相关论文: Numeration systems as dynamical systems -- introdu…

The Numerical Assembly Technique is extended to investigate arbitrary planar frame structures with the focus on the computation of natural frequencies. This allows us to obtain highly accurate results without resorting to spatial…

Let $G$ be a group. A subset $D$ of $G$ is a determining set of $G$, if every automorphism of $G$ is uniquely determined by its action on $D$. The determining number of $G$, denoted by $\alpha(G)$, is the cardinality of a smallest…

The dynamics of the family of maps $\displaystyle{f_{\alpha, \beta, \gamma, \delta}(z)=\frac{\alpha z + \beta}{\gamma z^2 +\delta z}}$ in complex plane is investigated computationally. This dynamical system $z_{n+1}=f_{\alpha, \beta,…

A summation is a shift-invariant ${\rm R}$-module homomorphism from a submodule of ${\rm R}[[\sigma]]$ to ${\rm R}$ or another ring. [11] formalized a method for extending a summation to a larger domain by telescoping. In this paper, we…

Let $S$ be a complete star-omega semiring and $\Sigma$ be an alphabet. For a weighted $\omega$-restricted one-counter automaton $\mathcal{C}$ with set of states $\{1, \dots, n\}$, $n \geq 1$, we show that there exists a mixed algebraic…

Let $G$ be a permutation group on a set $\Omega$. A subset of $\Omega$ is a base for $G$ if its pointwise stabilizer is trivial; the base size of $G$ is the minimal cardinality of a base. In this paper we initiate the study of bases for…

Following the Dirac Notation in Quantum Mechanics (QM), we propose the Bracket Notation (PBN) by defining a probability-bra (P-bra), P-ket, P-bracket, P-identity, etc. Using the PBN, many formulae, such as normalizations and expectations in…

Equipping a non-equivariant topological E_\infty operad with the trivial G-action gives an operad in G-spaces. The algebra structure encoded by this operad in G-spectra is characterised homotopically by having no non-trivial multiplicative…

A new class of Semantic Numeration Systems, namely, positive rational Semantic Numeration Systems is introduced. For cardinal semantic operators, differences in the formation of carry (common carry) and remainders are defined. The…

We develop a quenched thermodynamic formalism for open random dynamical systems generated by finitely branched, piecewise-monotone mappings of the interval. The openness refers to the presence of holes in the interval, which terminate…

This paper focuses on greedy expansions, one possible representation of numbers, and on arithmetical operations with them. Performing addition or multiplication some additional digits can appear. We study bounds on the number of such digits…

Intrinsic computation refers to how dynamical systems store, structure, and transform historical and spatial information. By graphing a measure of structural complexity against a measure of randomness, complexity-entropy diagrams display…

We describe $\omega$-limit sets of completely positive (CP) maps over finite-dimensional spaces. In such sets and in its corresponding convex hulls, CP maps present isometric behavior and the states contained in it commute with each other.…

Regularity properties of the pressure are related to phase transitions. In this article we study thermodynamic formalism for systems defined in non-compact phase spaces, our main focus being countable Markov shifts. We produce metric…

We study expansions in non-integer negative base -{\beta} introduced by Ito and Sadahiro. Using countable automata associated with (-{\beta})-expansions, we characterize the case where the (-{\beta})-shift is a system of finite type. We…

In this paper we study the ergodic theory of a class of symbolic dynamical systems $(\O, T, \mu)$ where $T:{\O}\to \O$ the left shift transformation on $\O=\prod_0^\infty\{0,1\}$ and $\mu$ is a $\s$-finite $T$-invariant measure having the…

This paper proposes a novel collocation-type numerical stochastic homogenization method for prototypical stochastic homogenization problems with random coefficient fields of small correlation lengths. The presented method is based on a…

For a closed-loop control system with a digital channel between the sensor and the controller, the notion of invariance entropy quantifies the smallest average rate of information above which a given compact subset of the state space can be…

The proposed system of integer functions is logically fully independent from the traditional mathematical analysis of the real functions, but there is a well-defined mutual correspondence between the two disciplines. The system of integer…

We consider the space of countable structures with fixed underlying set in a given countable language. We show that the number of ergodic probability measures on this space that are $S_\infty$-invariant and concentrated on a single…