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We prove some interesting multiplicative relations which hold between the coefficients of the logarithmic derivatives obtained in a few simple ways from 𝔽q-linear formal power series. Since the logarithmic derivatives connect power sums to elementary symmetric functions via the Newton identities, we establish, as applications, new identities between important quantities of function field arithmetic, such as the Bernoulli–Carlitz fractions and power sums as well as their multivariable generalizations. Resulting understanding of their factorizations has arithmetic significance, as well as applications to function field zeta and multizeta values evaluations and relations between them. Using specialization/generalization arguments, we provide much more general identities on linear forms providing a switch between power sums for positive and negative powers.
Cornell’s, Esteva’s, and classical formulations for seismic hazard analysis are theoretically described and mathematically unified by a suitable treatment of the random ground-motion variable. Differences and connections among the schemes are discussed, allowing for a better understanding of the underpinning principles of probabilistic seismic hazard analysis. The classical formulation is equivalent to that by Esteva, and they correspond to a general scheme. Although they are mathematically equivalent, the two formulations each has its own particular approach to express the hazard rate, so results may differ. Cornell’s original scheme is a particular case of classical and Esteva’s formulation. It is also shown that intensity exceedance rates for any index of structural performance or at a particular site can be recursively transformed into exceedance rates of other intensity indexes. Formulations are invariant under such a transformation.
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