Related papers: A generic absoluteness principle consistent with l…
We mechanize, in the proof assistant Isabelle, a proof of the axiom-scheme of Separation in generic extensions of models of set theory by using the fundamental theorems of forcing. We also formalize the satisfaction of the axioms of…
We prove a general congruence result for bisimilarity in higher-order languages, which generalises previous work to languages specified by a labelled transition system in which programs may occur as labels, and which may rely on operations…
In this paper, we investigate the conservation laws of different type of particles in theories with a universal gravity/matter coupling. The result brings new insights about previous studies on universal gravity/matter theories. Especially,…
Hybrid systems with memory refer to dynamical systems exhibiting both hybrid and delay phenomena. While systems of this type are frequently encountered in many physical and engineering systems, particularly in control applications, various…
In this work, we propose a new existence result for quasi-equilibrium problems using generalized monotonicity in an infinite dimensional space. Also, we show that the notions of generalized monotonicity can be characterized in terms of…
Any individual's preference represents his choice in the set of available options. It is said to be complete if the person can compare any pair of available options. We aim to initiate the notion of projected solutions for the generalized…
We prove an abstract Nyquist criterion in a general set up. As applications, we recover various versions of the Nyquist criterion, some of which are new.
There exist many examples of systems which have some symmetries, and which one may monitor with symmetry preserving controls. Since symmetries are preserved along the evolution, full controllability is not possible, and controllability has…
We propose some axioms for hierarchical clustering of probability measures and investigate their ramifications. The basic idea is to let the user stipulate the clusters for some elementary measures. This is done without the need of any…
After discussing the limitations inherent to all set-theoretic reflection principles akin to those studied by A. L\'evy et. al. in the 1960's, we introduce new principles of reflection based on the general notion of \emph{Structural…
General Relativity (GR), with or without matter fields, admits a natural extension to a scale invariant theory that requires a dilaton. Here we show that the recently formulated massive GR, minimally coupled to matter, possesses a new…
The generalized uncertainty principle is often used to modify various thermodynamics systems by regarding the greater-than-equal relation as an approximate relation. We give a method to improve this approximation and compare the differences…
This paper develops a new framework, \emph{simultaneous saturation}, designed to quantify the size of sets whose elements are simultaneously large. The framework establishes a correspondence between the magnitude of such sets and a system…
Irreversible aggregation is an archetypal example of a system driven far from equilibrium by sources and sinks of a conserved quantity (mass). The source is a steady input of monomers and the evaporation of colliding particles with a small…
We prove a new general differential identity and an associated integral identity, which entails a pair of solutions of the Poisson equation with constant source term. This generalizes a formula that the first and third authors previously…
The generalized uncertainty principle discloses a self-complete characteristic of gravity, namely the possibility of masking any curvature singularity behind an event horizon as a result of matter compression at the Planck scale. In this…
Let L be an infinite regular language on a totally ordered alphabet (A,<). Feeding a finite deterministic automaton (with output) with the words of L enumerated lexicographically with respect to < leads to an infinite sequence over the…
Based on the equivalence of the two different types of measurement protocols and the asymmetry between the Schr\"odinger and Heisenberg pictures, it has been previously proposed that negative sea fills the universe as a nondeterministic…
The axiomatic system introduced by H\'ajek axiomatizes first-order logic based on BL-chains. In this study, we extend this system with the axiom $(\forall x \phi)^2 \leftrightarrow \forall x \phi^2$ and the infinitary rule \[ \frac{\phi…
The possibility of avoiding the big bang singularity by means of a generalized uncertainty principle is investigated. In relation with this matter, the statistical mechanics of a free-particle system obeying the generalized uncertainty…