Reducing Cognitive Effort in Scoring Negotiation Space Using the Fuzzy Clustering Model

Negotiation scoring systems are fundamental tools used in negotiation support to facilitate parties searching for negotiation agreement and analyzing its efficiency and fairness. Such a scoring system is obtained in prenegotiation by implementing selected multiple criteria decision-aiding methods to elicit the negotiator’s preferences precisely and ensure that the support is reliable. However, the methods classically used in the preference elicitation require much cognitive effort from the negotiators, and hence, do not prevent them from using heuristics and making simple errors that result in inaccurate scoring systems. This paper aims to develop an alternative tool that allows scoring the negotiation offers by implementing a sorting approach and the reference set of limiting profiles defined individually by the negotiators in the form of complete packages. These limiting profiles are evaluated holistically and verbally by the negotiator. Then the fuzzy decision model is built that uses the notion of increasing the preference granularity by introducing a series of limiting sub-profiles for corresponding sub-categories of offers. This process is performed automatically by the support algorithm and does not require any additional preferential information from the negotiator. A new method of generating reference fuzzy scores to allow a detailed assignment of any negotiation offer from feasible negotiation space to clusters and sub-clusters is proposed. Finally, the efficient frontier and Nash’s fair division are used to identify the recommended packages for negotiation in the bargaining phase. This new approach allows negotiators to obtain economically efficient, fair, balanced, and reciprocated agreements while minimizing information needs and effort.     

An invariant trace formula for the universal covering group of SL(2,ℝ)

Automorphic forms of arbitrary real weight can be considered as functions on the universal covering group of SL(2, ). In this situation, we prove an invariant form of the Selberg trace formula for Hecke operators. For this purpose, the Fourier transforms of weightet orbital integrals, obtained by J. Arthur, R. Herb and P. Sally, jr., are explicitly calculated. Our formula does not follow from Arthur's invariant trace formula, since the group has infinite centre, and vector-valued automorphic forms with respect to non-congruence lattices are considered.     

Resonant electron transfer andL-shell excitation at 3.6 MeV/u Smq+→Xe collisions

Resonance energies and widths of four resonances in the reaction²⁵Mg(p,γ)²⁶Al were measured with the high resolution proton beam of the new 500 kV accelerator IONAS. The previously given large width of the 389 keV resonance, Γ= 460±70 eV. (1), used in the interpretation of stellar²⁶A1 production was shown to be incorrect and probably caused by target oxidation effects and insufficient energy resolution of the beam. The new value is Γ<4 eV.     

Quantum World with Quantum Time

Since the beginning of quantum mechanics there have been a lot of attempts to quantize time. In this paper we refer to the little known concept of quantum time proposed by E.Kapuscik [Hadronic J. 8 (1985) 75]. We analyze some properties of systems with quantum time. Moreover we comment and discuss the idea of quantum time.     

Vortex fluctuations in underdoped Bi(2)Sr(2)CaCu(2)O(8+delta) crystals

Vortex thermal fluctuations in heavily underdoped Bi(2)Sr(2)CaCu(2)O(8+delta) (T(c)=69.4 K) are studied using Josephson plasma resonance. From the zero-field data, we obtain the c-axis penetration depth lambda(L,c)(0)=230+/-10 micrometer and the anisotropy ratio gamma(T). The low plasma frequency allows us to study phase correlations over the whole vortex solid state and to extract a wandering length r(w) of vortex pancakes. The temperature dependence of r(w) as well as its increase with dc magnetic field is explained by the renormalization of the vortex line tension by the fluctuations, suggesting that this softening is responsible for the dissociation of the vortices at the first order transition.     

Study of the energy release region of a heavy-ion flux in nanomaterials by X-ray spectroscopy of multicharged ions

X-ray spectroscopic data are reported on the state of a silicon aerogel medium (SiO₂) irradiated by a Ni ion flux with an energy of 4.7 MeV/nucleon. Radiation from the electron transitions to the K shell in multicharged Si ions is detected with spatial resolution along the direction of the beam propagation in the medium. Calculations performed for the ionization state and population of the levels excited in the silicon atoms of the target provide the estimate T_e = 70–120 eV for the medium electron temperature in the ion tack region. Two-dimensional hydrodynamic calculations provide the estimate T_e = 60–116 eV for the same conditions and densities of 0.5–2.5 g/cm³ of the excited target medium.