Iranian Journal of Mathematical Sciences and Informatics
Volume:4 Issue: 1, May 2009

In this paper, first a new algorithm for pole assignment of closed-loop multi-variable controllable systems in a prescribed region of the z-plane is presented. Then, robust state feedback controllers are designed by implementing a neural fuzzy system for the placement of closed-loop poles of a controllable system in a prescribed region in the left-hand side of z-plane. A new method based on the parameterizations of condition number function of a closed-loop system whose poles are varied in a prescribed region by neural fuzzy system is also designed.

The notion of a Γ-semigroup was introduced by Sen [8] in 1981. We can see that any semigroup can be considered as a Γ-semigroup. The aim of this article is to study the concept of (0-)minimal and max- imal ordered bi-ideals in ordered Γ-semigroups, and give some charac- terizations of (0-)minimal and maximal ordered bi-ideals in ordered Γ- semigroups analogous to the characterizations of (0-)minimal and maxi- mal ordered bi-ideals in ordered semigroups considered by Iampan [5].

Let T be a compact Hausdorff topological space and let M denote an n–dimensional subspace of the space C(T), the space of real–valued continuous functions on T and let the space be equipped with the uniform norm. Zukhovitskii [7] attributes the Basic Theorem to E.Ya.Remez and gives a proof by duality. He also gives a proof due to Shnirel’man, which uses Helly’s Theorem, now the paper obtains a new proof of the Basic Theorem. The significance of the Basic Theorem for us is that it reduces the characterization of a best approximation to f ε C(T) from M to the case of finite T, that is to the case of approximation in l^{ω}(r). If one solves the problem for the finite case of T then one can deduce the solution to the general case. An immediate consequence of the Basic Theorem is that for a finite dimensional subspace M of C_{0}(T) there exists a separating measure forMand f ε C_{0}(T)M, the cardinality of whose support is not greater than dim M+1. This result is a special case of a more general abstract result due to Singer [5]. Then the Basic Theorem is used to obtain a general characterization theorem of a best approximation from M to f ε C(T). We also use the Basic Theorem to establish the sufficiency of Haar’s condition for a subspace M of C(T) to be Chebyshev.

In this paper we introduce some new conditions of the solu- tions existence for variational-like inequalities with relaxed η-α pseu- domonotone mappings in Banach spaces. The advantage of these new conditions is that they are easier to be veri ed than those that appear in some of the previous corresponding articles.

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.

In present study is concerned with the propagation of axisymmetric vibrations in a homogenous isotropic micropolar thermoelastic cubic crystal plate bordered with layers or half spaces of inviscid liquid subjected to stress free boundary conditions in context of Lord and Shulman (L-S) and Green and Lindsay (G-L) theories of thermoelasticity. The secular equations for symmetric and skew-symmetric leaky and nonleaky Lamb wave modes of propagation are derived. The amplitudes of displacement components, microrotation and temperature distribution are also computed numerically and presented graphically. Finally, in order to illustrate the analytical developments, numerical solution of secular equations corresponding to stress free thermally insulated micropolar thermoelastic cubic crystal plate is carried out for magnesium crystal material bordered with water layers of finite and infinite thickness.

In this note first we define a BCK‐algebra on the states of a deterministic finite automaton. Then we show that it is a BCK‐algebra with condition (S) and also it is a positive implicative BCK‐algebra. Then we find some quotient BCK‐algebras of it. After that we introduce a hyper BCK‐algebra on the set of all equivalence classes of an equivalence relation on the states of a deterministic finite automaton and we prove that this hyper BCKalgebra is simple, strong normal and implicative. Finally we define a semi continuous deterministic finite automaton. Then we introduce a hyper BCK‐algebra S on the states of this automaton and we show that S is a weak normal hyper BCK‐algebra.