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Seeable matter; unseeable antimatter

Geoffrey Dixon (2014)

Commentationes Mathematicae Universitatis Carolinae

The universe we see gives every sign of being composed of matter. This is considered a major unsolved problem in theoretical physics. Using the mathematical modeling based on the algebra $𝐓 : = 𝐂 \otimes 𝐇 \otimes 𝐎$ , an interpretation is developed that suggests that this seeable universe is not the whole universe; there is an unseeable part of the universe composed of antimatter galaxies and stuff, and an extra 6 dimensions of space (also unseeable) linking the matter side to the antimatter—at the very least.

Semiobservables on quantum logics

Sylvia Pulmannová (1980)

Mathematica Slovaca

Some distributivities in GBbi-QRs characterizing Boolean rings

Joanna Kaleta (2004)

Discussiones Mathematicae - General Algebra and Applications

This paper presents some manner of characterization of Boolean rings. These algebraic systems one can also characterize by means of some distributivities satisfied in GBbi-QRs.

Spaces of observables

Pavel Pták (1984)

Czechoslovak Mathematical Journal

Spectral resolutions for $σ$ -complete lattice effect algebras

Sylvia Pulmannová (2006)

Mathematica Slovaca

State space properties of finite logics

Mirko Navara (1987)

Czechoslovak Mathematical Journal

Statistical maps. I: Basic properties

Sławomir Bugajski (2001)

Mathematica Slovaca

Statistical maps. II: Operational random variables and the Bell phenomenon

Sławomir Bugajski (2001)

Mathematica Slovaca

Sum of observables in fuzzy quantum spaces

Anatolij Dvurečenskij, Anna Tirpáková (1992)

Applications of Mathematics

We introduce the sum of observables in fuzzy quantum spaces which generalize the Kolmogorov probability space using the ideas of fuzzy set theory.

Superpositions of states and a representation theorem

Sylvia Pulmannovà (1980)

Annales de l'I.H.P. Physique théorique

Supporting sequences of pure states on JB algebras

Jan Hamhalter (1999)

Studia Mathematica

We show that any sequence $(φ_{n})$ of mutually orthogonal pure states on a JB algebra A such that $(φ_{n})$ forms an almost discrete sequence in the relative topology induced by the primitive ideal space of A admits a sequence $(a_{n})$ consisting of positive, norm one, elements of A with pairwise orthogonal supports which is supporting for $(φ_{n})$ in the sense of $φ_{n} (a_{n}) = 1$ for all n. Moreover, if A is separable then $(a_{n})$ can be taken such that $(φ_{n})$ is uniquely determined by the biorthogonality condition $φ_{n} (a_{n}) = 1$ . Consequences of this result improving...

Symmetric difference in orthomodular lattices

Gerhard Dorfer, Anatolij Dvurečenskij, Helmut Länger (1996)

Mathematica Slovaca

Symmetric difference on orthomodular lattices and $Z_{2}$ -valued states

Milan Matoušek, Pavel Pták (2009)

Commentationes Mathematicae Universitatis Carolinae

The investigation of orthocomplemented lattices with a symmetric difference initiated the following question: Which orthomodular lattice can be embedded in an orthomodular lattice that allows for a symmetric difference? In this paper we present a necessary condition for such an embedding to exist. The condition is expressed in terms of $Z_{2}$ -valued states and enables one, as a consequence, to clarify the situation in the important case of the lattice of projections in a Hilbert space.

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