• Journal of applied mathematics & informatics
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• v.41 no.5
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• pp.1145-1153
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• 2023

The notion of maximal product of two fuzzy graphs was introduced by Radha and Arumugam in 2015 and the notion of balanced fuzzy graph was introduced by Al-Hawary in 2011. In this paper, we give a modification of the maximal product definition, which we call maximal strong product. We also introduce the relatively new notion of maximal-balanced fuzzy graphs. We give necessary and sufficient conditions for the maximal strong product of two balanced (resp., maximal-balanced) fuzzy graphs to be balanced (resp., maximal-balanced) and we prove that these two independent notions are preserved under isomorphism.

• Journal of the Korean Mathematical Society
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• v.32 no.4
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• pp.697-712
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• 1995

In the present article we consider multiparameter maximal averages and discover the crucial roles played by the number of parameters in their boundedness properties. The problem we shall deal with is initiated by Rubio de Francia [8] and will be in the spirit of an inductive extension to multiparameter cases, in which tools of our study rely on the theory of Harmonic Analysis on product spaces. Suppose that $d_\mu$ is a complex Borel measure supported on a compact subset S of $R^N$ having total mass one, $\smallint_S d_\mu = 1$.

• The korean journal of orthodontics
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• v.48 no.6
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• pp.384-394
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• 2018

Objective: This study was performed to investigate an appropriate degree of prestretch for orthodontic synthetic elastomeric chains focusing on time-dependent viscoelastic properties. Methods: Orthodontic synthetic elastomeric chains of two brands were prestretched to 50, 100, 150, and 200% of the original length in one and three cycles, and the hysteresis areas of the obtained stress-strain curves were determined. Acrylic plates were employed to maintain constant strain during the experiment. A total of 180 samples were classified into nine groups according to brand, and their stresses and permanent deformations were measured immediately after prestretch (0 hour), after 1 hour and 24 hours, and after 1, 2, 3, 4, 5, 6, 7, and 8 weeks. The relationship between stress relaxation and permanent deformation was investigated for various degrees of prestretch, and the estimated stress resulting from tooth movement was calculated. Results: The degree of prestretch and the stress relaxation ratio exhibited a strong negative correlation, whereas no correlation was found between the degree of prestretch and the average normalized permanent strain. The maximal estimated stress was observed when prestretch was performed in three cycles to 200% of the original length. Conclusions: Although prestretch benefited residual stress, it did not exhibit negative effects such as permanent deformation. The maximal estimated stress was observed at the maximal prestretch, but the difference between prestretch and control groups decreased with time. In general, higher residual stresses were observed for product B than for product A, but this difference was not clinically significant.

• Journal of Microbiology and Biotechnology
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• v.25 no.6
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• pp.893-902
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• 2015

Various Lactobacillus reuteri strains were screened for the ability to convert glycerol to 1,3-propanediol (1,3-PDO) in a glycerol-glucose co-fermentation. Only L. reuteri DSM 20016, a well-known probiotic, was able to efficiently carry out this bioconversion. Several process strategies were employed to improve this process. Co²⁺ addition to the fermentation medium, led to a high product titer (46 g/l) of 1,3-PDO and to improved biomass synthesis. L. reuteri DSM 20016 produced also ca. 3 µg/g of cell dry weight of vitamin B₁₂, conferring an economic value to the biomass produced in the process. Incidentally, we found that L. reuteri displays the highest resistance to Co²⁺ ions ever reported for a microorganism. Two waste materials (crude glycerol from biodiesel industry and spruce hydrolysate from paper industry) alone or in combination were used as feedstocks for the production of 1,3-PDO by L. reuteri DSM 20016. Crude glycerol was efficiently converted into 1,3-PDO although with a lower titer than pure glycerol (33.3 vs. 40.7 g/l). Compared with the fermentation carried out with pure substrates, the 1,3-PDO produced was significantly lower (40.7 vs. 24.2 g/l) using cellulosic hydrolysate and crude glycerol, but strong increases of the maximal biomass produced (2.9 vs 4.3 g/l CDW) and of the glucose consumption rate were found. The results of this study lay the foundation for further investigations to exploit the biotechnological potential of L. reuteri DSM 20016 to produce 1,3-PDO and vitamin B₁₂ using industry byproducts.