A further step in the strategy for proving Riemann hypothesis proposed earlier(M. Pitkänen, math.GM/0102031) is suggested. The vanishing of Rieman Zeta reduces to an orthogonality condition for the eigenfunctions of a non-Hermitian operator D having the zeros of Riemann Zeta as its eigenvalues. The construction of D is inspired by the conviction that Riemann Zeta is associated with a physical s...

We extend the formalism whereby boson mappings can be derived from generalized coherent states to boson-fermion mappings for systems with an odd number of fermions. This is accomplished by constructing supercoherent states in terms of both complex and Grassmann variables. In addition to a known mapping for the full so(2N+1) algebra, we also uncover some other formal mappings, together with mapp...

A relation between the Z3-graded Grassmann variables and parafermions is established. Coherent states are constructed as a direct consequence of such a relationship. We also give the analog of the Bargmann-Fock representation in terms of these Grassmann variables.

für Naturforschung in cooperation with the Max Planck Society for the Advancement of Science under a Creative Commons Attribution 4.0 International License. Dieses Werk wurde im Jahr 2013 vom Verlag Zeitschrift für Naturforschung in Zusammenarbeit mit der Max-Planck-Gesellschaft zur Förderung der Wissenschaften e.V. digitalisiert und unter folgender Lizenz veröffentlicht: Creative Commons Namen...

1 Generalities on Spectral Deligne-Mumford Stacks 4 1.1 Points of Spectral Deligne-Mumford Stacks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 Étale Morphisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.3 Localic Spectral Deligne-Mumford Stacks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 1.4 Quasi-Compactness of Sp...

Explicit forms of matrix elements of generalized coherent operators based on Lie algebras su(1,1) and su(2) are given. ∗E-mail address : [email protected]

In this paper we extend the concept of coherent pairs of measures from the real line to Jordan arcs and curves. We present a characterization of pairs of coherent measures on the unit circle: it is established that if ( 0, 1) is a coherent pair of measures on the unit circle, then 0 is a semi-classical measure. Moreover, we obtain that the linear functional associated with 1 is a specific ratio...

This paper examines the applicability o f belief functions methodology in three reasoning tasks: (1) representation of incomplete knowledge, (2) belief updating, and (3) evidence pooling. We find that belief functions have difficulties representing incomplete knowledge, primarily knowledge expressed in conditional sentences. In this context, we also show that the prevailing practices of encodin...

für Naturforschung in cooperation with the Max Planck Society for the Advancement of Science under a Creative Commons Attribution 4.0 International License. Dieses Werk wurde im Jahr 2013 vom Verlag Zeitschrift für Naturforschung in Zusammenarbeit mit der Max-Planck-Gesellschaft zur Förderung der Wissenschaften e.V. digitalisiert und unter folgender Lizenz veröffentlicht: Creative Commons Namen...