A right-sided, nearest neighbour cellular automaton (RNNCA) is a continuous transformation Φ : A−→A determined by a local rule φ : A{0,1}−→A so that, for any a ∈ A and any z ∈ Z, Φ(a)z = φ(az, az+1). We say that Φ is bipermutative if, for any choice of a ∈ A, the map A ∋ b 7→ φ(a, b) ∈ A is bijective, and also, for any choice of b ∈ A, the map A ∋ a 7→ φ(a, b) ∈ A is bijective. We characterize ...

For an n×n nonnegative matrix P , an isomorphism is obtained between the lattice of initial subsets (of {1, · · · , n}) for P and the lattice of P -invariant faces of the nonnegative orthant R+. Motivated by this isomorphism, we generalize some of the known combinatorial spectral results on a nonnegative matrix that are given in terms of its classes to results for a cone-preserving map on a pol...

The Kolmogorov-Sinai entropy is a far reaching dynamical generalization of Shannon entropy of information systems. This entropy works perfectly for probability measure preserving (p.m.p.) transformations. However, it is not useful when there is no finite invariant measure. There are certain successful extensions of the notion of entropy to infinite measure spaces, or transformations with ...

In this paper, we give an extension of the Wendel's theorem on KPC-hypergroups. We also show that every translation invariant mapping is corresponding with a unique positive measure on the KPC-hypergroup.

A new approach for pole placement of nonlinear systems using state feedback and fuzzy system is proposed. We use a new online fuzzy training method to identify and to obtain a fuzzy model for the unknown nonlinear system using only the system input and output. Then, we linearized this identified model at each sampling time to have an approximate linear time varying system. In order to stabilize...

we investigate the long-term behavior of solutions of the difference equation[ x_{n+1}=x_{n}x_{n-3}-1 ,, n=0 ,, 1 ,, ldots ,, ]noindent where the initial conditions $x_{-3} ,, x_{-2} ,, x_{-1} ,, x_{0}$ are real numbers.  in particular, we look at the periodicity and asymptotic periodicity of solutions, as well as the existence of unbounded solutions.

‎this paper presents two main results that the singular values of the hadamard product of normal matrices $a_i$ are weakly log-majorized by the singular values of the hadamard product of $|a_{i}|$ and the singular values of the sum of normal matrices $a_i$ are weakly log-majorized by the singular values of the sum of $|a_{i}|$‎. ‎some applications to these inequalities are also given‎. ‎in addi...

this paper presents h∞ control problem for input-delayed systems. a neutral system approach is considered to the design of pd controller for input delay systems in presence of uncertain time-invariant delay. using this approach, the resulting closed-loop system turns into a specific time-delay system of neutral type. the significant specification of this neutral system is that its delayed coeff...