Related papers: Some remarks on cyclization and periodicity
In this brief note the operatorial methods are applied to the study of the Airy function and its generalizations.
We show how one can use a trivialization of a function $f : \mathbb{R}^n\to\mathbb{R} $ to construct a trivialization of $f$ in $\mathbb{R}^n$. Additionally we adopt a method for trivialising functions which satisfy the $\rho_0$-regularity…
This paper introduces a class of linear programming examples which cause the simplex method to cycle indefinitely and which are the simplest possible examples showing this behaviour. The structure of examples from this class repeats after…
All clocks, classical or quantum, are open non equilibrium irreversible systems subject to the constraints of thermodynamics. Using examples I show that these constraints necessarily limit the performance of clocks and that good clocks…
We present a framework which allows a uniform approach to the recently introduced concept of pseudo-repetitions on words in the morphic case. This framework is at the same time more general and simpler. We introduce the concept of a…
The aim of this paper is to show how zeta functions and excision in cyclic cohomology may be combined to obtain index theorems. In the first part, we obtain a local index formula for "abstract elliptic pseudodifferential operators"…
In this paper, we investigate the existence and the global stability of periodic solution for dynamical systems with periodic interconnections, inputs and self-inhibitions. The model is very general, the conditions are quite weak and the…
In this paper we provide a theoretical analysis of counterfactual invariance. We present a variety of existing definitions, study how they relate to each other and what their graphical implications are. We then turn to the current major…
Motivated by the existence of cyclic phenomena in which some characteristics are mapped into corresponding ones over more than one phase, we introduce the $r$-cyclic operators with respect to a covering of a metric space and investigate…
In this note we describe some results concerning upper and lower bounds for the Jensen functional. We use several known and new results to shed light on the concepts of superterzatic functions.
In this paper we consider several families of potential non-isochronous systems and study their associated period functions. Firstly, we prove some properties of these functions, like their local behavior near the critical point or…
We examine examples of weakly nonlinear systems whose steady states undergo a bifurcation with increasing forcing, such that a forced subsystem abruptly ceases to absorb additional energy, instead diverting it into an initially quiescent,…
We try to define the more general form of iterative processes in which the Pomeau-Manneville and the Feigenbaum scenario may occur along with their specific scaling properties. Doing this we need to generalize other basic concepts. Thus,…
We discuss the problem of full counting statistics for periodic pumping. The probability generating function is usually defined on a circle of the "physical" values of the counting parameter, with its periodicity corresponding to charge…
If the zeta function regularization is used and a complex mass term considered for fermions, the phase does not appear in the fermion determinant. This is not a drawback of the regularization, which can recognize the phase through source…
We study several sufficient conditions for the existence of a L\'evy-Khinchin decomposition of generating functionals. We show that none of these conditions are equivalent and we show that such a decomposition does not always exist.
The paper discusses an applicability criterion for a cutoff regularization in the coordinate representation in the Euclidean space with a dimension larger than two. It is shown that the set of functions satisfying the criterion is not…
The formalism which has been developed to give general expressions for the determinants of differential operators is extended to the physically interesting situation where these operators have a zero mode which has been extracted. In the…
Let $(F_t)$ be a continuous flow on a topological manifold M. For every open $V \subset M$ denote by P(V) the set of all continuous functions $\alpha:V \to R$ such that $F_{\alpha(z)}(z)=z$ for all $z\in V$. Such functions vanish at…
This paper has been withdrawn, as it should not have been a new submission. Please instead see the latest version of arXiv:0904.0436.