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The aim of this paper is to construct an algebraic hyperstructure over a set G corresponding to a Boolean algebra B and a function S:GB. In order to accomplish this goal we will need to define a hyperoperation on the set G. We define, ab =a^6 b={gEG/s(g)<=s(a)vs(b)} and prove that if the image of G is a v -semilattice or constitute a partition of 1 in B, then (G, ^6) is a hypergroup.

In this paper, some new properties of EQ-algebras are investigated. We intro-duce and study the notion of Boolean center of lattice ordered EQ-algebras with bottom element. We show that in a good ℓ EQ-algebra E with bottom element the complement of an element is unique. Furthermore, Boolean elements of a good bounded lattice EQ-algebra are characterized. Finally, we obtain conditions under which Boolean center of an EQ-algebra E is the subalgebra of E.

This paper presents a new method for simplification of Boolean functions based on Boolean differences. The proposed method is applicable to various forms of Boolean functions, including truth tables and Binary Decision Diagrams (BDDs). The Boolean differences are extended to cover the truth tables with don't-care components and cutset graphs in BDDs. The results of simplification agree with Quine-McCluskey and ESPRESSO methods. Experimental tests on MCNC and Berkeley PLA benchmarks show that the proposed method gains a performance of 1.5-10 times faster than ESPRESSO. The algorithms of the proposed method are implemented in Java/Perl/C++, and a toolset for logic function simplification is developed.

In this paper, we discuss some properties of joint spectral {radius(jsr)} and  generalized spectral radius(gsr)  for a finite set of upper triangular matrices with entries in a Banach algebra and represent relation between geometric and joint/generalized spectral radius. Some of these are in scalar matrices, but  some are different. For example for a bounded set of scalar matrices,$\Sigma$, $r_*\left(\Sigma\right)= \hat{r}\left(\Sigma\right)$, but for a bounded set of  upper triangular matrices with entries in a Banach algebra($\Sigma$), $r_*\left(\Sigma\right)\neq\hat{r}\left(\Sigma\right)$. We  investigate when the set is  defective or not and equivalent properties for having a norm equal to jsr, too.

In this paper, we introduce the notions of (ʘ,⊕) -derivations and (ϴ,ʘ) -derivations for MV -algebras and discuss some related results.We study the connection between these derivations on an MV -algebra Aand the derivations on its Boolean center. We characterize the isotone (ʘ,⊕) -derivations and prove that (ϴ,ʘ) -derivations are isotone. Finally we determine the relationship between (ʘ,⊕) -derivation and (ϴ,ʘ) -derivation for MV -algebras.