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We formulate a microcanonical distribution for an arbitrary one-electron triatomic molecule. This distribution can be used to describe the initial state in strongly-driven two-electron triatomic molecules. Namely, in many semiclassical…
We give extensional and intensional characterizations of functional programs with nondeterminism: as structure preserving functions between biorders, and as nondeterministic sequential algorithms on ordered concrete data structures which…
A new characterization of the exponential distribution is obtained. It is based on an equation involving randomly shifted (translated) order statistics. No specific distribution is assumed for the shift random variables. The proof uses a…
Experimental studies of cell motility in culture have shown that under adequate conditions these living organisms possess the ability to organize themselves into complex structures. Such structures may exhibit a synergy that greatly…
We answer various questions concerning the distribution of extensions of a given central simple algebra $K$ over a number field. Specifically, we give asymptotics for the count of inner Galois extensions $L/K$ of fixed degree and center…
We introduce and study the noncommutative weak Extension Principle, a lifting principle aiming to characterise $^*$-homomorphisms between coronas of nonunital separable $\mathrm{C}^*$-algebras. While this principle fails if the Continuum…
We study notions of robustness of Markov kernels and probability distribution of a system that is described by $n$ input random variables and one output random variable. Markov kernels can be expanded in a series of potentials that allow to…
The extended de Finetti theorem characterizes exchangeable infinite random sequences as conditionally i.i.d. and shows that the apparently weaker distributional symmetry of spreadability is equivalent to exchangeability. Our main result is…
Liftings of endofunctors on sets to endofunctors on relations are commonly used to capture bisimulation of coalgebras. Lax versions have been used in those cases where strict lifting fails to capture bisimilarity, as well as in modeling…
Let $F$ be a non-Archimedian local field of characteristic zero and $E/F$ a quadratic extension. The aim of the present article is to study the multiplicity of an irreducible admissible representation of ${\rm GL}_2(F)$ occurring in an…
We introduce a new class of multiplications of distributions in one dimension merging together two different regularizations of distributions. Some of the features of these multiplications are discussed in a certain detail. We use our…
The density profiles and other quantities of physical interest for spherically symmetric systems are computed by assuming that a collisionless stellar gas may relax to the non-Gaussian power law distribution suggested by the nonextensive…
System I is a proof language for a fragment of propositional logic where isomorphic propositions, such as $A\wedge B$ and $B\wedge A$, or $A\Rightarrow(B\wedge C)$ and $(A\Rightarrow B)\wedge(A\Rightarrow C)$ are made equal. System I enjoys…
A characterization of a class of optimal three-weight cyclic codes of dimension 3 over any finite field was recently presented in [10]. Shortly after this, a generalization for the sufficient numerical conditions of such characterization…
The prolongation structure of a two-by-two problem is formulated very generally in terms of exterior differential forms on a standard representation of Pauli matrices. The differential system is general without making reference to any…
In the present paper we consider controllability and observability of second order linear time invariant systems in matrix form. Without reducing into first order systems we show how the classical conditions for first order linear systems…
Using a steady state process of node duplication and deletion we produce networks with 1/k scale-free degree distributions in the limit of vanishing connectance. This occurs even though there is no growth involved and inherent preferential…
We propose to extend ``invertibility'' to ``regularity'' for categories in general abstract algebraic manner. Higher regularity conditions and ``semicommutative'' diagrams are introduced. Distinction between commutative and…
We prove distributional limit theorems and one-sided laws of the iterated logarithm for a class of positive, mixing, stationary, stochastic processes which contains those obtained from non-integrable observables over certain piecewise…
We give a proof of the equivalence of the electric-magnetic duality on one side and helicity conservation of the tree level amplitudes on the other side within general models of nonlinear electrodynamics. Using modified Feynman rules…