respect to multiplicatively independent bases. In this work, we in ...

2024

Fractal Analysis in Pulmonary CT Images of COVID-19-Infected Patients

Maria-Alexandra Paun

In this paper, we propose to quantitatively compare the loss of human lung health under the influence of the illness with COVID-19, based on the fractal-analysis interpretation of the chest-pulmonary CT pictures, in the case of small datasets, which are us ...

MDPI2023

Fractal Analysis of Four Xerogels Based on TEGylated Phenothiazine and Chitosan

Maria-Alexandra Paun

The present article describes novel massive materials (in the solid phase) based on TEGylated phenothiazine and chitosan that possess great capability to recover mercury ions from constituent aqueous solutions. These were produced by chitosan hydrogelation ...

MDPI2023

Fifth-generation fractal antenna design based on the Koch Snowflake geometry. A fractal theory application

Maria-Alexandra Paun

The projection of fifth-generation (5G) fractal antennas and their advantageous geometry are examined. The fact that fractal-shaped antennas based on Koch Snowflake geometry are suitable for higher frequencies was shown above all. By the instrumentality of ...

WILEY2023

How roughness emerges on natural and engineered surfaces

Jean-François Molinari, Ramin Aghababaei

Roughness, defined as unevenness of material surfaces, plays an important role in determining how engineering components or natural objects interact with other bodies and their environment. The emergence of fractal roughness on natural and engineered surfa ...

SPRINGER HEIDELBERG2023

Polynomial-time universality and limitations of deep learning

The goal of this paper is to characterize function distributions that general neural networks trained by descent algorithms (GD/SGD), can or cannot learn in polytime. The results are: (1) The paradigm of general neural networks trained by SGD is poly-time ...

WILEY2023

Fractal Modeling of Polymer Plasma Laser Ablation, Plasma Plume Tsallis Entropy and Its q-Statistics Interpretation, Part I: Theory

Maria-Alexandra Paun

Polymer plasma produced by laser ablation is investigated in a theoretical manner. In relation to the fact that the charge carrier circulation is assumed to take place on fractal curves, the so-called fractality type, electrical charge transport can be res ...

MDPI2022

A Multifractal Vision of 5-Fluorouracil Release from Chitosan-Based Matrix

Maria-Alexandra Paun

A suite of four drug deliverance formulations grounded on 5-fluorouracil enclosed in a chitosan-founded intercellular substance was produced by 3,7-dimethyl-2,6-octadienal with in situ hydrogelation. The formulations have been examined from a morphological ...

MDPI2022

Spatial Series and Fractal Analysis Associated with Fracture Behaviour of UO2 Ceramic Material

Maria-Alexandra Paun

SEM micrographs of the fracture surface for UO2 ceramic materials have been analysed. In this paper, we introduce some algorithms and develop a computer application based on the time-series method. Utilizing the embedding technique of phase space, the attr ...

MDPI2022

Fractal Analysis and Time Series Application in ZY-4 SEM Micro Fractographies Evaluation

Maria-Alexandra Paun

SEM microfractographies of Zircaloy-4 are studied by fractal analysis and the time-series method. We first develop a computer application that associates the fractal dimension and lacunarity to each SEM micrograph picture, and produce a nonlinear analysis ...

MDPI2022

Fractal analysis in the quantification of medical imaging associated with multiple sclerosis pathology

Maria-Alexandra Paun

Backgrounds: Multiple sclerosis (MS) is an inveterate phlogistic situation characterized by focal and vaguely diffusive de-myelination and neurodegeneration, in the sphere of central nervous system (CNS). The brain's chronic inflammatory reaction includes ...

IMR PRESS2022

Wild solutions of the Navier-Stokes equations whose singular sets in time have Hausdorff dimension strictly less than 1

We prove non-uniqueness for a class of weak solutions to the Navier???Stokes equations which have bounded kinetic energy, integrable vorticity, and are smooth outside a fractal set of singular times with Hausdorff dimension strictly less than 1. ...

2022

Xerogels Morphology Details by Multifractal Analysis and Scanning Electron Microscopy Images Evaluations of 5-Fluorouracil Release from Chitosan-Based Matrix

Maria-Alexandra Paun

Four medicament delivery formulations based on 5-fluorouracil in a chitosan substantial matrix were realized in situ via 3,7-dimethyl-2,6-octadienal element hydrogelation. Representative samples of the final realized compounds were investigated from an ana ...

MDPI2022

Geometric Percolation of Spherically Symmetric Fractal Aggregates

Claudio Grimaldi

The connectedness percolation threshold (phi(c)) for spherically symmetric, randomly distributed fractal aggregates is investigated as a function of the fractal dimension (d(F)) of the aggregates through a mean-field approach. A pair of aggregates (each of ...

SPRINGER2022

Biocompatible Chitosan-Based Hydrogels for Bioabsorbable Wound Dressings

Maria-Alexandra Paun

Supramolecular hydrogels based on chitosan and monoaldehydes are biomaterials with high potential for a multitude of bioapplications. This is due to the proper choice of the monoaldehyde that can tune the hydrogel properties for specific practices. In this ...

MDPI2022

Conductive-Type Behaviors In The Dynamics Of Complex Systems Through Scale Relativity Theory

Maria-Alexandra Paun

Conductive-type dynamics in complex systems in the framework of Scale Relativity Theory are analyzed. Using the Madeling scenario in the description o f complex system dynamics through continuous and nondifferentiable curves (fractal/multifractal curves), ...

UNIV POLITEHNICA BUCHAREST, SCI BULL2022

Bistable-Type Interactions Of Complex Systems In A Fractal Paradigm Of Motion

Maria-Alexandra Paun

In the present paper the "interface" dynamics in the case of two complex systems interaction, assimilated to fractal-type mathematical objects, are analyzed. In such context, fractal bistable-type behaviors as transitions in the scale space are obtained. O ...

UNIV POLITEHNICA BUCHAREST, SCI BULL2022

Bistable-Type Interactions Of Complex Systems In A Fractal Paradigm Of Motion

Maria-Alexandra Paun

In the present paper the "interface" dynamics in the case of two complex systems interaction, assimilated to fractal-type mathematical objects, are analyzed. In such context, fractal bistable-type behaviors as transitions in the scale space are obtained. O ...

UNIV POLITEHNICA BUCHAREST, SCI BULL2022

Non-Linear Behaviors In The Dynamics Of Complex Systems Through A Multifractal Hydrodynamic Model

Maria-Alexandra Paun

Some non-linear behaviors in the dynamics of complex systems using the Scale Relativity Theory in the form of Multifractal Hydrodynamic Model are analyzed. By assimilating any complex system to a mathematical multifractal-type object, it is shown that the ...

UNIV POLITEHNICA BUCHAREST, SCI BULL2022

Self-Structuring Of Cellular And Channel Type In Complex System Dynamics In The Framework Of Scale Relativity Theory

Maria-Alexandra Paun

In the framework of Scale Relativity Theory, by analyzing dynamics of complex system structural units based on multifractal curves, both Schrodinger and Madelung approaches are functional and complementary. The Madelung selected approach involve synchronou ...

UNIV POLITEHNICA BUCHAREST, SCI BULL2022

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