Related papers: Exponential periods and o-minimality

The formalizations of periods of time inside a linear model of Time are usually based on the notion of intervals, that may contain or may not their endpoints. This is not enought when the periods are written in terms of coarse granularities…

We consider the rational potentials of the one-dimensional mechanical systems, which have a family of periodic solutions with the same period (isochronous potentials). We prove that up to a shift and adding a constant all such potentials…

Cluckers and Lipshitz have shown that real closed fields equipped with real analytic structure are o-minimal. This generalizes the well-known subanalytic structure $\mathbb{R}_{\mathrm{an}}$ on the real numbers. We extend this line of…

A real \alpha is called recursively enumerable ("r.e." for short) if there exists a computable, increasing sequence of rationals which converges to \alpha. It is known that the randomness of an r.e. real \alpha can be characterized in…

.We expound an alternative to the Copenhagen interpretation of the formalism of nonrelativistic quantum mechanics. The basic difference is that the new interpretation is formulated in the language of epistemological realism. The {\psi}…

Periods of rational integrals appear in quantum mechanics through asymptotic expansions of traces computed with the semiclassical symbol calculus. We develop a novel formal series expansion for the trace of the Dirac delta of a differential…

We look at a class of transcendental real numbers xi which, together with their square, satisfy some extremal property of simultaneous approximation by rational numbers with the same denominator. We give a sufficient condition for such a…

We study what we call topological cylindric algebras and tense cylindric algebras defined for every ordinal $\alpha$. The former are cylindric algebras of dimension $\alpha$ expanded with $\sf S4$ modalities indexed by $\alpha$. The…

Canonical variables for the Poisson algebra of quantum moments are introduced here, expressing semiclassical quantum mechanics as a canonical dynamical system that extends the classical phase space. New realizations for up to fourth order…

We show that separability and second-countability are first-order properties among topological spaces definable in o-minimal expansions of $(\mathbb{R},<)$. We do so by introducing first-order characterizations -- definable separability and…

We introduce a novel logical notion--partial entailment--to propositional logic. In contrast with classical entailment, that a formula P partially entails another formula Q with respect to a background formula set \Gamma intuitively means…

Here we briefly discuss how negative numbers, or "negative probabilities", can naturally arise in probabilistic expressions and be given an operational interpretation. Like the use of negative numbers in arithmetical expressions, the use of…

We first show that the projection image of a discrete definable set is again discrete for an arbitrary definably complete locally o-minimal structure. This fact together with the results in a previous paper implies tame dimension theory and…

The exponential family of models is defined in a general setting, not relying on probability theory. Some results of information geometry are shown to remain valid. Exponential families both of classical and of quantum mechanical…

We develop the theory of halving spaces to obtain lower bounds in real enumerative geometry. Halving spaces are topological spaces with an action of a Lie group $\Gamma$ with additional cohomological properties. For $\Gamma=\mathbb{Z}_2$ we…

This is the first of two papers devoted to connections between asymptotic functions of groups and computational complexity. One of the main results of this paper states that if for every $m$ the first $m$ digits of a real number $\alpha\ge…

We axiomatize the first-order theories of exponential integer parts of real-closed exponential fields in a language with $2^x$, in a language with a predicate for powers of 2, and in the basic language of ordered rings. In particular, the…

We prove that an algebraic flat connection has definable flat sections in the analytic exponential structure if and only if it is regular singular with unitary monodromy eigenvalues at infinity, refining previous work of Bakker and Mullane.…

The contemporary physics has revealed growing evidences that the emergence can be applied to not only biology and condensed matter systems but also gravity and spacetime. We observe that noncommutative spacetime necessarily implies emergent…

Let $\mathcal F=(F, +. \cdot, <, 0, 1, \dots)$ be a definably complete locally o-minimal expansion of an ordered field. We demonstrate the existence of definable quotients of definable sets by definable equivalence relations when several…