Motivated by quantum mechanics and geometric optics, it is a long-standing problem whether the length spectrum of a compact Riemannian manifold can be recovered from its Laplace spectrum. One route to proving that the length spectrum depends on the Laplace spectrum is by computing the singular support of the trace of the corresponding wave group. Indeed, it is well-known that the singular suppo...

We provide a new proof of the following Pa lasińska’s theorem: Every finitely generated protoalgebraic relation distributive equality free quasivariety is finitely axiomatizable. The main tool we use are Q-relation formulas, for a protoalgebraic equality free quasivariety Q, which are the counterparts of the congruence formulas used for describing the generation of congruences in algebras. Havi...

One can attempt to solve the problem of establishing the correctness of some software w.r.t. a formal speciication at the semantical level. For this purpose, the semantics of an algebraic speciication should be the class of all algebras which correspond to the correct realizations of the speciication. We approach this goal by deening an observational satisfaction relation which is less restrict...

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...

The notion of equality between two observables will play many important roles in foundations of quantum theory. However, the standard probabilistic interpretation based on the conventional Born formula does not give the probability of equality relation for a pair of arbitrary observables, since the Born formula gives the probability distribution only for a commuting family of observables. In th...

In this paper we provide a syntax for the cubical set model of type theory [3]. We start by defining a heterogeneous equality as a logical relation in an extended context (section 1.1). This can be seen as a different presentation of parametricity for dependent types [1]. We investigate the higher dimensional structure induced by the logical relation in section 1.2. The relation defined so far ...