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.

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 Lifting Idempotent Property (LIP) of ideals in commutative rings inspired the study of Boolean lifting properties in the context of other concrete algebraic structures (MV-algebras, commutative ℓ-groups, BL-algebras, bounded distributive lattices, residuated lattices, etc. ), as well as for some types of universal algebras (C. Muresan and the author defined and studied the Congruence Boolean Lifting Property (CBLP) for congruence modular algebras). A lifting ideal of a ring R is an ideal of R fulfilling LIP. In a recent paper, Tarizadeh and Sharma obtained new results on lifting ideals in commutative rings. The aim of this paper is to extend an important part of their results to congruence with CBLP in semidegenerate congruence modular algebras. The reticulation of such algebra will play an important role in our investigations (recall that the reticulation of a congruence modular algebra A is a bounded distributive lattice L(A) whose prime spectrum is homeomorphic with Agliano’ s prime spectrum of A). Almost all results regarding CBLP are obtained in the setting of semidegenerate congruence modular algebras having the property that the reticulations preserve the Boolean center. The paper contains several properties of congruences with CBLP. Among the results we mention a characterization theorem of congruence with CBLP. We achieve various conditions that ensure CBLP. Our results can be applied to a lot of types of concrete structures: commutative rings, ℓ-groups, distributive lattices, MV-algebras, BL-algebras, residuated lattices, etc.

This paper introduces a novel concept of Boolean function{based hypergraph with respect to any given T. B. T(total binary truth table). This study de, nes a notation of kernel set on switching functions and proves that every T. B. T corresponds to a Minimum Boolean expression via kernel set and presents some conditions on T. B. T to obtain a Minimum irreducible Boolean expression from switching functions. Finally, we present an algorithm and so Python programming(with complete and original codes) such that for any given T. B. T, introduces a Minimum irreducible switching expression.

This paper examines the key determinants of industrialization in Iran. The present analysis gives specific focuse to scientism, industrialization, economic welfare, and economic eqality as the key determinants of secularization. Methodologically, the results of this paper are based on Boolean analysis and the field of study also includes Iranian provinces with regard to the determinants of secularization. Generally speaking, the underlying conclusion of this analysis suggests that there are not single and constant patterns and explanations applying to all provinces. This can be partly due to the fact that the main determinants considered in this analysis including scientism, industrialization, economic welfare, and economic eqality may not lead to secularization in Iran.