For general asymptotically sub-additive potentials (resp. asymptotically additive potentials) on general topological dynamical systems, we establish some variational relations between the topological entropy of the level sets of Lyapunov exponents, measuretheoretic entropies and topological pressures in this general situation. Most of our results are obtained without the assumption of the exist...

In this paper, we study the algebraic structure of Z2[u]Z2[u, v]-additive codes which are Z2[u, v]-submodules where u 2 = v2 = 0 and uv = vu. In particular, we determine a Gray map from Z2[u]Z2[u, v] to Z 2α+8β 2 and study generator and parity check matrices for these codes. Further we study the structure of Z2[u]Z2[u, v]additive cyclic codes and constacyclic codes.

This elucidation studies ergodicity and equilibrium measures for additive cellular automata with prime states. Additive cellular automata are ergodic with respect to Bernoulli measure unless it is either an identity map or constant. The formulae of measure-theoretic and topological entropies can be expressed in closed forms and the topological pressure is demonstrated explicitly for potential f...

The well known Plotkin construction is, in the current paper, generalized and used to yield new families of Z2Z4-additive codes, whose length, dimension as well as minimum distance are studied. These new constructions enable us to obtain families of Z2Z4-additive codes such that, under the Gray map, the corresponding binary codes have the same parameters and properties as the usual binary linea...

Analysis is presented of a system whose dynamics are dramatically simplified by tiny amounts of additive noise. The dynamics divide naturally into two phases. In the slower phase, trajectories are close to an invariant manifold; this allows small random disturbances to exert a controlling influence. A map is derived which provides an accurate description of the trajectories.

We prove a version of Schanuel’s Conjecture for a field of Laurent power series in positive characteristic replacing C and a non-algebraic additive power series replacing the exponential map.

The aim of this paper is to show that between standard operator algebras every bijective map with a certain multiplicativity property related to the Jordan triple isomorphisms of associative rings is automatically additive.

In this paper, a reduced complexity Log-MAP algorithm based on a non-recursive approximation of the max∗ operator is presented and studied for turbo trellis-coded modulation (TTCM) systems. In the algorithm, denoted as AvN Log-MAP, the max∗ operation is generalized and performed on n ≥ 2 arguments. The approximation is derived from the Jensen inequality. The non-recursive form of the max∗ calcu...

Let T be a triangular ring. An additive map δ from T into itself is said to be Jordan derivable at an element Z ∈ T if δ(A)B +Aδ(B) + δ(B)A+Bδ(A) = δ(AB+BA) for any A,B ∈ T with AB + BA = Z. An element Z ∈ T is called a Jordan all-derivable point of T if every additive map Jordan derivable at Z is a Jordan derivation. In this paper, we show that some idempotents in T are Jordan all-derivable po...

In this section we introduce an exponential homomorphism for the Milnor K -groups for a complete discrete valuation field of mixed characteristics. In general, to work with the additive group is easier than with the multiplicative group, and the exponential map can be used to understand the structure of the multiplicative group by using that of the additive group. We would like to study the str...