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- Application of the Fractional Sturm–Liouville Theory to a Fractional Sturm–Liouville Telegraph EquationPublication . Ferreira, M.; Rodrigues, M. Manuela; Vieira, NelsonIn this paper, we consider a non-homogeneous time-space-fractional telegraph equation in n-dimensions, which is obtained from the standard telegraph equation by replacing the first- and second-order time derivatives by Caputo fractional derivatives of corresponding fractional orders, and the Laplacian operator by a fractional Sturm-Liouville operator defined in terms of right and left fractional Riemann-Liouville derivatives. Using the method of separation of variables, we derive series representations of the solution in terms of Wright functions, for the homogeneous and non-homogeneous cases. The convergence of the series solutions is studied by using well known properties of the Wright function. We show also that our series can be written using the bivariate Mittag-Leffler function. In the end of the paper, some illustrative examples are presented.
- Did You Enjoy It? The Role of Intensity-Trait Preference/Tolerance in Basic Psychological Needs and Exercise EnjoymentPublication . Teixeira, Diogo S.; Rodrigues, Filipe; Machado, Sergio; Cid, Luis; Monteiro, DiogoPromoting exercise regimens that aim at enhancing the quality of individuals’ subjective exercise experience can be challenging. Given the recent theoretical contributions regarding the possible interaction of exercise intensity-traits and several motivational variables, as well as their potential value for exercise adherence, the objective of this study was to examine the mediation role of basic psychological needs in the relationship between preference for and tolerance of exercise intensity and enjoyment. This cross-sectional study comprised a total of 160 exercisers (Mage = 34.12, SD = 9.23, 73 males) enrolled in several health clubs. All analyses were performed using SPSS v. 23.0/PROCESS v. 3.4. The results indicate that intensity-traits presented positive associations with enjoyment, and negative associations with all of needs frustration variables. A mediation role of needs frustration emerged in the intensity traits and enjoyment associations that was analyzed according to relatable theoretical considerations
- Anaerobic Mesophilic Co-Digestion of Swine Slurry and Hidrolyzate in Batch Reactors: A Case StudyPublication . Domingues, Paulo S.; Pala, Helena; Oliveira, Nelson S.The management of residual flows from swine farms, such as slurry and hydrolyzate, is a serious environmental problem in Portugal, so the search for new solutions is important, especially if they can be implemented in production sites, avoiding the transport of waste. Anaerobic co-digestion can configure a sustainable method of management and valorization of these flows in swine farms, resulting in biogas to produce energy and a digestate with agronomic value. The swine hydrolyzate is the product from the elimination of swine carcasses on the farms, through a hydrolysis process. Its use in the anaerobic process wasn’t found in the literature, identifying the need to evaluate its potential. Thus, anaerobic co-digestion of swine slurry and hydrolyzate was carried out and the main purpose of this research was to find the best feeding ratio between the two substrates in batch test, focusing on biogas production. The study was developed in two phases, both under mesophilic conditions. In the first one, using 100 ml syringes, the effect of the relative proportion of substrates on the anaerobic co-digestion potential was investigated and the effect of pressure sterilization of the substrates on biogas production was verified. In the second phase, a larger scale study was carried out in a 4,500 ml digestor, ran under the conditions identified as the most favorable in the preliminary tests. The results obtained allowed us to conclude that the largest volume of accumulated biogas was obtained with the proportion of 90.9% swine slurry: 9.1% swine hydrolyzate (v/v); and that the sterilization of the substrates doesn’t constitute an effective thermal pre-treatment. The larger scale test revealed an inefficient anaerobic process due to the inhibitory effect caused by the accumulation of ammonia and volatile organic acids. However, the production yield was 606.8 LBiogas/kgVS and 431.6 LMethane/kgVS, indicating that process allowed a production of biogas and methane higher than the values cited in literature for anaerobic digestion of swine slurry. This result showed that the use of swine hydrolyzate as a co-substrate results in a better balance of nutrients, promoting a better development of microorganisms.