The classic and the Lévy-Gnedenko central limit theorems play a key role in theory of probabilities, and also in Boltzmann-Gibbs (BG) statistical mechanics. They both concern the paradigmatic case of probabilistic independence of the random variables that are being summed. A generalization of the BG theory, usually referred to as nonextensive statistical mechanics and characterized by the index...

Physics is introduced as a semantics of a formal set theory. We consider a metatheory of a formal set theory S. We name this metatheory MS, indicating that it is a Meta-theory of S as well as a Meta-Scientific theory as Ronald Swan [1] refers to. The following arguments are all made in MS. We define in MS φ = the class of all well-formed formulae of S. This φ is a countable set in the context o...

We develop a novel optimization approach to tone. Its grammatical component consists of the similarityand proximity-based correspondence constraint framework of Agreement by Correspondence theory (ABC). Its representational component (Q theory) decomposes segments (Q) into temporally ordered, quantized subsegments (q), which comprise unitary sets of distinctive features, including tone. ABC+Q u...

Julia Robinson has given a first-order definition of the rational integers Z in the rational numbers Q by a formula (∀∃∀∃)(F = 0) where the ∀-quantifiers run over a total of 8 variables, and where F is a polynomial. This implies that the Σ5-theory of Q is undecidable. We prove that a conjecture about elliptic curves provides an interpretation of Z in Q with quantifier complexity ∀∃, involving o...

We examine the energetics of Q-balls in Maxwell-Chern-Simons theory in two space dimensions. Whereas gauged Q-balls are unallowed in this dimension in the absence of a Chern-Simons term due to a divergent electromagnetic energy, the addition of a Chern-Simons term introduces a gauge field mass and renders finite the otherwise-divergent electromagnetic energy of the Q-ball. Similar to the case o...

We show that, over an arbitrary field, q-rook monoid algebras are iterated inflations of Iwahori-Hecke algebras, and, in particular, are cellular. Furthermore we give an algebra decomposition which shows a q-rook monoid algebra is Morita equivalent to a direct sum of Iwahori-Hecke algebras. We state some of the consequences for the representation theory of q-rook monoid algebras.

MSSM predicts the existence of Q-balls, some of which can be entirely stable. Both stable and unstable Q-balls can play an important role in cosmology. In particular, Affleck–Dine baryogenesis can result in a copious production of stable baryonic Q-balls, which can presently exist as a form of dark matter. CERN-TH/98-218 June, 1998 Talk presented at the Sixth International Symposium on Particle...

Our work is a foundational study of the notion of approximation inQ-categories and in (U,Q)-categories, for a quantale Q and the ultrafilter monad U. We introduce auxiliary, approximating and Scott-continuous distributors, the way-below distributor, and continuity of Qand (U,Q)-categories. We fully characterize continuous Q-categories (resp. (U,Q)-categories) among all cocomplete Q-categories (...

This paper has a marked practical aspect. We wish to encourage and facilitate the use of Q methodology amongst psychologists interested in qualitative research. The paper duly answers a number of pertinent ‘how to do Q’ questions. Yet our primary intention is not to produce an exhaustive ‘how to do Q’ guide. In discussing issues of theory, method and interpretation in Q methodology, the main ai...

Wepresent an analytically tractable dynamic stochastic general equilibrium model that incorporates micro-level fixed and convex adjustment costs. We provide an explicit characterization of equilibrium dynamics by a system of nonlinear stochastic difference equations. We provide general conditions under which our model features investment lumpiness at the microeconomic level, but aggregate dynam...