We analyze the pointwise convergence of a sequence of computable elements of L 1 (2 ω) in terms of algorithmic randomness. We consider two ways of expressing the dominated convergence theorem and show that, over the base theory RCA 0 , each is equivalent to the assertion that every G δ subset of Cantor space with positive measure has an element. This last statement is, in turn, equivalent to weak weak König's lemma relativized to the Turing jump of any set. It is also equivalent to the conjunction of the statement asserting the existence of a 2-random relative to any given set and the principle of Σ 2 collection.
The dominated convergence theorem implies that if (fn) is a sequence of functions on a probability space taking values in the interval [0, 1], and (fn) converges pointwise a.e., then ( fn) converges to the integral of the pointwise limit. Tao [20] has proved a quantitative version of this theorem: given a uniform bound on the rates of metastable convergence in the hypothesis, there is a bound on the rate of metastable convergence in the conclusion that is independent of the sequence (fn) and the underlying space. We prove a slight strengthening of Tao's theorem which, moreover, provides an explicit description of the second bound in terms of the first. Specifically, we show that when the first bound is given by a continuous functional, the bound in the conclusion can be computed by a recursion along the tree of unsecured sequences. We also establish a quantitative version of Egorov's theorem, and introduce a new mode of convergence related to these notions.
This paper reports and discusses centrifuge test data of model three-leg jackups on kaolin clay. The tests modelled one prototype jackup with 6·5 m dia. 13° conical spudcans, one with 6·5 m dia. flat-based spudcans, and one with 13·0 m dia. flat-based spudcans. The model jackups were subjected to preloading, slow cyclic loading, rapid cyclic loading and pullout. The data obtained in this study are the loadpaths consisting of the vertical load, horizontal load and moment associated with each leg, the vertical settlement, horizontal displacement and rotation of the model jackups as well as of the model spudcans. Ce papier rend compte et discute les données d'essai de centrifugation de modèles de plates-formes é1évatrices à trois jambes sur du kaolin. Les essais ont modélisé une plate-forme prototype sur des caissons d'enfichage coniques de 6·5 m de diamètre et d'angle 13°, une autre sur des caissons de base plane de 6·5 m de diamètre, et une autre sur des caissons de base plane de 13 m de diamètre. Les modèles de plate-forme ont été soumis à des précharges, à des charges cycliques lentes, à des charges cycliques rapides et à des arrachements. Les données issues de cette étude sont des courbes de charge constituées de la charge verticale, de la horizontale et du moment associé à chaque jambe, du tassement vertical, du déplacement horizontal et de la rotation des plates-formes modélisées ainsi que des caissons d'enfichage modélisés.
Onshore bearing capacity methods have conventionally been used to predict the penetration of offshore jackup spudcans into the seabed. However, the Brinch Hansen depth factor has a step change in value at the point at which the lateral dimension of a footing equals its embedment. For soft clay seabeds, where penetrations can be greater than the spudcan diameter, the step produces a spurious, unrealistic prediction of punchthrough. A small modification is proposed to the depth factor to avoid this. Some consistent modifications are proposed for several related calculations.
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