In this paper, we describe a novel constructive method of proving the Craig interpolation property (CIP) based on cut-free hypersequent calculi and apply the method to prove the CIP for the modal logic S5.

We introduce an algorithm for construction of the Morse hierarchy, i.e. a hierarchy of Morse decompositions of a piecewise constant vector field on a surface driven by stability of the Morse sets with respect to perturbation of the vector field. Our approach builds upon earlier work on stable Morse decompositions, which can be used to obtain Morse sets of user-prescribed stability. More stable ...

A brief overviewof Forman’s discrete Morse theory is presented, from which analogues of the main results of classical Morse theory can be derived for discrete Morse functions, these being functions mapping the set of cells of a CW complex to the real numbers satisfying some combinatorial relations. The discrete analogue of the strong Morse inequality was proved by Forman for finite CW complexes...

We extend the equivariant holomorphic Morse inequalities of circle actions to cases with torus and non-Abelian group action. For torus actions, there is a set of inequalities for each choice of action chambers specifying directions in the Lie algebra of the torus. If the group is non-Abelian, there is in addition an action of the Weyl group on the fixed-point set of its maximal torus. The sum o...

the development of a conceptual model that best accounts for the different parameters influencing lnapl fate and transport in groundwater is ultimate the key to a successful simulation of lnapl concentration in groundwater. characterization of hydrocarbon sources and identification of areas with heavy lnapl loadings from point and non-point sources is important for land use planners and environ...

BACKGROUND There has been limited decline in undernutrition rates in South Asia compared with the rest of Asia and one reason for this may be low levels of household food security. However, the evidence base on the determinants of household food security is limited. To develop policies intended to improve household food security, improved knowledge of the determinants of household food security...