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For most mechanical loadings and various kinds of problems we need to know how the principal directions of the stress tensor are moving with time. The motion of the principal directions of stresses may be quite complicated and therefore easy to follow, especially with a variable amplitude loading. Following the motion of the principal directions is necessary for several kinds of problems. The algorithm proposed here is available in the most general case. The application deals with fatigue life predictions.
A cycle in a matroid is a disjoint union of circuits. This paper proves that every regular matroidM without coloops has a set S of cycles whose union is E(M) such that every element is in at most three of the cycles in S. It follows immediately from this that, on average, each element of M is in at most three members of the cycle cover S. This improves on a 1989 result of Jamshy and Tarsi who proved that there is a cycle Nike Free Run Womens Sale cover for which this average is at most 4, and conjectured that a cycle cover exists for which the average is at most 2.
The present paper analyzes the optimal investment strategy in a corporate (defaultable) bond, a stock and a bank account in a continuous Nike Free Tr Fit time model. We model the corporate bond price through a reduced-form approach and solve the dynamics of its price. The optimal investment process will be worked out first with a general risk-averse utility function, and then an optimal strategy with CARA utility will be presented using martingale methods. The optimal investment strategy is analyzed numerically for the CARA utility.