‎‎for any group $g$‎, ‎we define an equivalence relation $thicksim$ as below‎: ‎[forall g‎, ‎h in g gthicksim h longleftrightarrow |g|=|h|]‎ ‎the set of sizes of equivalence classes with respect to this relation is called the same-order type of $g$ and denote by $alpha{(g)}$‎. ‎in this paper‎, ‎we give a partial answer to a conjecture raised by shen‎. ‎in fact‎, ‎we show that if $g$ is a nilpot...

We highlight and resolve what we take to be three common misconceptions in general relativity, relating to (a) the interpretation of the weak equivalence principle and the relationship between gravity and inertia; (b) the connection between gravitational redshift results and spacetime curvature; and (c) the strong equivalence principle and the local recovery of special relativity in curved, dyn...

This paper describes some of the basic applications of the algebraic theory of canonical decomposition to the analysis of data. The notions of structured data and symmetry studies are discussed and applied to demonstrate their role in well known principles of analysis of variance and their applicability in more general experimental settings.

Privacy related properties in electronic voting are naturally expressed as indistinguishability properties. This motivates the study of observational equivalence, as well as static equivalence in the context of the AVOTÉ project. In this report we survey the existing results on the computational soundness of symbolic indistinguishability relations in the presence of a passive adversary, for whi...

We describe all binary simple homogeneous structuresM in terms of ∅de nable equivalence relations on M , which coordinatize M and control dividing, and extension properties that respect these equivalence relations.

Name passing calculi are nowadays an established field on its own. Besides their practical relevance, they offered an intriguing challenge, since the standard operational, denotational and logical methods often proved inadequate to reason about these formalisms. A domain which has been successfully employed for languages with asymmetric communication, like the π-calculus, are presheaf categorie...

In this note, we present a proof of Π2-completeness of contextual equivalence of Turing machines via a reduction of the language FIN to contextual inequivalence. FIN is the language of encodings 〈Mi〉 of Turing machines Mi for which the set Wi of inputs on which Mi halts (or the set of accepting inputs of Mi) is finite. FIN is known to be Σ 0 2-complete.

We discuss the Principle of Equivalence in its relationship with Weyl Theorem to induce the interpretation of gravity as geometrical effect; this geometrization of gravity is meaningful only if the geometry is restricted in a certain way. We show what is the most general geometry in which gravity can be geometrized according to the fundamental idea expressed through Weyl theorem by the Principl...