We will present an approach to deal with a problem of existence of (not) weakly invertible functions in various spaces of analytic functions in the unit ball and polydisk based on estimates for integral operators acting between functional classes of different dimensions.

Semi-input-memory finite automata are a generalization of input-memory finite automata by appending an autonomous finite automaton component. This paper gives a decision criterion of weakly invertible semi-input-memory finite automata with delay 2 of which the minimal output weight of length 2 and the sizes of input and output alphabets are identical. The results are used to generate a kind of ...

S-Boxes are important security components of block ciphers. We provide theoretical results on necessary or sufficient criteria for an (invertible) 4-bit S-Box to be weakly APN. Thanks to a classification of 4-bit invertible S-Boxes achieved independently by De Canniére and Leander-Poschmann, we can strengthen our results with a computeraided proof. We also propose a class of 4-bit S-Boxes which...

We study the algebraic and arithmetic structure of monoids invertible ideals (more precisely, $r$-invertible $r$-ideals for certain ideal systems $r$) Krull weakly Mori domains. also investigate all nonzero polynomial rings with at least two indeterminates over noetherian Among others, we show that they are not transfer but share several arithmetical phenomena having infinite class group prime ...

In this paper we show that for every n ≥ 2 there are minimal systems with perfect weakly mixing sets of order n and all weakly mixing sets of order n+1 trivial. We present some relations between weakly mixing sets and topological sequence entropy, in particular, we prove that invertible minimal systems with nontrivial weakly mixing sets of order 3 always have positive topological sequence entro...

In this paper,we introduce a new verifiable multi-use multi-secretsharing scheme based on automata and one-way hash function. The scheme has theadversary fuzzy structure and satisfy the following properties:1) The dealer can change the participants and the adversary fuzzy structure without refreshing any participants' real-shadow. 2) The scheme is based on the inversion of weakly invertible fin...

A time series is a random walk if 1 t t t y y u    where t u is iid. A time series is a martingale if 1 1 ( ) t t t E y y    . A time series is a martingale difference sequence if 1( ) 0 t t E y   . A time series is (weakly) stationary if it’s first two moments exist and do not change over time. A time series is invertible if it can be written as an autoregression. A time series is I(0)...