In this paper we introduce the notion of Boolean filters in a pseudo-complemented distributive lattice and characterize the class of all Boolean filters. Further a set of equivalent conditions are derived for a proper filter to become a prime Boolean filter. Also a set of equivalent conditions is derived for a pseudo-complemented distributive lattice to become a Boolean algebra. Finally, a Bool...

Pipelines function as blood vessels serving to bring life-necessities, so their safe usage is one of the foremost concerns. In our previous work, a fiber Bragg grating (FBG) hoop strain sensor with enhanced sensitivity was developed to measure the pressure drop induced by pipeline leakage. Some hoop strain information during the leakage transient process can be extracted from the amount of FBG ...

In the present paper we define the (pseudo) MV-algebras with n-ary operators, generalizing MV-modules and product MV-algebras. Our main results assert that there are bijective correspondences between the operators defined on a pseudo MV-algebra and the operators defined on the corresponding `-group. We also provide a categorical framework and we prove the analogue of Mundici’s categorical equiv...

Generalized tensor analysis in the sense of Colombeau’s construction is employed to introduce a nonlinear distributional pseudo-Riemannian geometry. In particular, after deriving several characterizations of invertibility in the algebra of generalized functions we define the notions of generalized pseudo-Riemannian metric, generalized connection and generalized curvature tensor. We prove a “Fun...

A simple axiomatic characterization of the general (infinite dimensional , noncommutative) Itô algebra is given and a pseudo-Euclidean fundamental representation for such algebra is described. The notion of Itô B*-algebra, generalizing the C*-algebra is defined to include the Banach infinite dimensional Itô algebras of quantum Brownian and quantum Lévy motion, and the B*-algebras of vacuum and ...

A simple axiomatic characterization of the general (infinite dimensional , noncommutative) Itô algebra is given and a pseudo-Euclidean fundamental representation for such algebra is described. The notion of Itô B*-algebra, generalizing the C*-algebra is defined to include the Banach infinite dimensional Itô algebras of quantum Brownian and quantum Lévy motion, and the B*-algebras of vacuum and ...

After the research on naBL-algebras gained by non-associative t-norms and overlap functions, inflationary BL-algebras were also studied as a recent kind of generalization BL-algebras, which can be obtained general functions. In this paper, we show that not every function induce an BL-algebra counterexample thus propose new concept weak BL-algebras. We prove each corresponds to BL-algebra; there...

As global populations and affluence rise, there is increasing demand for energy, animal protein, and construction materials. In many cases, available resource pools are insufficient to meet growing market demands, resulting in increased prices and competition for limited resources. This study evaluates key construction resources needed to build different types and scales of Iowa swine productio...

The aim of this paper is to derive pseudo-BCK algebras from directoids and vice versa. We generalize some results proved by Ivan Chajda et al. in the case BCK-algebras. assign an arbitrary algebra a semilattice-like structure observe that point where are different structures. Finally, relation between commutative deductive systems bounded pseudo-BCK(pDN) characterization terms discussed.

Nelson algebras were first studied by Rasiowa and BiałynickiBirula [1] under the name N-lattices or quasi-pseudo-Boolean algebras. Later, in investigations by Monteiro and Brignole [3, 4], and [2] the name “Nelson algebras” was adopted – which is now commonly used to show the correspondence with Nelson’s paper [14] on constructive logic with strong negation. By a Nelson algebra we mean an abstr...