A general framework for measuring inconsistency through minimal inconsistent sets

Hunter and Konieczny explored the relationships between measures of inconsistency for a belief base and the minimal inconsistent subsets of that belief base in several of their papers. In particular, an inconsistency value termed MIVC, defined from minimal inconsistent subsets, can be considered as a Shapley Inconsistency Value. Moreover, it can be axiomatized completely in terms of five simple axioms. MinInc, one of the five axioms, states that each minimal inconsistent set has the same amount of conflict. However, it conflicts with the intuition illustrated by the lottery paradox, which states that as the size of a minimal inconsistent belief base increases, the degree of inconsistency of that belief base becomes smaller. To address this, we present two kinds of revised inconsistency measures for a belief base from its minimal inconsistent subsets. Each of these measures considers the size of each minimal inconsistent subset as well as the number of minimal inconsistent subsets of a belief base. More specifically, we first present a vectorial measure to capture the inconsistency for a belief base, which is more discriminative than MIVC. Then we present a family of weighted inconsistency measures based on the vectorial inconsistency measure, which allow us to capture the inconsistency for a belief base in terms of a single numerical value as usual. We also show that each of the two kinds of revised inconsistency measures can be considered as a particular Shapley Inconsistency Value, and can be axiomatically characterized by the corresponding revised axioms presented in this paper.

The level sets of the resolvent norm and convexity properties of Banach spaces

We construct a bounded linear operator on a separable, reflexive and strictly convex Banach space whose resolvent norm is constant in a neighbourhood of zero.

A comparative analysis of multidimensional features of objects resembling sets of graphs

In the present paper, we introduce a notion of a style representing abstract, complex objects having characteristics that can be represented as structured objects. Furthermore, we provide some mathematical properties of such styles. As a main result, we present a novel approach to perform a meaningful comparative analysis of such styles by defining and using graph-theoretic measures. We compare two styles by comparing the underlying feature sets representing sets of graph structurally. To determine the structural similarity between the underlying graphs, we use graph similarity measures that are computationally efficient. More precisely, in order to compare styles, we map each feature set to a so-called median graph and compare the resulting median graphs. As an application, we perform an experimental study to compare special styles representing sets of undirected graphs and present numerical results thereof. (C) 2007 Elsevier Inc. All rights reserved.

Diphosphine analogues of proton sponge: X-ray crystal structure of [Pd(eta(3)-allyl)(dppn)]BF4 center dot CH2Cl2 (dppn equals 1,8-bis(diphenylphosphino)naphthalene)

The X-ray crystal structure of [Pd(eta(3)-allyl)(dppn)]BF4 . CH2Cl2 (1) where dppn = 1,8-bis(diphenylphosphino)naphthalene is reported. Comparison of the conformation of the ligand in 1 with that in the free state shows that there is a relief of strain on complexation analogous to the relief of strain observed upon protonation of proton sponge.

Organometallic polymers: An infinite organoplatinum chain in the solid state formed by (C CH center dot center dot center dot ClPt)hydrogen bonds

The new platinum complex [PtCl[C6H2(CH(2)NMe(2))(2) -2,6-(C=CH)-4)] exhibits a polymeric linear -C=CH ... ClPt-hydrogen-bonded structure in the solid state.

Versatile N,C,N coordination behavior of a monoanionic aryldiamine ligand in ruthenium(II) complexes: Syntheses and crystal structures of [Ru-II(C6H3(CH(2)NMe(2))(2)-2,6)X(L)] (L equals norbornadiene, X=Cl, SO3CF3; L=PPh(3), X=I) and [Ru-II{C6H3(CH(2)NMe(2))(2)-2,6}(2,2':6:2''-terpyridine)]Cl

The monoanionic ligand [C6H3(CH(2)NMe(2))(2)-2,6](-), a potentially terdentate N,C,N bonding system, has been employed to synthesize a series of new ruthenium(II) complexes [Ru{C6H3(CH(2)NMe(2))(2)-2,6}X(L)] (L = PPh(3) X = Cl (2a), I (2b); L = norbornadiene (nbd), X = Cl (4), eta(1)-OSO2CF3 (5)) and [Ru{C6H3(CH(2)NMe(2))(2)-2,6}(2,2':6',2 ''-terpyridine)]Cl (3). X-ray crystal structures of 2b and 3-5 have been determined, in which the N,C,N coordination geometry with respect to the metal center is found to differ considerably. In each complex the aryldiamine ligand is terdentate, eta(3)-N,C,N-bonded as a six electron donor system. However, depending on the other ligands in the Ru(II) coordination sphere, this ligand demonstrates considerable flexibility in adopting coordination geometries which range from meridional in 3 through pseudomeridional in 2b to pseudofacial in 4 and 5. In the structures of 4 and 5 significant distortions of the aryl ring, involving bending of the six-membered ring into a boatlike conformation, are found. The different combinations of the N,C,N ligand with sets of other ligands lead to a range of metal geometries, i.e. square pyramidal in 2b, octahedral in 3, and bicapped tetrahedral in 4 and 5.

Referral to an Extracorporeal Membrane Oxygenation Center and Mortality Among Patients With Severe 2009 Influenza A(H1N1)

Context Extracorporeal membrane oxygenation (ECMO) can support gas exchange in patients with severe acute respiratory distress syndrome (ARDS), but its role has remained controversial. ECMO was used to treat patients with ARDS during the 2009 influenza A(H1N1) pandemic.