We compute the mass spectrum of the fermionic sector of the Dirac-Kähler extension of the SM (DK-SM) by showing that there exists a Bogoliubov transformation that transforms the DK-SM into a flavor U(4) extension of the SM (SM-4) with a particular choice of masses and mixing textures. Mass relations of the model allow determination of masses of the 4th generation. Tree level prediction for the mass of the 4 th charged lepton is 370 GeV. The model selects the normal hierarchy for neutrino masses and reproduces naturally the near tri-bimaximal and quark mixing textures. The electron neutrino and the 4th neutrino masses are related via a seesaw like mechanism.
We study the heredity of local completeness and the strict Mackey convergence property from the locally convex spaceEto the space of absolutelyp-summable sequences onE,ℓp(E)for1≤p<∞.
We prove an extension of the Pareto optimization criterion to locally complete locally convex vector spaces to guarantee the existence of fixed points of set-valued maps.MSC: Primary 47H10; 47H04; secondary 46N10; 46A03
Ekeland's variational principle and the existence of critical points of dynamical systems, also known as multiobjective optimization, have been proved in the setting of locally complete spaces. In this article we prove that these two properties can be deduced one from the other under certain convexity conditions.
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