A note on projective and injective automata

In this paper we define a new short exact sequence of automata and we investigate module-like properties on projective and injective automata     

On right congruences associated with the input semigroupS of automata

LetA=(M, S, δ) be an automaton without outputs whereM is a nonemptyset andS is a nonempty semigroup. Then the right congruences μM and μ _m associated withS have been expressed in many different ways (μ _M is called the Myhill-Nerode congruence onS). Also, their algebraic properties have been investigated. We have introduced the right congruences μ _S and μ_α onM and we have obtained necessary and sufficient conditions thatS/μ andM/w have nontrivialS-homomorphisms where μ andw are any right congruences onS andM respectively. The faithfulness ofS has been introduced.     

On the free automata and tensor product

In this paper we shall introduce the algebraic structure of a tensor product for arbitrarily given automata, giving a defintion of the tensor product for automata. We introduce and study that for any setX there always exists a free automaton onX. The existence of a tensor product for automata will be investigated in the same way like modules do.     

Small and large automata

In this paper we define small and large(or big) automata. We investigate some algebraic properties associated with them     

On free and torsion-free automata

In this paper we define free, torsion-free and torsion-free completely on an automaton. We prove some properties of them which are important     

Ionicity of intramolecular charge-transfer molecule Ddelta+-pi-Adelta- based on 1,3,3-trimethyl-2-methyleneindoline and 7,7,8,8-tetracyanoquinodimethane

We report a simple and convenient method to evaluate the relative ionicity delta of the typical intramolecular charge-transfer (CT) molecules linked by pi-bond Ddelta+-pi-Adelta- (D, donor; A, acceptor; delta, degree of CT) derived from 1,3,3-trimethyl-2-methylene indoline and TCNQ derivatives on the basis of the solvatochromic effects of the CT band in various solvents and their redox properties. The functionality of the intramolecular CT molecules as dyes, photovoltaic materials, nonlinear optics, rectifiers, and conductors is discussed in terms of delta.     

On the numerical imbedding method

Journal of Applied Mathematics and Computing - WhenF(x) = 0 is a system of nonlinear equations, we have established the parametrizied Homotopy algorithm for solvingF(x) = 0 and some theorems for...     

Some remarks on the structure of free automata

In this paper we define automata-linearly independence. An automatonM has a basis B iffM is free provided that we assume that the action ofS onX × S is (x,s)a = (x,sa) for alla, s ∈ S andx ∈X. If a semigroupS is PRID, every subautomaton of a freeS-automaton is free.