Consistent union and prioritized consistent union: new operations for preference aggregation

We discuss some new approaches to preference aggregation, keeping the natural property of transitivity of strict preferences in mind. In a previous paper, we discussed various ways in which to construct and process strict partial order relations in the context of ranking objects on the basis of multiple criteria. We now broaden the scope to include more general expressions of preferences as inputs and introduce the concept of a NIP-triple, composed of a relation of necessary couples, a relation of impossible couples and a relation of possible couples. The use of NIP-triples allows for a more straightforward characterization of the consistent and prioritized consistent union as well as a smooth formulation of algorithmic implementations. We also introduce a NIP-triple closing operation, which can be combined with the consistent union operations for increased flexibility. Some properties of the proposed operations are examined. The consistent union operation is commutative, as is its composition with the closing operation. Both the consistent and prioritized consistent union are associative, but not when they are composed with the closing operation. Nevertheless, the composed operations surely have their use, which is also discussed.     

Low-Temperature TLC-MS of Essential Oils from Five Different Sage (Salvia) Species

JPC – Journal of Planar Chromatography – Modern TLC - In a previous paper we discussed the possibility of fractionating the essential oils of different sage species by low-temperature...     

Catalytic Ketonization over Oxide Catalysts, Part IV. Cycloketonization of Diethyl Hexanodiate

Activity of 20 wt.% MO₂/S catalysts, where M = Mn, Ce and Th, and S = Al₂O₃ or SiO₂, has been studied in cycloketonization of diethyl hexanodiate at the temperature range 573-698 K in a flow system. Only moderate yields of cyclopentanone (<35%) were achieved. The highest yields of ketone were obtained over MnO₂/Al₂O₃ and MnO₂/SiO₂ catalysts - 33 and 27%, respectively. ThO₂ containing catalysts were the most active, whereby ester transformations were detected below 573 K. In the presence of all catalysts the formation of the main product was accompanied by various amounts of 2-ethylcyclopentanone, cyclopent-2-en-1-one, cyclopentene, 2-cyclopentylidenecyclopentanone and numerous unidentified by-products.     

Topological structure of complete Riemannian manifolds with cyclic holonomy groups

Let M be a complete m-dimensional Riemannian manifold with cyclic holonomy group, let X be a closed flat manifold homotopy equivalent to M, and let L→X be a nontrivial line bundle over X whose total space is a flat manifold with cyclic holonomy group. We prove that either M is diffeomorphic to X×Rm-dimX or M is diffeomorphic to L×Rm-dimX−1.     

Rotation Sets of Billiards with One Obstacle

We investigate the rotation sets of billiards on the m-dimensional torus with one small convex obstacle and in the square with one small convex obstacle. In the first case the displacement function, whose averages we consider, measures the change of the position of a point in the universal covering of the torus (that is, in the Euclidean space), in the second case it measures the rotation around the obstacle. A substantial part of the rotation set has usual strong properties of rotation sets.The first author was partially supported by NSF grant DMS 0456748.The second author was partially supported by NSF grant DMS 0456526.The third author was partially supported by NSF grant DMS 0457168.     

Time-resolved streak camera system with solid state laser and optical parametric generator in different spectroscopic applications

Apparatus to study time-evolution of emission spectra over very wide time and spectral range is described. Excitation part of the equipment consists of solid state Nd:YAG laser and optical parametric generator. The heart of the detection system consists of spectrograph and streak camera. The significance of optics and electronics built in the system for proper, fast and convenient measurements is underlined. The results of donor-acceptor energy transfer in a rigid polyvinyl alcohol matrix serve here as an example of application our equipment to study complex systems.     

Multiplicity distribution inK + Al andK + Au collisions at 250 GeV/c and a test of the multiple collision model

Multiplicity distributions, observed inK ⁺ interactions with Al and Au nuclei at 250 GeV/c incident momentum are presented. They are analyzed in the framework of multiple collisions of the incident particle inside a nucleus. The probability distribution of the number of grey tracks is well described by the model of Andersson et al., if a negative binomial distribution is assumed for the distribution of the number of grey protons produced per elementary collision instead of the usual geometrical distribution. The analysis of the average and dispersion of the charge multiplicity distribution supports the validity of the multiple collision model, including results on correlations between forward and backward multiplicities.     

Towards Clathrates: Frozen States of Hydration of tert‐Butylamine

The dilution of tert‐butylamine (tBA) with water and subsequent cooling leads to a large series of different crystalline hydrates by an in situ IR laser melting‐zone procedure. The crystal structures were determined for tBA?n H₂O, with n=0, , 1, 7 , 7 , 9 , 11, and 17. For the two lower hydrates (n= , 1), one‐ and two‐dimensional hydrogen‐bonded networks are formed, respectively. The higher hydrates (n>1) exhibit a clathrate‐like three‐dimensional water framework with the tBA molecules as part of, or sitting inside, the cages. In all cases, tBA is hydrogen‐bonded to the H₂O framework. In the intermediate range (1相似文献