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On the structure of numerical event spaces

Gerhard Dorfer, Dietmar W. Dorninger, Helmut Länger (2010)

Kybernetika

The probability p ( s ) of the occurrence of an event pertaining to a physical system which is observed in different states s determines a function p from the set S of states of the system to [ 0 , 1 ] . The function p is called a numerical event or multidimensional probability. When appropriately structured, sets P of numerical events form so-called algebras of S -probabilities. Their main feature is that they are orthomodular partially ordered sets of functions p with an inherent full set of states. A classical...

On the theory of the 4-quasiplanar mappings of almost quaternionic spaces

Mikeš, Josef, Němčíková, Jana, Pokorná, Olga (1998)

Proceedings of the 17th Winter School "Geometry and Physics"

Authors’ abstract: “4-quasiplanar mappings of almost quaternionic spaces with affine connection without torsion are investigated. Geometrically motivated definitions of these mappings are presented. Based an these definitions, fundamental forms of these mappings are found, which are equivalent to the forms of 4-quasiplanar mappings introduced a priori by I. Kurbatova [Sov. Math. 30, 100-104 (1986; Zbl 0602.53029)]”.

On Threshold Eigenvalues and Resonances for the Linearized NLS Equation

V. Vougalter (2010)

Mathematical Modelling of Natural Phenomena

We prove the instability of threshold resonances and eigenvalues of the linearized NLS operator. We compute the asymptotic approximations of the eigenvalues appearing from the endpoint singularities in terms of the perturbations applied to the original NLS equation. Our method involves such techniques as the Birman-Schwinger principle and the Feshbach map.

On two possible constructions of the quantum semigroup of all quantum permutations of an infinite countable set

Debashish Goswami, Adam Skalski (2012)

Banach Center Publications

Two different models for a Hopf-von Neumann algebra of bounded functions on the quantum semigroup of all (quantum) permutations of infinitely many elements are proposed, one based on projective limits of enveloping von Neumann algebras related to finite quantum permutation groups, and the second on a universal property with respect to infinite magic unitaries.

On two quantum versions of the detailed balance condition

Franco Fagnola, Veronica Umanità (2010)

Banach Center Publications

Quantum detailed balance conditions are often formulated as relationships between the generator of a quantum Markov semigroup and the generator of a dual semigroup with respect to a certain scalar product defined by an invariant state. In this paper we survey some results describing the structure of norm continuous quantum Markov semigroups on ℬ(h) satisfying a quantum detailed balance condition when the duality is defined by means of pre-scalar products on ℬ(h) of the form ⟨ x , y ⟩ s : = t r ( ρ 1 - s x * ρ s y ) (s ∈ [0,1]) in order...

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