In turbulent flow, the normal procedure has been seeking means u of the fluid velocity u rather than the velocity itself. In large eddy simulation, we use an averaging operator which allows for the separation of largeand small-length scales in the flow field. The filtered field u denotes the eddies of size O(δ) and larger. Applying local spatial averaging operator with averaging radius δ to the...

ω-languages are becoming more and more relevant nowadays when most applications are “ever-running”. Recent literature, mainly under the motivation of widening the application of model checking techniques, extended the analysis of these languages from the simple regular ones to various classes of languages with “visible syntax structure”, such as visibly pushdown languages (VPLs). Operator prece...

We present a terminating tableau system for the modal logic K∗. K∗ extends the basic modal logic K with a reflexive transitive closure operator for relations and is a proper fragment of propositional dynamic logic. We investigate two different approaches to achieve termination, namely chain-based blocking and pattern-based blocking. Pattern based-blocking has not been applied to a modal logic w...

In this paper we derive and present an application of hypergraphic oriented matroids for the purpose of enumerating the variable interdependencies that define the chemical complexes associated with the kinetics of non-linear dynamical system representations of chemical kinetic reaction flow networks. The derivation of a hypergraphic oriented matroid is obtained by defining a closure operator on...

Operator precedence languages, designated as Floyd’s Languages (FL) to honor their inventor, are a classical deterministic context-free family. FLs are known to be a boolean family, and have been recently shown to strictly include the Visibly Pushdown Languages (VPDL); the latter are FLs characterized by operator precedence relations determined by the alphabet partition. In this paper we give t...

Recent literature extended the analysis of ω-languages from the regular ones to various classes of languages with “visible syntax structure”, such as visibly pushdown languages (VPLs). Operator precedence languages (OPLs), instead, were originally defined to support deterministic parsing and exhibit interesting relations with these classes of languages: OPLs strictly include VPLs, enjoy all rel...

We give a simple proof of a theorem of Gurevich and Shelah, that the inductive closure of an inflationary operator is equivalent, over the class of finite structures, to the inductive closure (i.e. minimal fixpoint) of a positive operator. A variant of the same proof establishes a theorem of Immerman, that the class of inductive closures of positive first order operators is closed under complem...

We consider the basic heat operator on functions on a Riemannian foliation of a compact, Riemannian manifold, and we show that the trace KB(t) of this operator has a particular asymptotic expansion as t → 0. The coefficients of t and of t(log t) in this expansion are obtainable from local transverse geometric invariants functions computable by analyzing the manifold in an arbitrarily small neig...

Many efforts have been made in recent years to construct formal systems for mechanizing mathematical reasoning. A framework which seems particularly suitable for this task is ancestral logic – the logic obtained by augmenting first-order logic with a transitive closure operator. While the study of this logic has so far been mostly modeltheoretical, this work is devoted to its proof theory (whic...

— The opérations of homomorphic repHcation and substitution are strongly independent forfull semiAFLs in the sense that if ££ is afull semiAFL closed under neither homomorphic repHcation nor substitution, then the closure of ^ under homomorphic repHcation («&,(&)) is incomparable with the closure of <£ under substitution {Jta(<£)). The leastfull AFL containing afull semiAFL ££ and closed under ...