The main result of this paper is a characterization of the strongly algebraically closed algebras in the  lattice of all real-valued continuous functions and the equivalence classes of $\lambda$-measurable. We shall provide conditions  which strongly algebraically closed algebras carry a strictly positive Maharam submeasure. Particularly, it is proved that if $B$ is a strongly algebraically closed lattice  and $(B,\, \sigma)$ is a Hausdorff space  and $B$ satisfies  the   $G_\sigma$ property, then $B$ carries a strictly positive Maharam submeasure.

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, the notion of an M-function and cut function on a set, are in-troduced and investigated several properties. We use algebraic properties to introduce an algorithm which show that every , nite MV-algebras and Fibonacci sequences determines a block-code and presented some connections between Fibonacci sequences, MV-algebras and binary block-codes. Furthermore, an MV-algebra arising from block-codes is established.

It is shown that every locally idempotent (locally m-pseudoconvex)Hausdorff algebra A with pseudoconvex von Neumann bornology is a regular (respectively, bornological) inductive limit of metrizable locally m-(kB-convex) subalgebras AB of A. In the case where A, in addition, is sequentially BA-Complete (sequentially advertibly Complete), then every subalgebraAB is a locally m-(kB-convex) Frechet algebra (respectively, an advertibly Complete metrizable locally m-(kB-convex) algebra) for some kB Î (0, 1]. Moreover, for a commutative unital locally m-pseudoconvex Hausdorff algebra A over C with pseudoconvex von Neumann bornology, which at the same time is sequentially BA-Complete and advertibly Complete, the statements (a)–(j) of Proposition 3.2 are equivalent.