Complexity: a new paradigm for fracture mechanics by A. Carpinteri, S. Puzzi

“…In fact, under the label of Complexity Sciences we comprehend a large variety of approaches: nonlinear dynamics, deterministic chaos theory, nonequilibrium thermodynamics, fractal geometry, intermediate asymptotics, complete and incomplete similarity, renormalization group theory, catastrophe theory, self-organized criticality, neural networks, cellular automata, fuzzy logic, etc. …”
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Improved 2D Discrete Hyperchaos Mapping with Complex Behaviour and Algebraic Structure for Strong S-Boxes Generation by Musheer Ahmad, Eesa Al-Solami

“…This paper proposes to present a novel method of generating cryptographic dynamic substitution-boxes, which makes use of the combined effect of discrete hyperchaos mapping and algebraic group theory. Firstly, an improved 2D hyperchaotic map is proposed, which consists of better dynamical behaviour in terms of large Lyapunov exponents, excellent bifurcation, phase attractor, high entropy, and unpredictability. …”
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On ∼n Notion of Conjugacy in Some Classes of Epigroups by Aftab Hussain Shah, Amal S. Alali, Mohd Rafiq Parray

“…The action of any group on itself by conjugation and the corresponding conjugacy relation plays an important role in group theory. Generalizing the group theoretic notion of conjugacy to semigroups is one of the interesting problems, and semigroup theorists had produced substantial amount of research in this direction. …”
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Complexity: a new paradigm for fracture mechanics by S. Puzzi, A. Carpinteri

“…In fact, under the label of Complexity Sciences we comprehend a large variety of approaches: nonlinear dynamics, deterministic chaos theory, nonequilibrium thermodynamics, fractal geometry, intermediate asymptotics, complete and incomplete similarity, renormalization group theory, catastrophe theory, self-organized criticality, neural networks, cellular automata, fuzzy logic, etc. …”
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Analytical Solution for the Gross-Pitaevskii Equation in Phase Space and Wigner Function by A. X. Martins, R. A. S. Paiva, G. Petronilo, R. R. Luz, R. G. G. Amorim, S. C. Ulhoa, T. M. R. Filho

“…The formalism is based on the noncommutative structure of the star product, and using the group theory approach as a guide a physically consistent theory is constructed in phase space. …”
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Interpreting convolutional neural networks' low-dimensional approximation to quantum spin systems by Yilong Ju, Shah Saad Alam, Jonathan Minoff, Fabio Anselmi, Han Pu, Ankit Patel

“…In this work, we use methodologies from information theory, group theory and machine learning, to elucidate how CNN captures relevant physics of quantum systems. …”
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IMPACTS OF INTERNAL PARTY DEMOCRACY ON PERFORMANCE OF ALL PROGRESSIVE CONGRESS IN THE 2023 GENERAL ELECTIONS IN NIGERIA by IBRAHIM NUAIMU DANBALA, CELESTINE OGECHUKWU OKAFOR

“…The study also utilized the group theory as it theoretical framework for analysis. …”
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Secret sharing in a special linear group by V. I. Yanchevskiĭ, I. A. Havarushka, G. V. Matveev

“…The development of a scheme on a new mathematical basis is intended to expand the list of these configurations, which creates more opportunities for the user in choosing the optimal option.Methods. Group theory, modular arithmetic and theory of secret sharing schemes are used.Results. …”
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Extensive composable entropy for the analysis of cosmological data by Constantino Tsallis, Henrik Jeldtoft Jensen

“…An entropy is composable if it satisfies that the entropy SA of a system A=B×C consisting of two statistically independent parts B and C is given in a consistent way as SA=Φ(SB,SC) where the composition function Φ(x,y) is obtained from group-theory.We further show that (α,γ)=(1,2/3) satisfactorily agrees with cosmological data measuring neutrinos, Big Bang nucleosynthesis and the relic abundance of cold dark matter particles, as well as dynamical and geometrical cosmological data sets.…”
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Adsorptive and Membrane-Type Separations: A Bibliographical Update (1998) by Martyn S. Ray

“…The papers included here have been divided into the following subject groups: theory; design data; adsorbents; PSA and cyclic systems, and applications; liquid-phase adsorption; ion exchange, chromatography and related separations; membranes; and membrane-type separations. …”
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Adsorptive and Membrane-Type Separations: A Bibliographical Update (1999) by Martyn S. Ray

“…The references included here have been divided into the following subject groups: theory; design data; adsorbents; PSA and cyclic systems, and applications; liquid-phase adsorption; ion exchange, chromatography and related separations; membranes; and membrane-type separations. …”
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