Algebras of Measurements: the logical structure of Quantum Mechanics

A new branch of the logical algebra: UP-algebras

In this paper, we introduce a new algebraic structure, called a UP-algebra (UP means the University of Phayao) and a concept of UP-ideals, UP-subalgebras, congruences and UP-homomorphisms in UP-algebras, and investigated some related properties of them. We also describe connections between UP-ideals, UP-subalgebras, congruences and UP-homomorphisms, and show that the notion of UP-algebras is a ...

Structure-Activity Relationship of Imidazobenzodiazepines, an AM1 Semi-Empirical Quantum Mechanics Study

Conformations and electronic properties of a series of imidazobenzodiazepines are investigated by AM1 semi-empirical quantum mechanics method. It is shown that substitution of Cl in position 7 instead of 8, changes the geometry of the seven membered lactam ring; this may put the N5 nitrogen in a better positon to act as a hydrogen bond acceptor, and the phenyl ring in position 6 is probably...

MV-Algebras and Quantum Computation

We introduce a generalization of MV algebras motivated by the investigations into the structure of quantum logical gates. After laying down the foundations of the structure theory for such quasi-MV algebras, we show that every quasi-MV algebra is embeddable into the direct product of an MV algebra and a "‡at" quasi-MV algebra, and prove a completeness result w.r.t. a standard quasi-MV algebra o...

(Modular) Effect Algebras are Equivalent to (Frobenius) Antispecial Algebras

Effect algebras are one of the generalizations of Boolean algebras proposed in the quest for a quantum logic. Frobenius algebras are a tool of categorical quantum mechanics, used to present various families of observables in abstract, often nonstandard frameworks. Both effect algebras and Frobenius algebras capture their respective fragments of quantum mechanics by elegant and succinct axioms; ...

Reiter’s Properties for the Actions of Locally Compact Quantum Goups on von Neumann Algebras