23:T413,

Rademacher (Mathematische Annalen87 (1922) 112–138), Steinhaus (Mathematische Zeitschrift31 (1930) 408–416) and Paley and Zygmund (Mathematical Proceedings of the Cambridge Philosophical Society26 (1930) 337–257, Mathematical Proceedings of the Cambridge Philosophical Society26 (1930) 458–474, Mathematical Proceedings of the Cambridge Philosophical Society28 (1932) 190–205) initiated the extensive study of random series. Using the theory of algorithmic randomness, which is a mix of computability theory and probability theory, we investigate the effective content of some classical theorems. We discuss how this is related to an old question of Kahane and Bollobás. We also discuss how considerations of such algorithmic questions about random series seem to lead to new notions of algorithmic randomness.

24:T415,

This article presents theoretical studies for parametrically excited vibrations of marine riser of the floating production, drilling, storage, and offloading system under random wave forces and earthquake excitation. The equation of motion of the riser is obtained by a mathematical method utilizing Euler beam theory and Galerkin method. The trigonometric series method is used to formulate random wave force and earthquake excitation in time domain. The dynamic analysis, spectral response analysis, and key parameters’ sensitivity analysis are conducted for the riser system. Parameter studies are conducted for the effects of wave and earthquake parameters and structural parameters on dynamics response of the riser system. The results from this study can provide valuable recommendations for the design and construction of the parametrically excited marine riser system under random wave forces and earthquake excitation and can promote widely practical application of the deep water riser in complicated environmental conditions.

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Algorithmically random series

Parametrically excited vibrations of marine riser under random wave forces and earthquake