Publisher Correction: Impact of wave whitecapping on land falling tropical cyclones
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Hurricane Irene Sensitivity to Stratified Coastal Ocean Cooling
AbstractCold wakes left behind by tropical cyclones (TCs) have been documented since the 1940s. Many questions remain, however, regarding the details of the processes creating these cold wakes and their in-storm feedbacks onto tropical cyclone intensity. This largely reflects a paucity of measurements within the ocean, especially during storms. Moreover, the bulk of TC research efforts have investigated deep ocean processes—where tropical cyclones spend the vast majority of their lifetimes—and very little attention has been paid to coastal ocean processes despite their critical importance to shoreline populations. Using Hurricane Irene (2011) as a case study, the impact of the cooling of a stratified coastal ocean on storm intensity, size, and structure is quantified. Significant ahead-of-eye-center cooling (at least 6°C) of the Mid-Atlantic Bight occurred as a result of coastal baroclinic processes, and operational satellite SST products and existing coupled ocean–atmosphere hurricane models did not capt...
Decidability of some intuitionistic predicate theories
Suppose T is a first order intuitionistic theory (more precisely, a theory of Heyting's predicate calculus, e.g., abelian groups, one unary function, dense linear order, etc.) presented to us by a set of axioms (denoted also by) T. Question. Is T decidable? One knows that if the classical counterpart of T (i.e., take the same axioms but with the classical predicate calculus as the underlying logic) is not decidable, then T cannot be decidable. The problem remains for theories whose classical counterpart is decidable. In [8], sufficient conditions for undecidability were given, and several intuitionistic theories such as abelian groups and unary functions (both with decidable equality) were shown to be undecidable. In this note we show decidability results (see Theorems 1 and 2 below), and compare these results with the undecidability results previously obtained. The method we use is the reduction-method, described fully in [12] and widely applied in [3], which is applied here roughly as follows: Let T be a given theory of Heyting's predicate calculus. We know that Heyting's predicate calculus is complete for the Kripke-model type of semantics. We choose a class M of Kripke models for which T is complete, i.e., all axioms of T are valid in any model of the class and whenever φ is not a theorem of T, φ is false in some model of M.