相关论文: On Katznelson's Question for skew product systems

Clocked Type Theory (CloTT) is a type theory for guarded recursion useful for programming with coinductive types, allowing productivity to be encoded in types, and for reasoning about advanced programming language features using an abstract…

In this paper, the notion of measure complexity is introduced for a topological dynamical system and it is shown that Sarnak's M\"{o}bius disjointness conjecture holds for any system for which every invariant Borel probability measure has…

This primary purpose of this paper is to succinctly state a number of verifiable and tractable sufficient conditions under which a particular class of conservative signal processing structures may be readily used to solve a companion class…

Collatz Conjecture sequences increase and decrease in seemingly random fashion. By identifying and analyzing the forms of numbers, we discover that Collatz sequences are governed by very specific, well-defined rules, which we call cascades.

New definitions are suggested for frequencies which may be instantaneous or not. The Heisenberg-Gabor inequality and the Shannon sampling theorem are briefly discussed.

The correspondence principle plays an important role in understanding the emergence of classical chaos from an underlying quantum mechanics. Here we present an infinite family of quantum dynamics that never resembles the analogous classical…

We study properties of strongly separately continuous mappings defined on subsets of products of topological spaces equipped with the topology of pointwise convergence. In particular, we give a necessary and sufficient condition for a…

We consider a linearised inverse conductivity problem for electromagnetic waves in a three dimensional bounded domain at a high time-harmonic frequency. Increasing stability bounds for the conductivity coefficient in the full Maxwell system…

We perform a thorough investigation of the first FPUT recurrence in the $\beta$-FPUT chain for both positive and negative $\beta$. We show numerically that the rescaled FPUT recurrence time $T_{r}=t_{r}/(N+1)^{3}$ depends, for large $N$,…

We consider systems of recursively defined combinatorial structures. We give algorithms checking that these systems are well founded, computing generating series and providing numerical values. Our framework is an articulation of the…

We study recursively defined functions associated with directed graphs on the k dimensional nonnegative integral lattice. The existence of certain combinatorial structures associated with these function classes are shown to be independent…

We consider Gell-Mann and Hartle's consistent histories formulation of quantum cosmology in the interpretation in which one history, chosen randomly according to the decoherence functional probabilities, is realised from each consistent…

The Goulden-Jackson cluster method is a powerful tool for counting words by occurrences of prescribed subwords, and was adapted by Elizalde and Noy for counting permutations by occurrences of prescribed consecutive patterns. In this paper,…

Every classical orthogonal polynomial system $p_n(x)$ satisfies a three-term recurrence relation of the type \[ p_{n+1}(x)=(A_nx+B_n)p_n(x)-C_np_{n-1}(x)~ (n=0,1,2,\ldots, p_{-1}\equiv 0), \] with $C_nA_nA_{n-1}>0$. Moreover, Favard's…

In this paper we introduce the concept of a quota complex and study how the topology of these quota complexes changes as the quota is changed. This problem is a simple "linear" version of the general question in Morse Theory of how the…

Randomly evolving systems composed by elements which interact among each other have always been of great interest in several scientific fields. This work deals with the synchronization phenomenon, that could be roughly defined as the…

Frequency tagging is a powerful approach to investigate the neural processing of sensory features, and is recently adapted to study the neural correlates of superordinate structures, i.e., chunks, in complex sequences such as speech and…

We consider the Helmholtz transmission problem with piecewise-constant material coefficients, and the standard associated direct boundary integral equations. For certain coefficients and geometries, the norms of the inverses of the boundary…

Let X be a metric space with metric d and T,S be two commutative measure-preserving maps of X. In this paper we obtain numerical results about multiple recurrence of almost every point of this dynamical system. On other words we study the…

We consider several Hamiltonian systems perturbed by external agents, that preserve their Hamiltonian structure. We investigate the corrections to the canonical statistics resulting from coupling such systems with possibly large but finite…