Mesh update techniques for free-surface flow solvers using spectral element method

This paper presents a novel mesh-update technique for unsteady free-surface Newtonian flows using spectral element method and relying on the arbitrary Lagrangian--Eulerian kinematic description for moving the grid. Selected results showing compatibility of this mesh-update technique with spectral element method are given

First-order and counting theories of ω-automatic structures

The logic L(Qu) extends first-order logic by a generalized form of counting quantifiers (“the number of elements satisfying... belongs to the set C”). This logic is investigated for structures with an injectively ω-automatic presentation. If first-order logic is extended by an infinity-quantifier, the resulting theory of any such structure is known to be decidable [5]. It is shown that, as in the case of automatic structures [19], also modulocounting quantifiers as well as infinite cardinality quantifiers (“there are κ many elements satisfying...”) lead to decidable theories. For a structure of bounded degree with injective ω-automatic presentation, the fragment of L(Qu) that contains only effective quantifiers is shown to be decidable and an elementary algorithm for this decision is presented. Both assumptions (ω-automaticity and bounded degree) are necessary for this result to hold. §1. Introduction. Automatic structures were introduced in [13, 16]. The idea goes back to the concept of automatic groups [9]. Roughly speaking, a structure is called automatic if the elements of the universe can be represented as words from a regular language and every relation of the structure can be recognized by a finite state automaton with several heads that proceed synchronously

Pricing a contract of linking home reversion plan and long-term care insurance via the principle of equivalent utility

Home reversion plans, Long-term care insurance, Indifference price, Hamilton-Jacobi-Bellman equation, Expected utility,

Automatic Structures of Bounded Degree

The rst-order theory of an automatic structure is known to be decidable but there are examples of automatic structures with nonelementary rst-order theories. We prove that the rst-order theory of an automatic structure of bounded degree (meaning that the corresponding Gaifman-graph has bounded degree) is elementary decidable. More precisely, we prove an upper bound of triply exponential alternating time with a linear number of alternations. We also present an automatic structure of bounded degree such that the corresponding rst-order theory has a lower bound of doubly exponential time with a linear number of alternations. We prove similar results also for tree automatic structures