The aim of this study was to evaluate the structural, physical, and antifungal characteristics of starch edible films added with nanocomposites and Mexican oregano (Lippia berlandieri Schauer) essential oil (EO). Starch edible films were formulated with Mexican oregano EO (0%, 1%, or 2% v/v) and bentonite or halloysite (2%). Physical properties such as L* (luminosity), hue, film thickness, and O₂ and CO₂ permeability were determined. Structural analysis was carried out via atomic force microscopy (AFM). Antifungal activity against Aspergillus niger, Fusarium spp., and Rhizopus spp. was evaluated. The addition of EO and nanocomposites reduced luminosity, providing color to the edible films. Film thickness increased through the addition of EO concentration. O₂ and CO₂ permeability was increased by bentonite/EO films, and for halloysite films, CO₂ permeability decreased as EO concentration increased. The addition of EO with both nanocomposites shows an evident morphological change in film structure, decreasing pore density and increasing pore size. In general, Mexican oregano EO added to edible starch films has an adequate fungicidal effect. The most sensitive microorganism tested was A. niger. Edible films added with Mexican oregano EO and nanocomposites show better physical and antifungal properties due to an adequate structural change in the biopolymer matrix.

We perform a detailed computational study of the recently introduced Sombor indices on random networks. Specifically, we apply Sombor indices on three models of random networks: Erdös-Rényi networks, random geometric graphs, and bipartite random networks. Within a statistical random matrix theory approach, we show that the average values of Sombor indices, normalized to the order of the network, scale with the average degree. Moreover, we discuss the application of average Sombor indices as complexity measures of random networks and, as a consequence, we show that selected normalized Sombor indices are highly correlated with the Shannon entropy of the eigenvectors of the adjacency matrix.

Singular-value statistics (SVS) has been recently presented as a random matrix theory tool able to properly characterize non-Hermitian random matrix ensembles []. Here, we perform a numerical study of the SVS of the non-Hermitian adjacency matrices A of directed random graphs, where A are members of diluted real Ginibre ensembles. We consider two models of directed random graphs: Erdös-Rényi graphs and random geometric graphs. Specifically, we focus on the singular-value-spacing ratio r and the minimum singular value λ min . We show that 〈 r 〉 (where 〈 · 〉 represents ensemble average) can effectively characterize the crossover between mostly isolated vertices to almost complete graphs, while the probability density function of λ min can clearly distinguish between different graph models. Published by the American Physical Society 2024

In this study, given the inherent nature of dissipation in realistic dynamical systems, we explore the effects of dissipation within the context of fractional dynamics. Specifically, we consider the dissipative versions of two well known fractional maps: the Riemann–Liouville (RL) and the Caputo (C) fractional standard maps (fSMs). Both fSMs are two-dimensional nonlinear maps with memory given in action-angle variables (In,θn), with n being the discrete iteration time of the maps. In the dissipative versions, these fSMs are parameterized by the strength of nonlinearity K, the fractional order of the derivative α∈(1,2], and the dissipation strength γ∈(0,1]. In this work, we focus on the average action ⟨In⟩ and the average squared action ⟨In2⟩ when K≫1, i.e., along strongly chaotic orbits. We first demonstrate, for |I0|>K, that dissipation produces the exponential decay of the average action ⟨In⟩≈I0exp⁡(−γn) in both dissipative fSMs. Then, we show that while ⟨In2⟩RL−fSM barely depends on α (effects are visible only when α→1), any α<2 strongly influences the behavior of ⟨In2⟩C−fSM. We also derive an analytical expression able to describe ⟨In2⟩RL−fSM(K,α,γ).

The preparation and properties of Nafion–TMS (Nafion–trimethylsilyl) and Nafion–TMS–Ru²⁺-complex modified GC electrodes are reported for the electrochemical oxidation reaction of adrenaline (AD). The structure of Nafion–TMS was studied by atomic force microscopy. The incorporation of [Ru(bpy)₃]²⁺ and [Ru(phen)₃]²⁺ complexes into Nafion–TMS was investigated by UV-vis spectroscopy, providing information about the interaction of the modified Nafion–TMS–Ru²⁺-complex composite. According to electrochemical studies, the electrodes modified with this composite polymer showed a faster electron transfer and greatly improved kinetics for the redox reaction of AD in standard solutions when compared to bare and Nafion–TMS modified electrodes. The oxidation current increased linearly with adrenaline concentration in the range from 1 to 20 mM and 1 to 100 mM for Nafion–TMS and the modified Nafion–TMS–Ru²⁺ complex, respectively. A strong pH dependence on the electroanalytical parameters was found for adrenaline detection, indicating that electron transfer reaction occurs in tandem with proton transfer.