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Matrix approach to the Shapley value and dual similar associated consistency
Replacing associated consistency in Hamiache's axiom system by dual similar associated consistency, we axiomatize the Shapley value as the unique value verifying the inessential game property, continuity and dual similar associated consistency. Continuing the matrix analysis for Hamiache's axiomatization of the Shapley value, we construct the dual similar associated game and introduce the dual similar associated transformation matrix as well. In the game theoretic framework we show that the dual game of the dual similar associated game is Hamiache's associated game of the dual game. For the purpose of matrix analysis, we derive the similarity relationship between the dual similar associated transformation matrix and associated transformation matrix for Hamiache's associated game, where the transformation matrix represents the duality operator on games. This similarity of matrices transfers associated consistency into dual similar associated consistency, and also implies the inessential property for the limit game of the convergent sequence of repeated dual similar associated games. We conclude this paper with three tables summarizing all matrix results
Revisiting the Quantum Group Symmetry of Diatomic Molecules
We propose a q-deformed model of the anharmonic vibrations in diatomic
molecules. We analyse the applicability of the model to the phenomenological
Dunham's expansion by comparing with experimental data. Our methodology
involves a global consistency analysis of the parameters that determine the
q-deformed system, when compared with fitted vibrational parameters to 161
electronic states in diatomic molecules. We show how to include both the
positive and the negative anharmonicities in a simple and systematic fashion.Comment: 15 pages, 3 Table
Hidden Q-structure and Lie 3-algebra for non-abelian superconformal models in six dimensions
We disclose the mathematical structure underlying the gauge field sector of
the recently constructed non-abelian superconformal models in six spacetime
dimensions. This is a coupled system of 1-form, 2-form, and 3-form gauge
fields. We show that the algebraic consistency constraints governing this
system permit to define a Lie 3-algebra, generalizing the structural Lie
algebra of a standard Yang-Mills theory to the setting of a higher bundle.
Reformulating the Lie 3-algebra in terms of a nilpotent degree 1 BRST-type
operator Q, this higher bundle can be compactly described by means of a
Q-bundle; its fiber is the shifted tangent of the Q-manifold corresponding to
the Lie 3-algebra and its base the odd tangent bundle of spacetime equipped
with the de Rham differential. The generalized Bianchi identities can then be
retrieved concisely from Q^2=0, which encode all the essence of the structural
identities. Gauge transformations are identified as vertical inner
automorphisms of such a bundle, their algebra being determined from a Q-derived
bracket.Comment: 51 pages, 3 figure
Self-consistency in non-extensive thermodynamics of highly excited hadronic states
The self-consistency of a thermodynamical theory for hadronic sys- tems based
on the non-extensive statistics is investigated. We show that it is possible to
obtain a self-consistent theory according to the asymptotic bootstrap principle
if the mass spectrum and the energy density increase q-exponentially. A direct
consequence is the existence of a limiting effective temperature for the
hadronic system. We show that this result is in agreement with experiments.Comment: 8 page
Correlation energy of a two-dimensional electron gas from static and dynamic exchange-correlation kernels
We calculate the correlation energy of a two-dimensional homogeneous electron
gas using several available approximations for the exchange-correlation kernel
entering the linear dielectric response of the system.
As in the previous work of Lein {\it et al.} [Phys. Rev. B {\bf 67}, 13431
(2000)] on the three-dimensional electron gas, we give attention to the
relative roles of the wave number and frequency dependence of the kernel and
analyze the correlation energy in terms of contributions from the plane. We find that consistency of the kernel with the electron-pair
distribution function is important and in this case the nonlocality of the
kernel in time is of minor importance, as far as the correlation energy is
concerned. We also show that, and explain why, the popular Adiabatic Local
Density Approximation performs much better in the two-dimensional case than in
the three-dimensional one.Comment: 9 Pages, 4 Figure
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