in this paper we introduce the concept of entropy operator for continuous systems of finite topological entropy. it is shown that it generates the kolmogorov entropy as a special case. if $phi$ is invertible then the entropy operator is bounded with the topological entropy of $phi$ as its norm.

In this paper, we address the problem of estimating a covariance matrix multivariate Gaussian distribution, relative to Stein loss function, from decision theoretic point view. We investigate case where is invertible and when it non--invertible in unified approach.

We study one-sided substitution subshifts, and how they can be respresented using BratteliVershik systems. In particular we focus on minimal recognizable substitutions such that the generated one-sided substitution subshift contains only one non-shift-invertible element (branch point), and we call these substitutions quasi-invertible. We characterise these substitutions, and show that if the su...

Reversibility is a concept widely studied in physics and computer science. Quantum systems evolution is described by the time evolution operator U , which is unitary and then invertible. Likewise, reversible computation is characterized by means of invertible properties. Reversible/invertible cellular automata (CA) are one of the most relevant reversible computational models. Here we introduce ...

Based on the ideas: “invertible cycle”, “tame transformation” and “special oil and vinegar”, three different nonlinear invertible transformations were constructed separately. Then making use of the idea of the extended multivariate public key cryptosystem, and combining the nonlinear invertible transformations above with Matsumoto-Imai (MI) scheme, three methods of designing extended multivaria...

(a) Prove that there exists a (left-right) inverse σ(t) in K [[t]] to the image of λ(t) if and only if a0 is invertible in K. In this case, prove that the inverse σ(t) is unique. More generally, for every element a0− a1t+ . . . in K [[t]], prove that the element is invertible if and only if a0 is invertible in K, in which case the inverse is unique. (b) Assume that λ(t) ∈ K[t] has an inverse σ(...

in this paper we introduce the concept of weakly prime ternary subsemimodules of a ternary semimodule over a ternary semiring and obtain some characterizations of weakly prime ternary subsemimodules. we prove that if $n$ is a weakly prime subtractive ternary subsemimodule of a ternary $r$-semimodule $m$, then either $n$ is a prime ternary subsemimodule or $(n : m)(n : m)n = 0$. if $n$ is a $q$-...

Reversibility is a concept widely studied in several research fields. Several contributions have been provided in physics and computer science. Reversible computation is characterized by means of invertible properties [1]. Reversibility is studied in computer science also in order to design less dissipative computers. The evolution of quantum systems is described by the time evolution operator ...

For Hölder continuous cocycles over an invertible, Lipschitz base, we establish the Hölder continuity of Oseledets subspaces on compact sets of arbitrarily large measure. This extends a result of Araújo et al [On Hölder-continuity of Oseledets subspaces J. Lond. Math. Soc. 93 (2016) 194–218] by considering possibly non-invertible cocycles, which, in addition, may take values in the space of com...

We construct a wavelet basis on the unit interval with respect to which both the (infinite) mass and stiffness matrix corresponding to the one-dimensional Laplacian are (truly) sparse and boundedly invertible. As a consequence, the (infinite) stiffness matrix corresponding to the Laplacian on the n-dimensional unit box with respect to the n-fold tensor product wavelet basis is also sparse and b...