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Fullerenes are cubic polyhedral molecules made of carbon atoms. They have attracted much attention in the chemical and the mathematical literature. In the present paper, we compare the orbit and Hosoya entropies with the total energy of some classes of fullerenes to determine a correlation between these measures. Besides, we investigate the correlation between eigenvalues-based entropy and the total-energy of more than 400 fullerenes. Our findings reveal that the correlation between the adjacency energy, the eigenvalue-entropy, the total energy, the orbit-entropy, and the Hosoya-entropy of selected fullerenes with distinct symmetry groups is approximately equal to one. [ABSTRACT FROM AUTHOR]

We give a topological classification of the orbit space of cohomogeneity two isometric actions on at Riemannian manifolds. [ABSTRACT FROM AUTHOR]

We show that typical elements of the set of continuous functions from a compact differentiable manifold M to Rn are nowhere differentiable. Then, we study the box dimensions of typical elements in the set of images of M in Rn. [ABSTRACT FROM AUTHOR]

For an efficient force method of frame analysis, the formation of localized self-equilibrating systems is an important issue. Such systems can be constructed on minimal cycle basis of the graph model of the structure. In this paper, algorithms are presented for the formation of minimal cycle bases of graph products corresponding to sparse cycle adjacency matrices, leading to the formation of highly sparse flexibility matrices. The algorithms presented employ concepts from three graph products namely Cartesian, strong Cartesian and lexicographic products. Though the formulation for the first two products exist, however, efficient implementations are made in this paper. The formulation for the generation of minimal cycle basis is extended to the lexicographic product. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This study shows the application of carbon supported electrodes containing Pt/NiO nanoparticles to catalyze the electrochemical oxidation of glucose in neutral media. In particular, this study describes the effect of the Pt content and type of carbon (carbon black, expanded graphite, or charcoal active) in the reaction layer on this oxidation process in neutral media. Pt/NiO nanoparticles were synthesized by a simple hydrothermal method, and further characterized by scanning electron microscopy (SEM), X-ray diffraction spectroscopy (XRD), and cyclic voltammetry. These nanoparticles were used to modify carbon electrodes. The effectiveness of these electrodes for electrochemical glucose oxidation was evaluated. The results revealed that the catalytic activity of the electrodes depends on the content of Pt/NiO nanoparticles and the type of carbon. The 10% Pt/NiO with 90% loading (use of activated charcoal in the reaction layer) as optimum electrode indicated good stability after 1200 voltammetry cycles. This modified electrode was highly active for glucose oxidation in neutral media, which could be attributed to the presence of Pt/NiO nanoparticles as catalyst and high surface area of activated charcoal on the electrode surface., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2020 Elsevier B.V. All rights reserved.)

Background and Purpose: Patulin is one of the important mycotoxins, produced by a wide range of molds, including Penicillium , Aspergillus, and Bysochlamys. Patulin is mainly found in the rotten parts of fruits and vegetables, such as apples, pears, peach, apricots, and grapes. Currently, the Codex Alimentarius and Food and Drug Administration have recommended a maximum level of 50 µg/L patulin for apple products. The purpose of this study was to investigate patulin contamination of apple juice and cans in 75 samples collected from 15 manufacturers in Shiraz, southern Iran., Materials and Methods: The detection of patulin was accomplished using a high-performance liquid chromatography with an ultraviolet detector., Results: A total of 38 apple juice samples (53%) and 17 apple cans (45%) were contaminated with patulin. Overall 50% and 3% of the apple juice and apple cans samples had a patulin level of > 3 µg/L., Conclusion: Although the maximum level of patulin in our samples was considerably lower than the permitted level established by the European Union (i.e., 50 µg/L), the high incidence of this mycotoxin in our samples should be lessen by improving their good manufacturing practice., Competing Interests: None declared.