Decomposition of multiattribute expected-utility functions

This paper integrates and extends the theory of the decomposition of multiattribute expected-utility functions based on utility independence. In a preliminary section, the standard decision model of expected utility is briefly discussed, including the fact that the decision maker's preference forlotteries with two outcomes determines the utility function uniquely. The decomposition possibilities of a utility function are captured by the concept ofautonomous sets of attributes, an affine separability of some kind known as generalized utility independence.Overlapping autonomous sets lead to biaffine-associative, i.e.multiplicative oradditive decompositions. The multiplicative representation shows that autonomy has strongerclosure properties than utility independence, for instance with respect to set-theoretic difference. Autonomy is also a concept with a wider scope since it applies to the decomposition of Boolean functions, games and a number of other topics in combinatorial optimization. This relationship to the well-known theory ofsubstitution decomposition in discrete mathematics also reveals a kind of discrete core behind the decomposition of utility functions. The entirety of autonomous sets can be represented by a compact data structure, the so-calledcomposition tree, which frequently corresponds to a natural hierarchy of attributes. Multiplicative/additive ormulti-affine functions correspond to the hierarchy steps. The known representation of multi-affine functions is shown to be given by aMoebius inversion formula. The entire approach has the advantage that it allows the application of more sophisticated representation methods on a detailed level, whereas it employs onlyfinite set theory andarithmetic on the main levels in the hierarchy.     

Assignment of the 5,6-Double-Bond Configuration in Iloprost and Isoiloprost from 13C-NMR Shifts Determined by 2D Methods

The configurations of the 5,6-double bond in the carbacyclins iloprost ( 3 ; (E)) and isoiloprost ( 4 ; (Z)) are based on a complete assignment of the ¹³C and ¹H resonances determined by 1D and 2D ¹³C-NMR and ¹H-NMR methods.     

13C- and 1H-NMR. Spectra of ortho-benzoquinones. On the assignment problem in 13C spectra

¹³C- and ¹H-NMR. spectra of ortho-benzoquinone 1 and its methyl derivatives have been analysed. By means of heteronuclear double resonance experiments it is shown that assignments given in the literature for the olefinic carbon resonances of 1 and of a series of substituted ortho-benzoquinones have to be inverted. ¹³C-carbonyl frequencies of various six-membered cyclic ketones are presented.     

Filiation structurale des phases de´rive´es de BaFeF5

Au sein d'un re´seau de type BaFeF₅ des chai?nes d'octae`dres fluore´sa`sommets communs peuvent disparai?tre en donnant naissance a des canaux dont l'occupation partielle ou totale par des files de cations Sr²⁺ et de couples d'anions F^?, conduit respectivement aux phases Sr₃(FeF₆)₂ ou Sr₅T₃F₁₉ (T = Cr, Co, Ga). Une discussion cristallochimique permet d'expliquer l'existence d'un domaine de solutions solides au sein du diagramme ternaire SrF₂BaF₂FeF₃.     

Cyclodehydration of N-[(2-heteroarylcarbamoyl)methyl] benzamides. Preparation of 5-(heteroarylamino)oxazoles

The cyclodehydration of N-[heleroarylcarbamoyl)methyl]benzamides was found to yield 5-(heteroarylamino)oxazoles     

Raman scattering from Pt(CN)42− adsorbed on Pt colloids

Raman scattering from Pt(CN)₄^2? adsorbed on Pt colloids (average diameter of 16 A) is compared with the Raman signal from the same amount of Pt(CN)₄^2? in solution. The wavelength dependence of the adsorbate Raman intensity is measured from 308 to 647 nm and compared with a Lorenz/Mie calculation of the enhancement factor for the electromagnetic field intensity on the surface of a Pt sphere as a function of sphere radius and incident wavelength.     

Relativistic atomic natural orbital type basis sets for the alkaline and alkaline-earth atoms applied to the ground-state potentials for the corresponding dimers

New basis sets of the atomic natural orbital (ANO) type have been developed for the atoms Li–Fr and Be–Ra. The ANOs have been obtained from the average density matrix of the ground states and the lowest excited states of the atom, the positive ion, and the dimer at its equilibirium geometry. Scalar realtivisitc effects are included through the use of a Douglas–Kroll Hamiltonian. Multiconfigurational wave functions have been used with dynamic correlation included using second-order perturbation theory (CASSCF/CASPT2). The basis sets are applied in calculations of the ground-state potentials for the dimers. Computed bond energies are accurate to within 0.05 eV for the alkaline dimers and 0.02 eV for the alkaline-earth dimers (except for Be₂).Acknowledgments.ensp;B.O.R. would like to express his gratitude to Prof. Jacopo Tomasi for all the inspiration that his scientific work has given him through the years and continues to do in particular through the work on solvent effects on molecular properties. This work has been supported by a grant from the Swedish Science Research Council, VR.Contribution to the Jacopo Tomasi Honorary Issue