On nearly parallel G2-structures

A nearly parallel G₂-structure on a seven-dimensional Riemannian manifold is equivalent to a spin structure with a Killing spinor. We prove general results about the automorphism group of such structures and we construct new examples. We classify all nearly parallel G₂-manifolds with large symmetry group and in particular all homogeneous nearly parallel G₂-structures.     

Kravchuk polynomials and group representations

Kravchuk polynomials of a discrete variable and different types of Kravchuk q-polynomials are determined. The importance of these polynomials for the theory of representations of Lie and Chevalley groups and the theory of symmetric and quantum groups is shown. The article presents a survey of the contemporary results in these areas.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 7, pp. 888–901, July, 1992.     

New olefinic functionalized disilanes. Synthesis and NMR spectroscopical investigations

The new olefinic substituted aminodisilanes, which are obtained from the reaction of organometallic reagents with aminochlorodisilanes, are converted into the chlorodisilanes by equilibration reactions or treatment with HCI. The resulting olefinic functionalized disilanes are identified by means of ²⁹Si, ¹³C, ¹H NMR and GC MS measurements.     

Formation of Fe i –B pairs in silicon at high temperatures

We report on the detection of Fe _i –B pairs in heavily B doped silicon using ⁵⁷Fe emission Mössbauer spectroscopy following implantation of radioactive ⁵⁷Mn⁺ parent ions (T _1/2?=?1.5 min) at elevated temperatures >?850 K. The Fe _i –B pairs are formed upon the dissociation of Fe _i –V pairs during the lifetime of the Mössbauer state (T _1/2?=?100 ns). The resulting free interstitial Fe_i diffuses over sufficiently large distances during the lifetime of the Mössbauer state to encounter a substitutional B impurity atom, forming Fe _i –B pairs, which are stable up to ～1,050 K on that time scale.     

Characterization of high-order harmonic radiation on femtosecond and attosecond time scales

We characterize the temporal structure of high-order harmonic radiation on both the femtosecond and attosecond time scales. The harmonic emission is characterized by mixed-color two-photon ionization with an infrared femtosecond laser using a Mach–Zehnder interferometer where both pump and probe arms travel completely separate paths. In a first experiment, we measure the duration and chirp of individual harmonics. In a second experiment, we resolve, for the first time with this type of setup, the attosecond beating of several harmonics generated under conditions similar to the first experiment. We suggest that the results of both measurements can be combined to determine the full attosecond time structure of the harmonic emission. PACS 32.80.Rm; 42.65.Ky     

Hindered motions in a ketonea-urea inclusion compound. An ESR and ENDOR study

We have studied by ESR and ENDOR spectroscopy the free radicals produced in γ-irradiated inclusion compound formed between the ketone 10-nonadecanone and urea. Only one type of long lived radical is formed by the removal of an α-proton from the ketone. The hyperfine (hf) coupling constants of the α- and β-protons of the radicals have been measured by ESR at different temperatures in the range 110–292 K and at different orientations of the crystals. The hf coupling of the γ-protons of the radical and of the urea protons have been studied by ENDOR. The temperature and angular dependences of the coupling constants have been analyzed in terms of the internal and overall motions of the radical inside the hexagonal channels formed by the urea molecules. It has been found that the radical cannot perform complete reorientations around the long molecular axis, but it undergoes restricted rotational diffusion. This process is explained by assuming a coupling between the rotational and translational degrees of freedom of the radical inside the urea channels.     

The Shapley value for cooperative games under precedence constraints

Cooperative games are considered where only those coalitions of players are feasible that respect a given precedence structure on the set of players. Strengthening the classical symmetry axiom, we obtain three axioms that give rise to a unique Shapley value in this model. The Shapley value is seen to reflect the expected marginal contribution of a player to a feasible random coalition, which allows us to evaluate the Shapley value nondeterministically. We show that every exact algorithm for the Shapley value requires an exponential number of operations already in the classical case and that even restriction to simple games is #P-hard in general. Furthermore, we outline how the multi-choice cooperative games of Hsiao and Raghavan can be treated in our context, which leads to a Shapley value that does not depend on pre-assigned weights. Finally, the relationship between the Shapley value and the permission value of Gilles, Owen and van den Brink is discussed. Both refer to formally similar models of cooperative games but reflect complementary interpretations of the precedence constraints and thus give rise to fundamentally different solution concepts.