Pairs Generating as a Consequence of the Fractal Entropy: Theory and Applications

Grigorovici, Alexandru; Băcăiță, Elena Simona; Pãun, Viorel-Puiu; Grecea, Constantin; Butuc, Irina; Agop, M.; Popa, Ovidiu

doi:10.3390/e19030128

Cited by 8 publications

(6 citation statements)

References 19 publications

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“…In these harmonic scale resolutions (ω = 20, 30), the system is clearly more influenced by the fractal background matter which, according to our reports from [ 32 , 33 , 34 ], usually leads to a quasi-chaotic state. The role of information at this scale was investigated in detail and reported by our group in [ 35 , 36 , 37 , 38 ].…”

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

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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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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

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“…with Ψ the complex conjugated of Ψ, is implicit and unmanifest, while in the presence of the growth factor it becomes explicit and manifest. For other details, see [22][23][24]; v)we prove that on a fractal medium, the implicit-explicit transition of information implies the fractal type spontaneous breaking symmetry (for general details, see [25][26][27]). Then, a specific calibration becomes functional, calibration which enables a holographic implementation of the interaction entity-fractal medium (for example celltissue).…”

Section: Mathematical Modelmentioning

confidence: 99%

Tissue Engineering - Collagen Matrix Based Flaps - a Simple Construct. Experimental and Theoretical Aspects

Susanu¹,

Moraru²,

Costin³

et al. 2019

Rev. Chim.

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In our study we demonstrate the possibility to create a free flap using only a collagen matrix and a vascular pedicle. The processes of cell migration and differentiation, endogenous collagen synthesis, vascular network development, all rely on the arteriovenous loop introduced in the scaffold with no participation of surrounding vascularity. The flap has the capability to revascularize a full thickness skin graft, and also to establish vascular connections with adjacent vascular territories. Also, a fractal mathematical model was built based on spontaneous breaking symmetry to explain the behaviors of biostructures mentioned above.

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“…Since, by means of this mathematical procedure, Quantum Mechanics becomes a particular case of Fractal Mechanics (in the fractal dimension = 2 at Compton scale resolution = ℏ/2 0 ), all the results of Quantum Mechanics can be extended (generalized) to any scale resolution. Thus, "fundamental concepts" of Quantum Mechanics as quantum entanglement, quantum superposition, quantum information, and so forth have to be substituted by those of "fractal entanglement", "fractal superposition", "fractal information" (Agop et al [49][50][51] and Grigorovici et al [52]), and so forth. Moreover, we shall substitute the notion of an atom/pseudo-atom with that of a fractal atom/fractal pseudoatom, respectively.…”

Section: Theorem 16 If the Scale Covariance Principle Is Functional Then The Transition From The Dynamics Of The Classical Physics (Diffementioning

confidence: 99%

Extended Minimal Atomicity through Nondifferentiability: A Mathematical-Physical Approach

Gavriluț

Gavriluţ

Agop

2019

Advances in Mathematical Physics

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The mathematical concept of minimal atomicity is extended to fractal minimal atomicity, based on the nondifferentiability of the motion curves of physical system entities on a fractal manifold. For this purpose, firstly, different results concerning minimal atomicity from the mathematical procedure of the Quantum Measure Theory and also several physical implications are obtained. Further, an inverse method with respect to the common developments concerning the minimal atomicity concept has been used, showing that Quantum Mechanics is identified as a particular case of Fractal Mechanics at a given scale resolution. More precisely, for fractality through Markov type stochastic processes, i.e., fractalization through stochasticization, the standard Schrödinger equation is identified with the geodesics of a fractal space for motions of the physical system entities on nondifferentiable curves on fractal dimension two at Compton scale resolution. In the one-dimensional stationary case of the fractal Schrödinger type geodesics, a special symmetry induced by the homographic group in Barbilian’s form “makes possible the synchronicity” of all entities of a given physical system. The integral and differential properties of this group under the restriction of defining a parallelism of directions in Levi-Civita’s sense impose correspondences with the “dynamics” of the hyperbolic plane so that harmonic mappings between the ordinary flat space and the hyperbolic one generate (by means of a variational principle) a priori probabilities in Jaynes’ sense. The explicitation of such situation specifies the fact that the hydrodynamical variant of a Fractal Mechanics is more easily approached and, from this, the fact that Quantum Measure Theory can be a particular case of a possible Fractal Measure Theory.

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Pairs Generating as a Consequence of the Fractal Entropy: Theory and Applications

Cited by 8 publications

References 19 publications

The Role of Information in Managing Interactions from a Multifractal Perspective

The Role of Information in Managing Interactions from a Multifractal Perspective

Tissue Engineering - Collagen Matrix Based Flaps - a Simple Construct. Experimental and Theoretical Aspects

Extended Minimal Atomicity through Nondifferentiability: A Mathematical-Physical Approach

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