• 대한수학회논문집
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• 제35권4호
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• pp.1057-1073
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• 2020

In this paper, we study some of the factorization aspects of rational multicyclic monoids, that is, additive submonoids of the nonnegative rational numbers generated by multiple geometric sequences. In particular, we provide a complete description of the rational multicyclic monoids M that are hereditarily atomic (i.e., every submonoid of M is atomic). Additionally, we show that the sets of lengths of certain rational multicyclic monoids are finite unions of multidimensional arithmetic progressions, while their unions satisfy the Structure Theorem for Unions of Sets of Lengths. Finally, we realize arithmetic progressions as the sets of distances of some additive submonoids of the nonnegative rational numbers.

• Geomechanics and Engineering
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• 제20권3호
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• pp.191-205
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• 2020

Soil shear strength parameters play a remarkable role in designing geotechnical structures such as retaining wall and dam. This study puts an effort to propose two accurate and practical predictive models of soil shear strength parameters via hybrid artificial neural network (ANN)-based models namely genetic algorithm (GA)-ANN and particle swarm optimization (PSO)-ANN. To reach the aim of this study, a series of consolidated undrained Triaxial tests were conducted to survey inherent strength increase due to addition of polypropylene fibers to sandy soil. Fiber material with different lengths and percentages were considered to be mixed with sandy soil to evaluate cohesion (as one of shear strength parameter) values. The obtained results from laboratory tests showed that fiber percentage, fiber length, deviator stress and pore water pressure have a significant impact on cohesion values and due to that, these parameters were selected as model inputs. Many GA-ANN and PSO-ANN models were constructed based on the most effective parameters of these models. Based on the simulation results and the computed indices' values, it is observed that the developed GA-ANN model with training and testing coefficient of determination values of 0.957 and 0.950, respectively, performs better than the proposed PSO-ANN model giving coefficient of determination values of 0.938 and 0.943 for training and testing sets, respectively. Therefore, GA-ANN can provide a new applicable model to effectively predict cohesion of fiber-reinforced sandy soil.